Philosophy A path through The Default Library ======================================== How to argue well about the questions that don't go away: what we can know, what exists, what minds are, and how to live, asked on every continent. Step 1. Logic & Argument: Why the Conclusion Follows, or Doesn’t ---------------------------------------------------------------- Why: Validity, soundness, fallacies and the logic every other subject uses. Logic is the study of one thing: when the truth of some claims forces the truth of another. A graduate learns to see that shape under every argument, and to test it by hunting for a single counterexample. Someone tells you: “If the bridge were unsafe, they would have closed it. They haven’t closed it. So it’s safe.” It sounds fine. Someone else says: “If it rained, the street is wet. The street is wet. So it rained.” That sounds fine too, until you picture a street cleaner. The first argument is a good one. The second has the same outward look and is a bad one, and a philosophy graduate can tell you why in about three seconds, because they have stopped listening to what the argument is about and started looking at its shape. That is the whole trick of the subject, and it is why Logic & Argument is the first door into the philosophy major. Every other subject in it (36/02 Ethics, 36/03 Epistemology, and the rest) is built from arguments, so you need a way to ask of any of them: if the starting points were true, would the end have to be? This piece gives you the working tools: a truth-table machine, a syllogism tester, and a fallacy spotter on invented arguments. It is a first look, not a logic course. For the same ground at a gentler pace, read What Is a Good Argument? (05/03); this goes a step further. The course in one box Who takes itPhilosophy majors in year 1; most philosophy programmes put it first, and many require it. Mathematics, computer science and law students meet it too, under names such as “discrete mathematics” and “legal reasoning”. Some universities call it “critical thinking” when it is informal, and “symbolic logic” when it is formal; many teach both in sequence. What it is forTelling a valid argument from an invalid one, a sound one from an unsound one, and seeing what kind of support the argument actually claims. Comes afterNothing. It is the entry point. Leads toEpistemology (36/03), Metaphysics (36/04), Philosophy of Language (36/07), and, outside this major, Foundations: Sets, Logic & Infinity (34/71) and Legal Reasoning & Writing (35/02). What this piece gives youYou will not be able to prove a theorem in predicate logic. You will be able to test a short argument for validity on paper, say what “sound” adds, and name ten common ways arguments go wrong. Validity is about form; soundness adds true premises An argument is a set of statements, the premises, offered to support another, the conclusion. Logic asks one question first: is it valid? An argument is valid when it is impossible for all the premises to be true and the conclusion false. Not unlikely. Impossible. valid = no way for (all premises true) and (conclusion false)An argument is sound when it is valid and its premises are in fact true. The surprising part is that validity does not care whether anything is true. “All fish are mammals; whales are fish; so whales are mammals” is perfectly valid: if the two premises were true the conclusion would have to be. It is not sound, because a premise is false. Meanwhile an argument can have a true conclusion and still be invalid. Validity is a promise about the connection; soundness is that promise plus true starting points. A good critic asks both, in that order. Try six arguments and place each one. A few are traps. Interactive · Valid, sound, or neither? Pick an answer for each argument. Without JavaScript: “All fish are mammals…” is valid and unsound. “All mammals breathe air; whales are mammals; so whales breathe air” is valid and sound. “If it’s Tuesday the library is open; it’s open; so it’s Tuesday” is invalid. “Every swan I’ve seen is white, so the next one is” is not valid (it is induction). “Paris is in France, so 2+2=4” is valid in classical logic, since the conclusion cannot be false. Contradictory premises make any argument valid and unsound. Two of those answers bother people, and they should. If the conclusion cannot possibly be false, nothing can make the argument go from true premises to a false conclusion, so classical logic calls it valid even though the premise is irrelevant. And from a contradiction, anything follows. Logicians who find this unacceptable built relevance logics and paraconsistent logics. Classical logic remains the default textbook system; the others are live rivals, not cranks. Connectives are machines that turn truth values into truth values Take the simplest sentences, ones that are either true or false. Join them with “and”, “or”, “not”, “if…then”. Logic says the truth of the whole depends only on the truth of the parts: each connective is a little machine, a truth function. That is the entire foundation of propositional logic, set out by the Stoic Chrysippus in the 3rd century BCE and rebuilt in symbols by George Boole in the 1840s and Gottlob Frege in 1879. Set P and Q below and read off every connective at once. Interactive · Truth-function explorer P: True Q: False Without JavaScript: “P and Q” is true only when both are true. “P or Q” (inclusive) is false only when both are false. “If P then Q” is false only when P is true and Q false; it is true whenever P is false. The one that surprises everyone is “if P then Q”. In logic it is the material conditional: false in exactly one case, P true and Q false. So “If the moon is cheese then 2+2=5” counts as true, because the “if” part is false. This is a feature of the simplest tool, not a claim about how “if” works in English. Philosophers have argued about the gap since the Hellenistic period; C. I. Lewis built stricter conditionals in 1912 partly to avoid these “paradoxes”, and Dorothy Edgington and others argue that ordinary conditionals express something closer to conditional probability. You will see that debate again in Philosophy of Language (36/07). To test validity, hunt for the counterexample Here is the method a graduate runs in their head. Don’t ask “does this feel right?” Ask: can I describe a situation where every premise is true and the conclusion is false? If you can, the argument is invalid, and that situation is the counterexample. If you honestly can’t, it’s valid. The rule is old: it is how Aristotle’s Prior Analytics (4th century BCE) refutes bad syllogisms, and how Indian logicians tested inferences with cases of “similar” and “dissimilar” instances. For propositional logic you can do it mechanically: list every combination of true and false for the letters, and look for a row where the premises are all true and the conclusion false. Choose a preset, or type your own formulas using P, Q, R and ~ (not), & (and), | (or), -> (if…then), <-> (if and only if), plus brackets. Interactive · Validity checker Premise 1 Premise 2 (optional) Premise 3 (optional) Conclusion Highlighted rows are those where every premise is true. A red row is a counterexample: premises true, conclusion false. Without JavaScript: modus ponens (P→Q; P; so Q) and modus tollens (P→Q; not Q; so not P) are valid. Affirming the consequent (P→Q; Q; so P) and denying the antecedent (P→Q; not P; so not Q) are invalid; both fail on the same row: P false, Q true. Notice what the table does not do: it never asks whether P is true. That is why logic is useful on arguments about anything. Notice also the hole in the street-cleaner example: “it rained → wet” plus “wet” leaves open the row where P is false and Q is true, so the argument has a counterexample, and a counterexample is a proof of invalidity. Syllogisms are about overlapping classes Aristotle’s first logic was about kinds: “All mammals are warm-blooded; all whales are mammals; so all whales are warm-blooded.” Each statement has one of four forms: A (all X are Y), E (no X are Y), I (some X are Y), O (some X are not Y). A syllogism has two premises and a conclusion sharing three terms: S (the conclusion’s subject), P (its predicate) and M (the “middle” term that appears in both premises but not the conclusion). The middle term can sit in four positions, the four figures. That gives 4 × 4 × 4 × 4 = 256 possible forms. How many are valid? It depends on a quiet assumption. Modern logic, following Boole and John Venn (his diagrams date from 1880), does not assume that every term has members, so “All unicorns are horned” is true even though there are none. On that reading, 15 of the 256 forms are valid. Medieval logicians, assuming that terms name things that exist, counted 24. The extra nine are valid only if the classes are not empty. The tester below computes both by brute force: it tries all 256 ways of deciding which of the eight Venn regions contain something. Interactive · Syllogism tester Major premise Minor premise Conclusion Figure (where the middle term M sits) Dots mark regions that contain something in a world where the premises are true and the conclusion false. Without JavaScript: of 256 syllogistic forms, 15 are valid on the modern reading and 24 on the traditional one. Barbara (AAA, figure 1) is valid. All-A in figure 2 (“All dogs are mammals; all cats are mammals; so all cats are dogs”) is invalid: two things can share a group without sharing each other. Look at the most common failure. “All dogs are mammals; all cats are mammals; so all cats are dogs.” The middle term (mammals) never says anything about all of itself, so the two premises can both be true while cats and dogs are separate circles inside the mammal circle. Logicians call that the undistributed middle. You will meet it in the wild as “Every extremist reads the news; I read the news; so…”. Fallacies are patterns that look like good arguments A fallacy is a mistake in reasoning that is common enough to have a name. Some are formal, like affirming the consequent, which your checker already refuses. Others are informal: the structure is fine, or loose, but something else goes wrong, such as changing the subject, quietly redefining a word, or putting the conclusion in a premise. Below are ten invented arguments. Name the problem before you look. Treat this as practice in seeing the move, not in winning arguments with Latin: “that’s a fallacy” is not a rebuttal until you show where the support fails. Interactive · Fallacy spotter (invented arguments) Score: 0 of 0 Without JavaScript: the ten arguments commit, in order, affirming the consequent, ad hominem, straw man, false dilemma, slippery slope, begging the question, equivocation, post hoc, irrelevant appeal to authority, and hasty generalization. Two cautions a graduate keeps. First, a fallacy name describes the reasoning, not the conclusion: a bad argument can have a true conclusion, and assuming it is false because the argument was bad is its own mistake, sometimes called the fallacy fallacy. Second, the same surface move can be fine. Citing an expert is reasonable when she is an expert in this field and other experts agree; questioning a witness’s record is relevant when the claim rests on her honesty; a slope can really be slippery when each step is likely. The question is always whether the support is relevant and strong enough. Induction and abduction: strength comes in degrees Valid arguments never say more than their premises already contain. That makes them safe and sterile. Most of what we reason about is different: from the sun rising every day so far to tomorrow’s sunrise; from a wet street and a closed café to “there was a burst main”. These are inductive and abductive (“inference to the best explanation”, a term from C. S. Peirce’s work) arguments. They are not valid or invalid; they are stronger or weaker, and a new fact can overturn them. David Hume pointed out in 1739–48 that no argument can show the future must resemble the past without assuming it; that is the problem of induction (36/03 and Philosophy of Science, 36/06, return to it). A toy version helps. Laplace’s rule of succession (1774) says that after n successes in a row and no failures, starting from a deliberately blank prior, the chance that the next one also succeeds is (n + 1) / (n + 2). It is a model with an assumption baked in, not the truth about the sun; but it shows evidence as a slider, not a switch. Interactive · How strong is “it has always happened”? Observed so far, no exceptions How many more in a row do you want to bet on? Laplace’s rule with a uniform prior. It assumes the trials are independent and equally likely to succeed; real swans and real suns need more than that. Without JavaScript: after 10 successes the chance of an 11th is 11/12, about 92%, but the chance that the next 100 all succeed is 11/111, about 10%. The sliders make a quiet point: a conclusion that says “always” is much harder to support than one that says “next time”. A universal claim can be killed by one counterexample (the black swan), which is why scientists prefer claims that stick their necks out. Logic was found in many places It is tempting to tell this story as Greek and then European. The record is wider. Aristotle’s syllogistic and the Stoic propositional logic are the Greek strands. In China the Later Mohists (around the 4th–3rd centuries BCE) left a set of Canons discussing names, definition and “the way things are alike and different”. In India the Nyāya Sūtra, dated by scholars anywhere from the 6th century BCE to the 2nd century CE, gave a five-part inference (claim, reason, example, application, conclusion: the standard illustration is “there is fire on the hill, because there is smoke, as in a kitchen”), and Dignāga (about 480–540 CE) said a good reason must pass three tests, which Epistemology (36/03) turns into a game. In the Islamic world al-Fārābī and Ibn Sīnā (Avicenna) wrote logic as the tool of all sciences and extended Aristotle to modal and conditional reasoning. Each tradition had to answer the same question: what makes one statement follow from another? The modern landmark is symbolic: Boole’s algebra of logic (1847, 1854), Frege’s Begriffsschrift (1879), which brought quantifiers (“for all”, “there is”) into the system, and Gödel’s results in 1930–31 on what such systems can and can’t prove. Claude Shannon’s 1937 master’s thesis showed that Boolean algebra describes relay switching circuits, which is why logic is also, quietly, the bottom layer of every computer. Foundations: Sets, Logic & Infinity (34/71) and the library’s Gödel’s Incompleteness Theorems (12/08) pick that thread up. What a graduate just sees Valid means “if the premises were true the conclusion would have to be”; it says nothing about whether they are true. “Sound” is “valid, plus true premises”. Ask about the connection and the facts separately. To refute an argument’s form, find one counterexample: one imaginable case with true premises and a false conclusion. “If P then Q” plus Q gives you nothing about P. “If P then Q” plus not-Q gives you not-P. Two things sharing a group are not thereby related to each other (the undistributed middle). A sentence that sounds like an argument may only be a demand, a story or a definition. Find the premises and the conclusion first. A bad argument for a conclusion does not make the conclusion false. Inductive strength is a matter of degree, and “always” claims are the fragile ones. Where it shows up next Epistemology (36/03): the Gettier problem, the regress of justification and Dignāga’s three tests are all exercises in finding the counterexample. Metaphysics (36/04) and Philosophy of Language (36/07): what “if” means, what a name refers to, and why “The present king of France is bald” was a puzzle (Russell, 1905). Ethics (36/02): moral arguments are valid or not like any others; the work is in the premises. The thought-experiment tools there show how a principle commits you to verdicts in other cases. Computer science and law: Boolean logic in circuits, SQL queries and search filters; contract clauses with “and/or” ambiguity; Legal Reasoning & Writing (35/02). In the world: reading a leaflet, a policy brief or a headline for the move “this correlates with that, so…”. See How to Spot Bullshit (17/03). If you want to go deeper 📘 Textbook. Patrick Hurley, A Concise Introduction to Logic (Cengage, many editions), the most common first logic text in the English-speaking world, strong on syllogisms and informal fallacies; or Graham Priest, Logic: A Very Short Introduction (Oxford, 2000; 2nd ed. 2017) for a compact tour. 📘 Gentler. Raymond Smullyan, What Is the Name of This Book? (1978), logic puzzles that teach by play, or Julian Baggini and Peter Fosl, The Philosopher’s Toolkit (Wiley-Blackwell). 🌐 Free text. forall x (the Open Logic Project, with a Calgary edition by P. D. Magnus and others), a free open textbook of symbolic logic used in many universities. 🌐 Free course. MIT OpenCourseWare 24.241 Logic I (Fall 2009), a full first course in formal logic with problem sets and solutions. The takeaway Logic is the study of what follows from what. An argument is valid if no case makes its premises true and its conclusion false, sound if it is valid and the premises are true; you test validity by looking for that one case. Fallacies are shapes that feel convincing without the support, and most everyday reasoning is not deduction but a matter of degree. Try this: take one argument from a newspaper or a chat today, write it as “premises, therefore conclusion”, and try to describe a world where the premises are true and the conclusion false. Sources & Further Reading Sources. Aristotle, Prior Analytics; Stoic logic (Chrysippus) and Mohist Canons per the Stanford Encyclopedia of Philosophy entries on ancient logic, Mohism and Chinese logic; Nyāya Sūtra and Dignāga, SEP “Epistemology in Indian Philosophy” and “Dignāga”; Boole 1847 and 1854; Frege 1879; Venn 1880; Gödel 1930–31; Shannon 1937; Hume 1739–40 and 1748; Laplace 1774; Lewis 1912 on strict implication; Edgington on conditionals (SEP “Indicative Conditionals”). The counts of 15 and 24 valid syllogistic forms were computed for this piece by brute force and agree with standard accounts (SEP “Medieval Syllogistic”, “Venn diagrams”). The ten fallacy examples are invented. 📘 Hurley, A Concise Introduction to Logic 🌐 Stanford Encyclopedia of Philosophy: Classical Logic 🌐 forall x (Open Logic Project) Step 2. Ethics: Five Ways to Answer “What Should I Do?” ------------------------------------------------------- Why: Consequences, duties, virtues and care: the main theories of how to live. Every moral argument quietly runs on a principle: count the results, keep the rules, be the right kind of person, look after the people near you, or act on terms nobody could reasonably refuse. A graduate learns to name the principle, and to see what it costs. A runaway trolley is about to kill five people. You can pull a lever and send it onto a side track where it will kill one. Most people say pull. Now the five are in the same danger, but the only way to stop the trolley is to push a stranger off a bridge into its path. Most people say no. The numbers are identical: one for five. The answers differ. Something is deciding, and it isn’t the arithmetic. That “something” is what ethics, as a philosophy course, is about. It is not a list of dos and don’ts, and it is not a debate about whose opinions are nicest. It is a toolkit of principles, each with a long history, each with an elegant core and a case that makes it squirm. A graduate keeps the toolkit: in a hospital, a boardroom or a family argument they can say, “you are reasoning as a consequentialist here, and the cost of that is…”. The library already has an easier start in How Should I Live? (05/01), The Trolley Problem (05/05) and Moral Philosophy, Seriously (05/15). This piece goes a step further: it lets you trace which principle your own answers follow, and adds the two families that introductions often skip, care and contractualism. The course in one box Who takes itPhilosophy majors, usually in year 1 or 2, often split into “normative ethics” (what to do) and “metaethics” (what morality is). Medicine, nursing, law, business and public-policy students take applied versions; many universities in Asia, Africa and Latin America now teach Confucian, Buddhist, Ubuntu and liberation-ethics texts beside Aristotle and Kant. What it is forReasoning about right and wrong with principles you can state, test and argue about, instead of only with feelings or slogans. Comes afterNothing. It helps to have seen Logic & Argument (36/01). Leads toMedical Ethics & Law (35/60), Political Theory (35/12), Contemporary Philosophy (36/12), and the ethics sections of business, engineering and journalism courses. What this piece gives youYou will not settle the trolley problem, and neither has anyone else. You will be able to name five approaches in their best form, say what each recommends in a standard case, and say what it has to swallow. Consequentialism: judge the act by what it brings about The idea is easy to state and hard to escape: the right act is the one with the best results. Jeremy Bentham (Introduction to the Principles of Morals and Legislation, 1789) said to count everyone’s pleasure and pain equally; Mill reports his rule as “everybody to count for one, nobody for more than one”. John Stuart Mill (Utilitarianism, 1861) added that some pleasures are better in kind. Henry Sidgwick, Derek Parfit and Peter Singer carried it into the present. Singer’s 1972 essay “Famine, Affluence, and Morality” asks what separates a child drowning in a pond in front of you (saving her costs you some muddy clothes) from a child far away whom a donation could save. If nothing, he argues, we owe far more than we give. right act = the act with the best total outcomeThe word to watch is “total”: every person counts equally, near or far, family or stranger. Its strengths: it takes suffering seriously wherever it happens, it explains why we judge a policy by its effects, and it gives an answer when principles collide. Its hardest cases: the surgeon who could kill one healthy visitor to save five patients, the framing of an innocent to calm a riot. If only the total matters, why not? Rule consequentialists (Brad Hooker, Ideal Code, Real World, 2000) reply that we should follow the rules whose general acceptance would do the most good, and a world where doctors might harvest visitors would be a worse one. Act consequentialists reply that our intuitions here are tuned to a world of small groups, not to the logic of the case. Deontology: some things you may not do Deontology (from the Greek deon, duty) says that actions have a moral character before you count results. There are duties and there are rights, and they are not just heavy items on the scale. The best-known version is Immanuel Kant’s (Groundwork of the Metaphysics of Morals, 1785). One form of his test: act only on a maxim you could will to be a universal law. Another: treat humanity, in yourself and others, never merely as a means but always also as an end. W. D. Ross (The Right and the Good, 1930) offered a more flexible family of “prima facie duties” (keep promises, repay kindness, do not harm) that you weigh case by case. Kant’s universalising test is easier to feel than to describe. Take the maxim “when I’m short of money I’ll promise to repay a loan, knowing I won’t.” Suppose everyone did that. Then no one would believe a promise, and the practice that makes the maxim work would vanish. That is a contradiction in conception. Or take “I’ll never help anyone”: a world could run on it, but you could not will it, since you will sometimes need help (a contradiction in will). Move the slider to see how the first one eats itself. Interactive · The universalisation test (a toy) Make a false promise Never help anyone Share of people who also act on the maxim A toy: Kant gave no formula. Here “a promise is believed” and “a stranger helps” each fall as the share of people using the maxim rises. The point is the endpoint. Without JavaScript: if everyone made false promises, nobody would believe a promise, so the maxim destroys the practice it needs. If nobody ever helped, a person in need would get no help, which the maxim’s own follower could not will. The critics: Hegel said the test is empty, since you can describe almost any maxim so that it passes; Kant’s own insistence that you may not lie even to a murderer at the door (“On a Supposed Right to Lie from Philanthropy”, 1797) strikes most people as a reductio. Defenders (Christine Korsgaard, Onora O’Neill) reply that the test is meant to expose a kind of practical self-defeat, not to generate a rulebook, and that Kant’s own harsh example is not forced by the theory. Same dilemma, different principles Here is where the theories earn their keep. Take three standard cases: the switch (divert the trolley, one dies, n are saved), the footbridge (push a stranger, one dies, n are saved), and the transplant (a surgeon takes one healthy visitor’s organs to save n patients). Set the number saved, decide what you would do, and see which principles give your pattern. The verdicts are stylised, since each theory comes in versions, and nothing here scores your morality. It shows what each answer would commit you to. Interactive · Which principle does my pattern follow? People saved if you act (the one dies) Threshold deontologist’s breaking point Tap “act” or “refrain” for each case. Rule consequentialism here assumes the best rule forbids killing a bystander even when it saves many; versions with a “prevent disaster” clause would differ. Without JavaScript: act-consequentialism says act in all three cases once more than one person is saved. A “means principle” deontologist (never use a person as a tool) diverts the trolley but won’t push or harvest. An absolute prohibition on killing refuses all three. A threshold deontologist refuses until the numbers pass a breaking point. A common answer, “switch yes, footbridge no, transplant no”, fits the means principle and the stylised rule-consequentialist. Two facts frame it. In the 2020 PhilPapers Survey of professional philosophers (about 1,800 respondents in the main group), 63% chose to switch and 13% not to, and when asked about normative ethics, people who could tick more than one answer gave deontology 32%, consequentialism 31% and virtue ethics 37%, so the field has not picked a winner. And the pattern “switch yes, footbridge no” is not just a Western habit: the Moral Machine experiment (Awad and colleagues, Nature, 2018) collected tens of millions of decisions from people in over two hundred countries and found some shared preferences (save more lives, save the young) and real regional differences in others. Philosophers have proposed several differences between the switch and the footbridge: the doctrine of double effect (Philippa Foot, 1967; the death is a side effect in one and a means in the other), the distinction between redirecting a threat and creating a new one (Judith Jarvis Thomson, 1976 and 1985), and the claim that some of our reaction is gut revulsion rather than principle (Joshua Greene’s imaging work from 2001, itself contested). The honest summary: the pattern is common, the principle behind it is argued over. Virtue ethics: ask what a good person is like Consequentialists ask “what should I do?” and Kantians “what is my duty?”. Virtue ethics asks a different question: what kind of person should I be? Aristotle (Nicomachean Ethics, 4th century BCE) argued that the aim of life is eudaimonia, flourishing, and that flourishing needs the virtues: courage, temperance, justice, practical wisdom. A virtue is a settled trait that gets the response right, in the right amount, to the right things, at the right time. Courage sits between cowardice and rashness, and Aristotle insists the “mean” is relative to us and the situation (NE II.6), not a fixed number. The mean moves with the case. Running into a fire is rash when the danger is high and little is at stake, and cowardly to hold back when the child you could save is inside and the fire is small. The tool below uses a made-up formula to show the shape of it. Interactive · The mean moves with the situation (a toy) Danger to you What is at stake for others How far in you go (0 stay out, 10 all in) Invented formula for illustration (fitting level = 10 × stakes ÷ (stakes + danger), with a margin of 1.5). Aristotle gave no formula; his point is that practical wisdom, not a rule, finds the mean. Without JavaScript: with danger 6 and stakes 8, the toy’s fitting level is about 5.7 out of 10; going in at 9 would be rash, staying out at 2 would be cowardly. Virtue thinking is also a worldwide family. In the Analects, Confucius (551–479 BCE) puts ren, humaneness, at the centre, practised through li, the ritual forms of respect, and by shu, reciprocity: asked for a single word to live by, he answers it is shu, not doing to others what you would not want done to you (15.24). Mencius argued that everyone has the “sprouts” of virtue, and offers the sight of a child about to fall into a well, and the pang we feel, as his proof (2A6); Xunzi replied that human nature is raw and needs shaping by ritual and teaching. Southern African ubuntu thought, in the saying that a person is a person through other persons, grounds virtue in community. Modern Western revival began with Elizabeth Anscombe’s “Modern Moral Philosophy” (1958) and Philippa Foot, and Rosalind Hursthouse’s On Virtue Ethics (1999). The usual objections: “be virtuous” is thin guidance in a hard case (replies: so is “maximise good”, and wise people do give guidance), and social psychology’s “situationist” challenge that behaviour depends more on situations than on stable traits (see Social Psychology, 35/25, for how much of that evidence held up). Care ethics: begin with relationships Most moral theories start from a detached chooser weighing options for strangers. Care ethics starts where most of life starts: with dependence. Everyone was once a baby, and many will be old; a morality that forgets this leaves caregivers out. Carol Gilligan’s In a Different Voice (1982) argued that psychology’s picture of moral development had measured everyone against a justice-and-rights ideal and under-rated the ethic of responsibility and responsiveness. Nel Noddings (Caring, 1984), Virginia Held and Eva Feder Kittay (Love’s Labor, 1999) built it into a moral theory, and Joan Tronto’s Moral Boundaries (1993) tied it to politics. On this view a duty to your mother is not a rule that happens to cover her; it comes from who she is to you. The tension with impartial theories can be put as a dial: how much more do those close to you count? Bentham and Mozi (the 5th-century BCE Chinese philosopher of “impartial care”, jian ai) say not at all. Confucians, including Mencius, who criticised Mozi for it, say love begins with the family and extends outward with differences. Bernard Williams (1976) added that a husband who, rescuing his wife, pauses to check that it is morally permitted has “one thought too many”. Interactive · How much more does someone you love count? Extra weight on your loved one Strangers on the other side The slider runs from 1× (impartial: Bentham, Mozi) to 1000×. Care ethicists would say no number captures it: the point is the shape of the choice. Without JavaScript: with weight 1 (strict impartiality) one loved person is outweighed by any two or more strangers. With weight 10 you save your loved one unless more than ten strangers are at risk. The critiques: care can slide into favouritism and clannishness, and it can be used to tell women they should do the caring; Gilligan’s claim about gender differences in moral reasoning has met mixed evidence, with meta-analyses finding small differences. Care ethicists answer that the remedy is to make care a public and shared task, and that the ethics of everyday dependence is not a minor corner of morality but most of it. Contractualism: principles no one could reasonably reject The contract tradition asks what we could agree to live by. Thomas Hobbes (Leviathan, 1651) argued from self-interest; John Rawls (A Theory of Justice, 1971; see The Veil of Ignorance, 05/09) from fairness behind a veil. T. M. Scanlon’s What We Owe to Each Other (1998) turned it into a theory of right and wrong: an act is wrong if it would be disallowed by principles that no one could reasonably reject as the basis for informed, unforced general agreement. The test looks at each person’s complaint separately. That is why contractualism has a different attitude to numbers. Scanlon’s example: Jones is injured in the transmitter room of a TV station, and rescuing him means cutting the broadcast of a World Cup match for fifteen minutes. A utilitarian can add up the mild annoyance of a vast audience until it exceeds Jones’s agony. Scanlon says no viewer’s complaint is anywhere near as strong as Jones’s, and a principle that left him in pain would be one he could reasonably reject, however many viewers there are. Slide the numbers. Interactive · Add up the complaints, or compare them? Each viewer’s loss, against Jones’s agony of 100 Number of viewers Illustrative units, not measured. Critics (including some who admire Scanlon) ask where a principle that refuses to add can stop: surely enough tiny harms matter. This is a live debate, not a solved one. Without JavaScript: if each viewer loses 0.01 against Jones’s 100, the sum passes Jones’s harm at 10,000 viewers. Summing says let Jones suffer once the audience is larger than that; comparing individual complaints says rescue him whatever the audience. Metaethics: what are we even doing? So far we have asked what is right. Metaethics asks what kind of thing a moral claim is. Is “cruelty is wrong” true in the way “water is H₂O” is true (moral realism)? Is it an expression of attitude (expressivism, from A. J. Ayer in 1936 to Simon Blackburn and Allan Gibbard)? Is it always false because there are no such facts, as J. L. Mackie argued in 1977 (error theory)? Or is it the result of a procedure rational agents would follow (constructivism, Korsgaard)? David Hume (Treatise, 1739–40) noticed writers sliding from “is” to “ought” without saying why; G. E. Moore’s “open question” argument (Principia Ethica, 1903) says that for any natural property you can still ask “but is it good?”. The field has an opinion: in the 2020 PhilPapers Survey, 62% of target philosophers accepted or leaned towards moral realism and 26% towards anti-realism. That is a majority, not a consensus, and each position has respected defenders. Cultural variety in moral codes is a fact (the anthropologists’ point); whether it implies that morality is relative is a separate argument, and a weaker one than it first sounds. Ethical disagreement is a fact too; so is wide agreement on a thin core, such as that gratuitous cruelty is bad. What a graduate just sees An ethical argument is an argument: find the principle behind it, then ask what it says about the sibling cases. If you pull the lever but won’t push the stranger, you hold some principle that distinguishes them. Name it. Consequentialism counts everyone equally, and the cost is that nothing is off the table in principle. Deontology protects individuals, and the cost is cases where keeping the rule looks like a disaster. Virtue ethics asks what a good person is like and does, and the cost is thinner guidance in a hard case. Care ethics begins from dependence, and the cost is the risk of favouritism. Contractualism asks who can reasonably object, and the cost is a hard line between “adds up” and “doesn’t”. “It’s only subjective” settles nothing: even anti-realists have to say what follows. Where it shows up next Medical Ethics & Law (35/60): the four principles used in hospitals are a pluralist blend of these families. Political Theory (35/12): Rawls and Nozick are contractarian and rights-based; welfare economics is consequentialist. Epistemology (36/03): “what should I believe?” has an ethics of its own, and testimony involves trust. Contemporary Philosophy (36/12): the revival of virtue ethics and of Confucian and African moral thought. In the world: autonomous-vehicle rules, triage protocols, AI alignment, a company’s code of conduct, how a family decides about an old parent’s care. If you want to go deeper 📘 Textbook. James Rachels and Stuart Rachels, The Elements of Moral Philosophy (McGraw-Hill, many editions), the standard clear first text; or Russ Shafer-Landau, The Fundamentals of Ethics (Oxford), which also covers metaethics. 📘 Gentler. Michael Sandel, Justice: What’s the Right Thing to Do? (2009), built on the lectures below; or Julia Annas, Intelligent Virtue (2011) for virtue ethics. 🌐 Free course. Harvard’s Justice with Michael Sandel lectures are free online; MIT OpenCourseWare 24.231 Ethics (Fall 2009) is a full university course. 🌐 Free text. The Stanford Encyclopedia of Philosophy has an entry on each family (this one is virtue ethics; the others are easy to find by name). The takeaway Behind every moral answer is a principle: results, duties, character, care or what could be justified to each person. Each gets many cases right and a few awkwardly wrong. A graduate does not pick one and defend it to the death; they can say which one is speaking, what it costs, and what the others would add. Try this: the next time you hear “that’s just wrong” or “it’s for the greater good”, ask which of the five principles it follows, and what that principle would say about a similar case you’d answer differently. Sources & Further Reading Sources. Bentham 1789; Mill 1861; Singer, “Famine, Affluence, and Morality”, Philosophy & Public Affairs 1972; Hooker 2000; Kant, Groundwork 1785 and “On a Supposed Right to Lie from Philanthropy” 1797; Ross 1930; Foot, “The Problem of Abortion and the Doctrine of the Double Effect”, 1967; Thomson, “The Trolley Problem”, Yale Law Journal 1985; Greene et al., Science 2001; Awad et al., “The Moral Machine experiment”, Nature 2018; PhilPapers Survey 2020 (Bourget and Chalmers; trolley switch 63% vs 13%, moral realism 62% vs 26%, normative ethics 32/31/37 among respondents who could select more than one); Aristotle, Nicomachean Ethics II.6; Analects 15.24 and Mencius 2A6; Anscombe 1958; Hursthouse 1999; Gilligan 1982; Noddings 1984; Kittay 1999; Williams, “Persons, Character and Morality”, 1976; Hobbes 1651; Rawls 1971; Scanlon 1998; Hume 1739–40; Moore 1903; Mackie 1977. The interactives’ numbers are invented for illustration. 📘 Rachels and Rachels, The Elements of Moral Philosophy 📘 Scanlon, What We Owe to Each Other 🌐 Stanford Encyclopedia of Philosophy: Consequentialism Step 3. Ancient & Medieval Philosophy: The Questions Before the Questions ------------------------------------------------------------------------- Why: From the Presocratics and Plato to Augustine, Avicenna and Aquinas. Two thousand years, three continents and at least four languages. Almost every move later philosophers make (that reality is not what it seems, that argument can settle things, that reason and faith must be reconciled) was first made here, mostly by people who disagreed fiercely. In the 5th century BCE a man in southern Italy argued that a fast runner can never overtake a slow one with a head start. Everyone knew this was false: runners overtake. The point was that the argument looked airtight, and so something in our ordinary picture of motion, space or number must be wrong. Finding out what took, by some counts, until the 19th century, and some philosophers think it is not over. That is the spirit of the whole period. Ancient and medieval philosophy is not a museum of wrong physics. It is the invention of a method: state a claim, find the strongest objection, and follow the argument where it goes. The chain runs from Miletus and Athens through Alexandria, Baghdad, Córdoba and Cairo to Paris and Oxford, and it depends, at every link, on people reading, translating and arguing with those before them. The course in one box Who takes itPhilosophy majors, almost always in year 1 or 2, because it is the foundation for everything after it; in some programmes it is split into an ancient and a medieval course. Classics, history and religious studies students take it too. What it is forGiving you the vocabulary and the arguments (form, cause, virtue, substance, essence, the first mover) that later philosophers answer without saying so. Comes afterNothing. It helps to have read Logic & Argument (36/01) alongside it. Leads toModern Philosophy: Descartes to Nietzsche (36/09), Islamic, African & Latin American Philosophy (36/11), and, further on, Ethics (36/02) and Metaphysics (36/04). The Chinese and Indian traditions of the same centuries are in Chinese & Indian Philosophy (36/10). What this piece gives youYou will not have read the texts. You will know seven big moves, who made them, and what the critics said. Easier first reads: The Allegory of the Cave (05/06), Stoicism for Real Life (05/02) and The Good Life Across Traditions (05/14). The Presocratics: Zeno's race and the first physics "Presocratic" lumps together thinkers of the 6th and 5th centuries BCE who asked what the world is made of. Thales of Miletus (in modern Turkey) was said by Aristotle to have answered "water". Anaximander said an unlimited something (apeiron). Heraclitus said all is change and held together by a pattern, the logos. Democritus said atoms and void. These are guesses, but they were the first guesses that came with reasons. Parmenides of Elea, in southern Italy, pushed the other way: what is cannot come from what is not, so change is impossible and the senses deceive. His student Zeno devised arguments to defend that conclusion by showing that belief in motion leads to absurdity, as reported by Aristotle in the Physics. In "Achilles and the tortoise", Achilles must first reach where the tortoise started, by which time it has moved on, and so on without end. The tool below runs the race and adds up the stages. total = head start × (1 + r + r² + r³ + …) = head start ÷ (1 − r)r is the tortoise's speed divided by Achilles' speed, and it must be less than 1. Interactive · Add up Zeno's stages Tortoise speed as a fraction of Achilles' (r) Stages counted Head start 100 m, Achilles 10 m/s; the tortoise's speed is 10r m/s. Infinitely many stages, finite distance and finite time: that is the modern answer. Philosophers still ask whether it explains how an infinite series is completed. Without JavaScript: with r = 0.5 the stages are 100, 50, 25 … metres and sum to 200 m, reached after 20 s; with r = 0.9 they sum to 1000 m after 100 s. The sum was not made rigorous until the 19th century. The Greeks themselves answered in different ways, and Aristotle distinguished a potential infinity of divisions from an actual one. Socrates: the art of the unanswerable question Socrates (470/469–399 BCE) wrote nothing. We know him from Plato, Xenophon and Aristophanes, whose portraits differ (the "Socratic problem"). In Plato's early dialogues he questions someone who claims to know what courage, piety or justice is, and shows, step by step, that the definitions contradict the person's other beliefs. This method, the elenchus, produces no final answer, only the discovery of ignorance. He was tried in Athens in 399 BCE for impiety and corrupting the young and executed by hemlock. "The life which is unexamined is not worth living."Plato, Apology 38a, Benjamin Jowett's translation The best-known case is the Euthyphro. Euthyphro defines piety as what the gods love. Socrates asks (10a): is the pious loved by the gods because it is pious, or is it pious because they love it? Try both horns. Interactive · The two horns Loved because it is piousPious because it is loved Choose a horn to see what follows. Without JavaScript: if the gods love it because it is pious, piety exists independently of the gods' say-so; if it is pious because they love it, their love looks arbitrary. Philosophers of religion still discuss this. Plato: the line from shadows to Forms Plato (c. 428/427–348/347 BCE), who founded the Academy in Athens, turned Socrates' search into a theory. We know many beautiful things, but never beauty itself; yet we recognise them as beautiful by something. That something, the Form of the Beautiful, is perfect, unchanging and grasped by reason, not by the senses. In the Republic (Book VII, 514a on) he pictured ordinary life as prisoners in a cave watching shadows; the one who climbs out sees the sun, the Form of the Good. (See 05/06 for the cave in full.) Just before the cave (509d–511e) he draws a divided line. Cut a line into two unequal parts, visible and intelligible, then cut each in the same ratio. The four segments give four grades of cognition: images, things, mathematical reasoning and understanding of the Forms. A small result follows from the geometry, and you can check it. Interactive · Cut the line Ratio intelligible : visible Plato says only "unequal" and "in the same ratio"; the line's total length of 100 is arbitrary. The tradition makes the intelligible part longer. Without JavaScript: for any ratio, the two middle segments come out equal. With a ratio of 2 they are each 22.2 on a line of 100. The objections began at once. Aristotle asked where the Forms are and what they add. Plato himself, in the Parmenides, lays out the "third man" regress: if a Form makes many men alike, what makes the men and the Form alike? And the Republic is political philosophy as well: its guardians include women, an extraordinary idea for the time, though it also proposes strict state control of education and a ruling class. Readers have disagreed since about whether to call it utopia or warning. Aristotle: four ways to ask "why?" Aristotle (384–322 BCE), Plato's student for twenty years and later tutor of Alexander of Macedon, reversed the direction. Forms are not elsewhere; they are in things. Study the world as it is. He wrote on logic (the first system of formal inference, the syllogism), biology (he studied and dissected animals, many of them marine), ethics, politics, poetry and what he called first philosophy. "All men by nature desire to know."Aristotle, Metaphysics I.1, W. D. Ross's translation To explain anything, he said, give four causes (Physics II.3): what it is made of (material), its form or structure (formal), what made it (efficient), and what it is for (final). Choose a thing. Interactive · Four causes of one thing Without JavaScript: for a bronze statue, the material cause is bronze, the formal cause is the shape of the figure, the efficient cause is the sculptor and the final cause is to honour the person shown. Final causes, purposes in nature, were rejected by much of early modern science and are still disputed in biology, where some philosophers say natural selection brought them back. In ethics, Aristotle held that virtue is a habit that finds the mean between two excesses, relative to the person and the situation. His views on slavery and on women in the Politics are among the worst of his writing, and later thinkers, including Christine de Pizan, argued with them. The Hellenistic schools: living with what you can't control After Alexander's conquests (d. 323 BCE) the Greek world was larger and less secure, and philosophy turned to a practical question: how do I live well when I cannot control events? Four schools answered. The Epicureans (Epicurus, 341–270 BCE, taught in a Garden) said pleasure is the good, mainly the quiet of having few fears and few needs; death is nothing to us. The Stoics (Zeno of Citium, c. 334–262 BCE; later Epictetus, c. 50–135 CE, born a slave; and the emperor Marcus Aurelius, 121–180) said virtue is the only good and we should accept what is outside our control. The Pyrrhonian sceptics (Pyrrho, c. 360–270 BCE; Sextus Empiricus, around 200 CE) suspended judgment on everything and reported that calm followed. The Cynics (Diogenes) lived by nature in public, ignoring convention. "Of things some are in our power, and others are not."Epictetus, Enchiridion 1, George Long's translation Interactive · Up to me, or not? Up to meNot up to me Choose one. Next Without JavaScript: for the Stoics, judgments and efforts are up to us; the result, other people's opinions, and our bodies are not wholly so. Stoicism was no passive creed: Marcus governed an empire, and Stoic ideas of a common human reason fed into later law and ethics. Critics from Aristotle's side say that making virtue everything undervalues the goods a life needs. See Stoicism for Real Life (05/02) for practice. Late antiquity to Avicenna and Maimonides: the bridge When Roman power wavered, philosophy did not stop. In Alexandria, Plotinus's Neoplatonism (Enneads, c. 3rd century) held that everything flows from an ineffable One. Hypatia (born between about 350 and 370, murdered in March 415) taught philosophy and mathematics there; she edited a book of Ptolemy's Almagest, and some scholars credit her with material in an Arabic version of Diophantus, but no philosophical writing of hers survives. The quote "Reserve your right to think" often credited to her was written in 1908 by Elbert Hubbard, who made it up. In North Africa, Augustine (354–430) joined Christian faith to Platonism and asked about time. "What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not."Augustine, Confessions XI.14, E. B. Pusey's translation Boethius (c. 477–524), writing in prison awaiting execution under Theodoric, finished The Consolation of Philosophy and had already translated Aristotle's logic into Latin, which kept it alive in the West. Meanwhile, from the 8th century in Baghdad, translators turned Greek into Arabic. Al-Kindī, al-Fārābī and then Ibn Sīnā (Avicenna, 980–1037) built systems on them. Avicenna's "floating man", suspended in air with no sensation, still knows he exists, an argument that the self is not the body. His distinction between what a thing is and that it is, with a Necessary Existent whose essence is existence, drove the next three centuries. Al-Ghazālī (1058–1111) attacked the philosophers' claim that causes necessitate effects; Ibn Rushd (Averroes, 1126–1198) answered him and wrote the commentaries on Aristotle that Latin Europe read. Moses Maimonides (1138–1204), writing in Judeo-Arabic in Cairo, held that we can say only what God is not (Guide of the Perplexed). More on this world in 36/11. Interactive · Who was alive in the year… Year Dates are conventional and many early ones are approximate (c.). Hypatia's birth year is uncertain (350–370). Confucius, Mencius and Nāgārjuna are added from other traditions (36/10). Without JavaScript: in 400 BCE Democritus, Socrates and Plato were alive, and in 1100 CE Anselm and al-Ghazālī were; try the year slider with JavaScript on. Aquinas, Christine de Pizan and the medieval university In the Latin West, Anselm (1033–1109) argued in the Proslogion that God is "that than which nothing greater can be conceived", and so must exist in reality; his contemporary Gaunilo replied that the same move would prove a perfect island. Peter Abelard (1079–1142) worked on universals. By the 13th century the new universities of Paris and Oxford were reading Aristotle in translation, partly through Ibn Rushd, and Thomas Aquinas (1225–1274) built the largest synthesis, in the Summa Theologiae. His "Five Ways" (I, q.2, a.3) are short arguments from features of the world to a first cause. The first, reconstructed: Some things are changing. Whatever changes is changed by something else. This chain of changers cannot run back without a first member. So there is something that changes things without being changed. Critics deny 2 (after Newton, steady motion needs no cause), deny 3, or deny that the conclusion is God. Defenders reply that Aquinas means a chain of simultaneous dependence, not a series of past events, which is a different matter. The 1277 condemnation by the bishop of Paris of more than 200 propositions, many of them Aristotelian, shows that this was no calm synthesis. Many believers and non-believers still find the argument worth testing. Christine de Pizan (1364–c. 1430), born in Venice and writing in France, supported her family by writing after being widowed. In The Book of the City of Ladies (1405) she answered the misogyny of the Romance of the Rose and of authorities including Aristotle, and built an allegorical city from the examples of learned women. Her case that women's apparent inferiority comes from lack of education is an early entry in a long argument we meet again in 36/09. What a graduate just sees An argument that seems valid with a false conclusion is a gift: something in the premises is wrong, and finding it is the work. "What is X?" questions expose how much we assume (Socrates). Explanations can be of four kinds, and "what is it for?" is one of them (Aristotle). Much of what we call ancient wisdom is advice on what is and isn't within our control. Greek philosophy survived because Arabic, Syriac, Hebrew and Latin readers copied, translated and disputed it. Reason and faith were argued as partners and as rivals, within every tradition. Women philosophers were there from the start and were often written out; check the sources before repeating a quote. Where it shows up next Modern Philosophy (36/09): Descartes's doubt is the Pyrrhonian sceptics' tool in a new setting, and Spinoza and Leibniz rework Aristotle's substance. Ethics (36/02): virtue ethics is Aristotle and the Stoics, restored in the 20th century by Anscombe and Foot. Islamic, African & Latin American Philosophy (36/11): the other half of the bridge, in the traditions' own terms. In the world: the Socratic method in law schools, the universities themselves (the lecture and the disputation are medieval forms), and the argument about religion and science that Aquinas, Ibn Rushd and Maimonides all faced. If you want to go deeper 📘 Textbook. Anthony Kenny, Ancient Philosophy (Oxford University Press, 2004), the first volume of his New History of Western Philosophy, then volume 2, Medieval Philosophy. A standard classroom alternative is Terence Irwin's Classical Thought (OUP). Check which edition your library has. 📘 Gentler. Peter Adamson, Classical Philosophy (Oxford University Press, 2014) and its sequels, which grew out of his free podcast; Jostein Gaarder's novel Sophie's World for a first pass. 🌐 Free course. The History of Philosophy without any gaps, Peter Adamson's podcast, which covers the Greek, Islamic, Jewish and Latin traditions in order. For the texts, the free public-domain translations by Jowett (Plato) and Ross (Aristotle) are on Project Gutenberg and the Internet Classics Archive. The takeaway Ancient and medieval philosophy invented the method of following an argument to its end. Its big structures (Plato's Forms, Aristotle's causes, the Stoic line between what we can and cannot control, Avicenna's essence and existence, Aquinas's synthesis) are still the ones modern debates are built on or against, and they were shaped by a chain of readers from Athens to Cairo to Paris, including women whose voices were often lost. Try this: take a belief you hold firmly and ask Socrates' question, "what exactly do I mean by it?", until your definition contradicts something else you believe. Sources & Further Reading Sources. Plato, Apology, Euthyphro and Republic (Jowett); Aristotle, Physics II.3 and VI.9, Metaphysics I.1 (Ross), Nicomachean Ethics II.6; Epictetus, Enchiridion (Long); Augustine, Confessions (Pusey); Anselm, Proslogion; Aquinas, Summa Theologiae I q.2 a.3; Maimonides, Guide of the Perplexed; Christine de Pizan, Le Livre de la Cité des Dames (1405); Stanford Encyclopedia of Philosophy entries on Zeno's paradoxes, Hypatia, Avicenna, Boethius, Christine de Pizan and Aquinas; Wikipedia's Hypatia entry on Hubbard's 1908 invention of the "right to think" quote. 📘 Kenny, Ancient Philosophy 📘 Adamson, Classical Philosophy 🌐 History of Philosophy without any gaps Step 4. Epistemology: What Knowing Is, and When a Belief Is Earned ------------------------------------------------------------------ Why: What knowledge is, scepticism, and how belief should follow evidence. You know your own birthday, that the Earth is old, and that you are not dreaming right now (or do you?). Epistemology asks what separates knowing from lucky guessing, where good reasons come from, and how strongly to believe things. You check the time on a clock in a railway station. It says 3:00, and it is 3:00. You know the time, surely. Now suppose the clock stopped exactly twelve hours ago, and you happened to look at the one moment of the day when it is right. Your belief is true. You had good reason for it, since clocks usually work. And yet most people feel you don’t know the time; you were lucky. Writing down exactly what is missing has occupied philosophers for twenty-four centuries, and the attempts to do it show a lot about knowledge, evidence and doubt. That is epistemology (from the Greek epistēmē, knowledge): the study of what knowledge is, how we get it, and what we are entitled to believe. It sits under every other subject. A scientist, a judge and a journalist are all doing applied epistemology. The library’s Epistemology: How Do We Know What Is Actually True? (05/07) is the easy first read and Bayesian Thinking for Everyday Life (17/07) the gentle one on probability. This piece goes further, with tools you can poke and, at the end, with the Indian and Buddhist traditions that were doing the same job in parallel. The course in one box Who takes itPhilosophy majors in year 2, and a standard unit in the “core areas” of the discipline alongside metaphysics, ethics and logic. Cognitive-science, law and statistics students often take an elective version. Many newer courses add social epistemology (testimony, expertise, disagreement) and non-Western traditions. What it is forUnderstanding what separates knowledge from true belief, where justification comes from, and how evidence should change confidence. Comes afterLogic & Argument (36/01). Leads toPhilosophy of Science (36/06), and it feeds Philosophy of Mind (36/05), Philosophy of Language (36/07) and Contemporary Philosophy (36/12). What this piece gives youYou will not solve the Gettier problem (nobody has). You will be able to say why true belief is not enough, what a chain of reasons must rest on, what the sceptic’s argument is, and how to update a belief on evidence. Plato to Gettier: knowledge is more than true belief Plato put the problem first. In the Meno (97–98) Socrates says a true opinion is as useful as knowledge for finding the road to Larissa, but true opinions are like the statues of Daedalus, which run away unless tied down. What ties them is “working out the reason why”. In the Theaetetus the suggestion that knowledge is true belief plus an account ends without a firm answer. The tradition took it as: knowledge is justified true belief (JTB). S knows that p ⇔ p is true, S believes p, and S is justified in believing pThe “traditional analysis”. Each part is necessary, said everyone; together they are sufficient, said most, until 1963. Then Edmund Gettier published a three-page paper, “Is Justified True Belief Knowledge?” (Analysis, 1963), with two cases in which someone has a justified true belief that looks like luck. Others had noticed the shape earlier: Bertrand Russell gave the stopped clock in Human Knowledge (1948), and in India Dharmottara (about 770 CE), commenting on Dharmakīrti, described a traveller who sees something that looks like water, which is a mirage, and walks to it, where there is in fact water hidden under a rock. His belief is true, and justified in the sense of being reasonable, but it is not knowledge. A generation of proposals followed. Causal and reliabilist accounts (Goldman, 1967 and 1979): the belief must be produced by a reliable process that connects it to the fact. Sensitivity (Robert Nozick, 1981): if p were false, you would not believe it. Safety (Ernest Sosa, Duncan Pritchard): you could not easily have been wrong in a similar case. No false lemmas: your reasoning must not pass through a falsehood. And a radical one: Timothy Williamson (Knowledge and Its Limits, 2000) suggests knowledge is basic and can’t be analysed into belief plus extras at all, and Linda Zagzebski (1994) argued that any analysis that leaves justification independent of truth will be open to Gettier-style cases. Eight cases follow. Decide for each whether the person knows, then see what four theories say. Interactive · Does she know? Four theories compared Answer a case to see how the theories compare. Verdicts are the textbook ones on simple statements of each theory. Each theory has defenders with refinements; the fake-barn and lottery verdicts in particular are argued over. JTB = justified true belief; +Safe = JTB plus safety; Sens = sensitivity; NFL = JTB plus no false lemmas. Without JavaScript: in the stopped-clock, fake-barn, lottery and Gettier’s own job-and-coins case, JTB counts the person as knowing while most philosophers say not. Safety and sensitivity rule most of these out. A good clock and good testimony count as knowledge on every theory. The brain-in-a-vat case splits them. One more twist: in the 2000s, experimental philosophers asked whether the Gettier intuition is universal. Weinberg, Nichols and Stich (2001) reported variation across cultures, but later studies failed to replicate that, and a large cross-cultural study by Machery and colleagues found people in several countries judged Gettier cases much alike. That is itself a result about the evidence for epistemology’s own intuitions. The regress: where does justification stop? Suppose you justify belief A by B, and B by C. Then what justifies C? Sextus Empiricus (Outlines of Pyrrhonism, around 200 CE) records the sceptic’s trick, attributed to Agrippa: whenever a claim is challenged, you have three moves, and all look bad. Go on forever (infinite regress), loop round (circularity), or stop somewhere and just assert (dogmatism). Modern epistemology is largely the three ways of picking from that menu. Foundationalism (Descartes, and the empiricists in another way): the chain stops at basic beliefs that justify others without needing justification from other beliefs, for example perceptual experience or self-evident truths. The worry: why are those privileged, and does the support thin out along the chain? Coherentism (Neurath’s raft, BonJour, Davidson): beliefs justify one another in a web, as the planks of a boat rebuilt at sea. The worry: a perfectly coherent fairy tale would score as well. This is the isolation objection. Infinitism (Peter Klein): a reason can be followed without end, because you only need to be able to give the next one. The worry: finite minds. Externalism (reliabilism, Goldman; virtue epistemology, Sosa and Zagzebski): justification may depend on facts you can’t see by reflection, such as whether the process that produced the belief is reliable. The worry: the “new evil demon” case where a deceived person seems just as justified. The toy below puts numbers to the first two pictures. It is a caricature, but it shows why each camp worries about the other’s weakness. Interactive · A chain versus a web (a toy) Foundationalist chain: steps from the base belief Strength of each inferential step Coherentist web: beliefs that support each other How strongly each supports the others Chain: confidence = 95% base × (step strength)^steps. Web: each belief starts at 20% and is raised by its supporters until it settles. Invented rules for illustration, not a theory anyone holds in this form. Without JavaScript: a chain of four steps each of strength 90% from a 95% base leaves about 62%. A web of six beliefs supporting each other at 30% lifts each from 20% to about 80%, and a six-belief fairy tale with the same links would reach the same number. Watch the two failure modes: the chain decays with every step, and the web inflates with every extra link, whether or not the web touches the world. Real accounts mix the two (BonJour’s later move to observation, “foundherentism” in Susan Haack’s term). Scepticism: the argument that you might be dreaming Scepticism is the challenge that we know much less than we think. Pyrrhonian sceptics in ancient Greece suspended judgment on everything. In Chinese philosophy, Zhuangzi (4th century BCE) woke from a dream of being a butterfly unsure whether he was a man who dreamed it. The Islamic theologian al-Ghazālī (about 1100) described doubting the senses and then reason in his Deliverance from Error. Descartes (Meditations, 1641) made it the method: dreams and then an all-powerful deceiver. Hilary Putnam’s brain in a vat (1981) is the modern form. Nāgārjuna (about 2nd–3rd century CE) argued in the Vigrahavyāvartanī that the “means of knowledge” cannot be shown valid without circularity or regress, and the Nyāya school argued back. The strongest modern form uses closure: if you know p, and know that p implies q, you know q. If I know I have hands, then I know I am not a handless brain in a vat. I do not know I am not a handless brain in a vat (nothing I can observe tells the two apart). So I do not know I have hands. It is valid, so you must give up a premise. Pick your response. Interactive · Which premise do you reject? Without JavaScript: the Moorean (G. E. Moore, 1939) rejects 2, saying he is more sure he has hands than of any premise. Nozick and Dretske reject 1, denying closure. Contextualists (Lewis, DeRose) say “know” has different standards in different conversations. Externalists say knowing needs a reliable connection, not a proof against vats. The sceptic accepts all three. On the question of how this all comes out among professional philosophers, the PhilPapers Survey of 2020 found a large majority who describe themselves as non-sceptical realists about the external world. That does not make the sceptical argument easy to answer; it means most philosophers think it is the premises, not the world, that fail, and disagree about which. Bayesian updating: belief in degrees Beliefs aren’t all or nothing. You are more sure of your name than of the weather next Tuesday. Bayesian epistemology makes this exact: a degree of belief is a probability, and evidence changes it by a rule. The rule is named for Thomas Bayes, whose essay was published after his death in 1763 (edited by Richard Price) and was developed by Laplace. posterior odds = prior odds × likelihood ratioPrior odds: how plausible before. Likelihood ratio: how much more likely the evidence is if the hypothesis is true than if it is false. Worked: a smoke alarm sounds. Say fires are rare (1% of such evenings), the alarm sounds in 90% of real fires, and also in 9% of non-fires (burnt toast). The likelihood ratio is 90 ÷ 9 = 10, so the odds go from about 1 to 99 to 10 to 99, a probability of about 9.2%. A loud, true alarm still leaves a fire unlikely, because fires started so rare. Move the sliders. Interactive · Update on one piece of evidence Prior: chance of the hypothesis before the evidence Evidence appears if the hypothesis is true Evidence appears even if it is false Without JavaScript: prior 1%, 90% true-positive, 9% false-positive gives a posterior of about 9.2% (likelihood ratio 10). With a prior of 30% the same evidence gives about 81%. Why trust the rule? The Dutch book argument (Ramsey 1926, de Finetti 1937): if your degrees of belief break the probability laws, a bookmaker can make bets you each regard as fair that guarantee you a loss. And a second payoff: people who start far apart but update on the same evidence tend to meet. Try it: two people who disagree about whether a coin is loaded (80% heads) or fair watch the same flips. A dogmatist who gave the idea a zero never moves, which is why Dennis Lindley named “Cromwell’s rule” after Oliver Cromwell’s plea in 1650, “think it possible you may be mistaken”: avoid prior probabilities of exactly 0 or 1 on anything empirical. Interactive · Do different priors converge? The coin is loaded (80% heads) The coin is fair Flips observed Hypotheses: “loaded 80% heads” against “fair”. Starting beliefs that it is loaded: Ana 5%, Ben 95%, Cy exactly 0%. Flips come from a fixed pseudo-random sequence, so the page is repeatable. Without JavaScript: after 100 flips of a loaded coin, Ana (5%) and Ben (95%) are both above 99.9% that it is loaded, while Cy, who began at exactly 0%, is still at 0%. The open problems are real. Where do priors come from? Subjective Bayesians (Ramsey, de Finetti, Savage) allow any coherent prior; objective Bayesians (Jaynes) look for rules that fix one. How can old evidence be used (Glymour’s problem, 1980)? And how can a finite person be that coherent? Bayesianism is a model of ideal belief that real minds approximate, with some famous exceptions (see The Biases That Fool Everyone, 17/02). Testimony: most of what you know, you were told How do you know the Earth is about 4.5 billion years old, that your birthday is when it is, that Lagos is in Nigeria? Not by testing it yourself. The philosopher John Hardwig called this epistemic dependence (1985): a scientific paper may have hundreds of authors, none of whom could check all the rest. Testimony is a source of knowledge as basic as perception or memory, or so most epistemologists now say. The old disagreement is between Hume and Reid. Hume (Enquiry, section 10, 1748) held that we believe others only because experience has shown reports to be reliable, so testimony reduces to evidence we have. Thomas Reid answered (1764) that we are born credulous, with a natural disposition to believe what we’re told, and are right to be unless there are reasons not to. Elizabeth Fricker defends a form of the Humean view, C. A. J. Coady an anti-reductionist one. A newer strand, from Miranda Fricker’s Epistemic Injustice (2007), asks who gets believed and why; prejudice about speakers can wrong them as knowers. Two things matter for how much to believe a report: how reliable each source is, and whether sources are independent. Ten newspapers copying one press release are one witness. The Marquis de Condorcet proved in 1785 that independent voters who are each right more than half the time give a group that is almost surely right as it grows; the proof fails when they share an error. In the tool, “copying” means reports that trace back to one origin. Interactive · Witnesses and retellings Chance each source gets it right Number of reports agreeing Share that are really copies of one report Two-option claim starting at 50/50; each independent report is right with the given chance. “Effective independent reports” = 1 + (reports − 1) × (1 − copy share). The retelling line assumes each hand-off flips the message with probability (1 − reliability). A model, not a measurement. Without JavaScript: three independent reports from sources that are each 80% reliable make a claim about 98% likely; if all three are copies of one, it is back to 80%. A message passed through five tellers who are each 90% reliable is right about 66% of the time. Nyāya and Buddhist epistemology: means of knowing, argued in India The Sanskrit word for this is pramāṇa, a “means of valid cognition”, and Indian philosophy argued over how many there are and which can be trusted. The materialist Cārvāka school (known mainly through its opponents’ reports, since its own texts are lost) is traditionally said to accept only perception, doubting that inference can reach what is unseen. Buddhist logicians from Dignāga (about 480–540 CE) to Dharmakīrti (7th century) accept two: perception and inference. The Nyāya school, whose root text is the Nyāya Sūtra, accepts four: perception, inference, comparison and testimony. Mīmāṃsā and Advaita thinkers add further sources such as postulation and non-perception. Another debate: is a cognition’s validity certified from within (svataḥ, the Mīmāṃsā answer) or by something outside it (parataḥ, the Nyāya answer)? Philosophers such as Stephen Phillips find in Nyāya something like what we now call externalism. SchoolAccepted means of knowing CārvākaPerception only (as reported by opponents) Buddhist (Dignāga, Dharmakīrti)Perception, inference NyāyaPerception, inference, comparison, testimony Mīmāṃsā (Kumārila), AdvaitaThose four, plus postulation and non-perception The part a logic student will love is Dignāga’s test of a good reason (hetu). The standard example is inferring fire on a hill from smoke. The reason must pass three tests: (1) it is present in the subject (smoke is on the hill), (2) it is present in some similar cases, where the thing to prove is present (kitchens with fire), and (3) it is absent in every dissimilar case, where the thing to prove is absent (a lake). Dignāga’s “wheel of reasons” (hetucakra) lists the 3 × 3 ways a reason can be spread over similar cases (all, some, none) and dissimilar cases (all, some, none). Only two of nine cells give a good inference. Click a cell, or try the examples. Interactive · Dignāga’s wheel of reasons Rows: how widely the reason is found among similar cases. Columns: among dissimilar cases. Condition (1), that the reason belongs to the subject, is assumed. Later Nyāya thinkers added further conditions. Without JavaScript: a good reason is present in some or all similar cases and absent from all dissimilar ones; that is two of the nine combinations. Smoke for fire passes. “It has horns, so it is a cow” fails, since goats have horns. “Sound is eternal because it is audible” fails because audible things are not found among eternal or non-eternal things other than sound. Notice what the test is: a search for counterexamples, the same method as the truth table in Logic & Argument (36/01). Dharmakīrti tightened it by asking why smoke never occurs without fire: because one thing is caused by the other, or because one is a kind of the other. That is an early account of the connection that makes inductive reasoning safe, and it is at the root of the problem of induction in Philosophy of Science (36/06). What a graduate just sees True belief isn’t knowledge: luck can sit between your reasons and the truth. No analysis of knowledge survives every case, and that is itself informative. Every justification chain ends somewhere, loops, or goes on; know which one you are using. A very coherent story proves nothing by itself being coherent. A valid argument for scepticism means you must reject a premise; the interesting question is which. Update by the likelihood ratio, remember the prior, and avoid probabilities of exactly 0 or 1. Ten reports that trace to one source are one report. Ask of any reason: what would a counterexample look like, and have I looked in the similar and dissimilar cases? Where it shows up next Philosophy of Science (36/06): induction, confirmation, and how evidence supports theories. Philosophy of Mind (36/05): what you can know of other minds and of your own. Philosophy of Language (36/07): what a speaker knows when she knows a meaning. Ancient & Medieval (36/08) and Chinese & Indian Philosophy (36/10): the Pyrrhonists, Ghazālī, Nāgārjuna and the Nyāya replies in full. In the world: how courts weigh witnesses, how journalists corroborate a story, how doctors reason from a test, how a language model’s confident wrong answer differs from knowing. If you want to go deeper 📘 Textbook. Robert Audi, Epistemology: A Contemporary Introduction to the Theory of Knowledge (Routledge, 4th ed.), the standard university text; or Duncan Pritchard, What Is This Thing Called Knowledge? (Routledge, 4th ed.). 📘 Gentler. Jennifer Nagel, Knowledge: A Very Short Introduction (Oxford, 2014). For the Indian side, Stephen Phillips, Epistemology in Classical India (Routledge, 2012). 🌐 Free course. MIT OpenCourseWare 24.211 Theory of Knowledge (Spring 2014, Declan Smithies), focused on scepticism and its responses. 🌐 Free text. The Stanford Encyclopedia of Philosophy entry on the analysis of knowledge, and the free OpenStax Introduction to Philosophy. The takeaway Knowing is more than believing something true for decent reasons; luck must not be the link. Reasons need somewhere to rest, whether on basic beliefs, a web or a reliable process, doubt can be built into a valid argument, and belief comes in degrees that evidence should move. Most of what you know comes from others, so how many independent sources you really have matters. Try this: take a belief you hold firmly, write down its prior odds and the strongest piece of evidence for it, ask what you’d expect to see if it were false, and see whether your confidence should move. Sources & Further Reading Sources. Plato, Meno 97–98 and Theaetetus; Gettier, Analysis 23(6), 1963, pp. 121–23; Russell, Human Knowledge 1948; Goldman 1967, 1976, 1979; Nozick, Philosophical Explanations 1981; Sosa; Pritchard; Williamson 2000; Zagzebski, “The Inescapability of Gettier Problems”, 1994; Dharmottara (c. 770 CE) via the Wikipedia and SEP accounts of Gettier-like cases in Indian epistemology; Weinberg, Nichols and Stich 2001 and later cross-cultural replication studies; Sextus Empiricus, Outlines of Pyrrhonism I.164–77; Descartes 1641; Putnam 1981; Moore 1939; Lewis 1996; DeRose 1995; Dretske 1970; al-Ghazālī, Deliverance from Error; Nāgārjuna, Vigrahavyāvartanī; Bayes 1763; Ramsey 1926; de Finetti 1937; Lindley on Cromwell’s rule; Hume 1748 §10; Reid 1764; Hardwig 1985; Condorcet 1785; Fricker 2007; Dignāga (about 480–540 CE) and Dharmakīrti (7th century) via Wikipedia, the SEP and Phillips 2012; PhilPapers Survey 2020. The interactives’ numbers were computed for this piece; the models are toys. 📘 Audi, Epistemology 📘 Nagel, Knowledge: A Very Short Introduction 🌐 Stanford Encyclopedia of Philosophy: Epistemology Step 5. Metaphysics: What Stays the Same When Everything Changes ---------------------------------------------------------------- Why: Existence, identity, causation, time and free will. Replace every plank of a ship and ask whether it is the same ship; replace every cell of a body and ask the same of a person. Metaphysics is the study of what such questions assume: things, selves, causes, time, and the edges of words like “heap”. Somewhere in a farmhouse there is an axe. Its owner says it was his grandfather’s. The head has been replaced twice and the handle three times. It is, he says, the same axe. A comedian made a joke of this in a British sitcom (a road-sweeper’s broom with “17 new heads and 14 new handles”), and the joke works because we sense that two things we believe cannot both be quite right: that a thing is the same only if it is made of the same stuff, and that a thing can survive change. Your body is a slower version of the axe: the molecules in it are exchanged all the time, yet nobody thinks they become a new person each year. A river is “the same river” while its water is never the same water twice, a puzzle Heraclitus was chewing on around 500 BCE. These are not word games. Whether you survive is what a hospital, a court and a will all quietly assume. Metaphysics asks what such assumptions rest on. It is not “the paranormal” (the word is usually explained as an accident of how Aristotle’s books were shelved, “after the Physics”, though that story is itself uncertain). It asks what it is to be the same thing over time, what makes one event a cause of another, whether the present is special, and what to do about words with blurry edges. The course in one box Who takes itPhilosophy majors, usually in year 2, often under a name like “Metaphysics” or “Problems of Philosophy”. Most programmes make it part of the core, and the UK’s Subject Benchmark Statement for Philosophy names the questions of what exists and what persons are among the subject’s central topics. Physics, law and cognitive-science students meet pieces of it in other courses. What it is forMaking explicit the assumptions about things, persons, causes and time that every other subject takes for granted, and testing them against puzzle cases. Comes afterLogic & Argument (36/01): you need to spot a valid argument to see which premise of a paradox you are giving up. Leads toPhilosophy of Mind (36/05), which needs the idea of identity and of causation between mind and body; it also feeds Philosophy of Science (36/06) and Philosophy of Language (36/07, vagueness and reference). The Indian and Chinese schools are told in full in Chinese & Indian Philosophy (36/10). What this piece gives youYou will not be able to defend a theory of time in a seminar. You will know six classic puzzles, the best answer each side gives, what the survey of professional philosophers (PhilPapers, 2020) shows about where opinion lies, and why none of them is closed. Easier first reads: Why Time Is Weirder Than You Think (13/03) and Free Will: Do You Actually Choose? (05/12). Things that persist: the ship of Theseus The Greek biographer Plutarch (around 100 CE) records the puzzle in his Life of Theseus. The Athenians kept the ship of the hero Theseus in harbour for centuries, replacing planks as they rotted, so that philosophers argued whether it was the same ship or another. The twist that makes it bite came later. In 1655 Thomas Hobbes asked: suppose someone collected the discarded planks and rebuilt them into a ship. Now there are two candidates. Which one, if either, is the ship of Theseus? Reconstruct each answer in its best form. The material view: a thing is its matter, so the rebuilt ship, which has the original planks, is the original. The continuity view: a thing is what is traced through unbroken change of place and form; the repaired ship in the harbour was never out of service, so it is the original and the rebuilt one is a copy built from salvaged parts. The conventional view: nothing in the world settles it; “same ship” serves a purpose (sailing, ownership, a museum) and the answer follows the purpose. The four-dimensionalist view (David Lewis and others): ships are extended in time, like roads. Two ships share their early stages the way two roads share a stretch before they fork. Then there was never one thing that “became” two; there were two all along, overlapping. Each has a cost: the material view ties identity to atoms you cannot feel; the continuity view says a perfect rebuild from your original parts is not you; the conventional view makes identity look like taste; the four-dimensional view asks you to believe in stretched-out objects. The machine below applies each rule to the same ship. They agree until the rule is forced to choose. Interactive · The ship of Theseus Planks replaced in the harbour ship (of 100) Old planks kept and rebuilt Old planks thrown away original plank new plank Ship A, in the harbour Ship B, rebuilt from the old planks Planks are counted exactly; the “verdicts” apply each rule as its defenders state it. Without JavaScript: when half the planks are replaced and the old ones are rebuilt into a second ship, the material view and the continuity view disagree about which ship is Theseus’s; at 100 replaced, the rebuilt ship has every original plank and the harbour ship none. At 10 replaced planks nobody doubts ship A is the ship; at 100, with the old planks reassembled, many people’s intuition flips to B. That flip is evidence about how the concept works: we use both matter and continuity, and they come apart only in odd cases we never had to settle. The puzzle has relatives, such as the statue and the clay that makes it (squash the clay and the statue is gone; the clay is not). Who is the same person? Now replace the ship with you. John Locke argued in 1694 (the second edition of his Essay, Book II, chapter 27) that a person is not a body or a soul but a being that can think of itself as the same thinking thing at different times: identity follows consciousness, chiefly memory. Thomas Reid objected in 1785 with the brave officer. A boy is flogged for stealing apples; as a young officer he captures a standard; as an old general he remembers capturing the standard but no longer remembers the flogging. The officer is the boy, the general the officer, yet the general is not the boy, which breaks the transitivity of identity (if A = B and B = C, then A = C). The usual repair separates connectedness (direct links, such as a memory) from continuity (overlapping chains of them). Identity needs only continuity, so the general is the boy. The best-known modern development is Derek Parfit’s Reasons and Persons (1984). Parfit pushed the thought experiments until the question “will it be me?” starts to look empty. In the teletransporter, you step into a booth; your body is scanned and destroyed, and a perfect copy is built on Mars from local atoms. Is that travel or death? In the branch-line version the scan is made but the original survives for a while: now there is a you on Earth and a you on Mars, each with your memories, each convinced they are you. They cannot both be identical to you, for then they would be identical to each other. Parfit concluded that identity is not what matters. What matters is “relation R”, psychological connectedness and continuity (with the right kind of cause), and R can hold in degrees and can branch. He added that he found this liberating. Parfit’s view is one position among several. The biological (animalist) view says you are a living organism, so the copy is a replica and you died. A further-fact view says there is a deep fact about whether you continue, such as a soul, even if no test could detect it. In the 2020 PhilPapers survey of professional philosophers, among those who answered the personal-identity question about 44% leaned to the psychological view, 19% to the biological view and 15% to a further fact; the rest chose other options. Elsewhere persons are understood differently again: in the Akan tradition of Ghana, as Kwame Gyekye and Kwasi Wiredu describe it, a person has several elements and is partly constituted by community, and ubuntu thought (“a person is a person through other persons”) pushes the same way. Interactive · How much of you survives a decade, and a booth? Share of your memories and character carried from one year to the next An ordinary life Teletransporter Branch line Accuracy of the copy A toy model, not data: connection between two moments n years apart is taken to be (carry-over)n. Parfit calls two moments “strongly connected” when they share at least half the direct links that hold over a single day in nearly everyone’s life; here half is the cut-off. Without JavaScript: with 90% carried over each year, the seventy-year-old shares well under 1% of direct connections with the ten-year-old, yet every year is strongly linked to the next, so psychological continuity holds all the way. No self: the Buddhist answer, and Nāgārjuna’s emptiness Parfit noted that his conclusion resembled the Buddha’s. Indian philosophers reached theirs by their own road and argued about it for centuries, so it deserves its own telling. Early Buddhist teaching holds that what we call a person is a stream of five aggregates (body, feeling, perception, mental formations, consciousness), none of which is a self, and that clinging to a permanent “I” is the root of suffering. The doctrine is anattā (Pali) or anātman (Sanskrit): no-self. The classic illustration is in the Milindapañha (“Questions of King Milinda”, compiled between roughly the first century BCE and the second century CE). The monk Nāgasena says he is called “Nāgasena” only as a name. The king asks if the self is the hair, the nails, the body, the feelings. No. Nāgasena asks how the king came, and the king says by chariot. Is the chariot the axle? The wheels? The pole? The frame? None of them, and not the collection, and not something apart from them. So “chariot” is a convenient designation for parts arranged in a certain way, and so is “person”. This is conventional truth, not nothing: chariots carry kings and persons suffer and reap what they sow. Not everyone agreed. The Nyāya school argued that there must be a self, because one and the same knower recognises “I saw this and now touch it”; no momentary state could do that. Advaita Vedānta (Śaṅkara, around the 8th century) held that a self (ātman) exists but is pure awareness, not the personality, and is ultimately one with Brahman. Buddhists answered that the unity of experience is produced by causal continuity, not by a thing underneath. Nāgārjuna (around the 2nd century CE) took the argument further, in the Mūlamadhyamakakārikā (“Fundamental Verses on the Middle Way”). His target was not the self alone but svabhāva, intrinsic nature: the idea that anything exists in its own right, independent of causes, parts and the concepts we apply. Everything arises in dependence on other things, so nothing has an intrinsic nature, and that absence is emptiness (śūnyatā). It is not that nothing exists. In chapter 24 he writes that dependent arising, emptiness and conventional designation are one and the same “middle way”. And emptiness is itself empty: it is not a deeper substance behind appearances, which is why he warned that those who make emptiness a view are “incurable”. Candrakīrti later put the chariot through a sevenfold analysis. Whether this is a form of nihilism, as critics said, or the rescue of ordinary life from the demand for ultimate foundations, as Madhyamaka defenders say, is argued to this day. Parfit, Nāgasena and Nāgārjuna agree that the demand for a deep fact about “me” cannot be met. They disagree about what to say next. Side by side they make a map, not a winner: analytic work asks which criterion decides a case (body, memory, brain); Buddhist work asks what the “I” is that the criterion is meant to track, and answers that it is a process, not a thing. Causation: the “because” in the world David Hume (Enquiry Concerning Human Understanding, 1748, section 7) found that we never observe a necessary connection between a cause and its effect, only one event following another. He gives two definitions in one passage. The first is regularity: an object followed by another, such that all objects like the first are followed by objects like the second. The second is counterfactual: “where, if the first object had not been, the second never had existed.” Two centuries later David Lewis (“Causation”, 1973) built the second into a theory: c is a cause of e if, had c not happened, e would not have happened. The test is called “but-for” in law, and it is the right first move in the doctor’s office and the courtroom. Its famous trouble is preemption. Suzy and Billy throw rocks at a bottle. Suzy’s arrives first and breaks it; Billy’s would have broken it a moment later. Without Suzy’s throw the bottle still breaks, so on the simple test Suzy’s throw is not a cause. Yet she plainly broke it. The reverse trouble is overdetermination: both rocks arrive at the same instant, so neither passes the test, though together they surely did it. Lewis and others repaired the theory with chains of events, but the repairs have their own counterexamples, and no analysis is accepted by everyone. Judea Pearl’s causal models (Causality, 2000) shifted the question to what would happen if you intervened. Interactive · Suzy, Billy and the bottle Only Suzy throws Suzy first, Billy a beat later Both arrive together Suzy’s rock arrives at tick Billy’s rock arrives at tick Suzy throws Billy throws The bottle breaks when the first thrown rock arrives. “But-for” asks whether it would still have broken, and when, with that throw deleted. Without JavaScript: when Suzy’s rock arrives first, the bottle still breaks if her throw is removed (Billy’s arrives), so the but-for test says she did not cause it, though she did. Free will is this puzzle aimed at you. If every event has causes, and the causes reach back before you were born, is your choice one more link? Peter van Inwagen’s Consequence Argument (1983) says that if determinism is true, your acts are consequences of the laws and the remote past, neither of which is up to you. Compatibilists answer that “free” means acting from your own reasons without coercion, which causation does not threaten; libertarians say the argument shows determinism must be false; hard determinists accept the conclusion. In the 2020 PhilPapers survey about six in ten philosophers lean to compatibilism, around one in eight to libertarianism and one in ten to no free will. The full debate, with Frankfurt’s cases and Libet’s clock, is in Free Will: Do You Actually Choose? (05/12). Time: does the present exist? In 1908 J. M. E. McTaggart separated two ways of ordering events. The A-series places them as past, present or future, and this changes: the present moves. The B-series orders them as earlier or later than one another, and this never changes. Rival camps follow. A presentist says only the present exists. An eternalist says past, present and future are equally real, as London and Paris are both real though you are in only one. A growing-block theorist says past and present exist and the future is still to be made. McTaggart himself argued that time is unreal, because the A-series is contradictory and the B-series alone is not change; few followed him there. Physics sharpened the question. Einstein’s special relativity (1905) says that two observers in relative motion disagree about which distant events are simultaneous with a given moment. In 1966–67 Rietdijk and Putnam argued that if “what is real” is whatever is simultaneous with me, then my reality includes events that, for you, are still in the future, so the future is already real. Roger Penrose popularised the point in 1989 with an Andromeda thought experiment: two people walking past each other in the street disagree by a few days about whether a decision in the Andromeda galaxy has been taken. The size of that disagreement is the product of walking speed and distance divided by the speed of light squared, and the tool below computes it. Interactive · Whose “now” is it in Andromeda? Your walking speed relative to the other person Δt = v · d / c², valid for speeds far below light speed, with c = 299 792 458 m/s. The tilt in the picture is exaggerated for visibility; the real angle is smaller than a billionth of a degree even at 120 km/h. Without JavaScript: at walking pace (5 km/h) the two “nows” differ by about four days at the distance of the Andromeda galaxy (about 2.5 million light-years), and by far less than a nanosecond at the distance of the Moon. What follows from this is contested. Eternalists say it supports their view, since relativity has no privileged “now”. Presentists reply that relativity may need a hidden preferred frame, or that “real” should not be defined by simultaneity at all. Others say the argument proves nothing about time itself. In the 2020 PhilPapers survey, among those who answered the question, 38% leaned to the B-theory (no moving present) and 27% to the A-theory; again the rest chose neither. Older, independent traditions also deny that the world is a set of static things: Buddhist momentariness, and Mullā Ṣadrā’s “substantial motion” (things change in their very being at every instant). Vagueness: when does a heap begin? Eubulides of Miletus, a contemporary of Aristotle in the fourth century BCE, is credited with the paradox of the heap (sōros, hence “sorites”). One grain of sand is not a heap. Adding one grain never turns a non-heap into a heap. So no number of grains is a heap. Both premises seem true, the logic is valid, and the conclusion is plainly false. The same shape serves for bald, tall, red, child and adult, and it matters whenever law, medicine or policy draws a line through a continuum. The responses are the map. Epistemicism (Timothy Williamson, Vagueness, 1994) accepts the shocking reply: there is a sharp cut-off, and we can never know where, because meaning depends on usage in ways too subtle for us to detect. Supervaluationism (Kit Fine, 1975, and van Fraassen) says a vague word has many acceptable ways of being made sharp. A sentence is true if true on all of them, false if false on all, and neither otherwise; “there is some cut-off” is true, but no particular cut-off is. Degree theories use fuzzy logic (Lotfi Zadeh, 1965): “heap” is true to a degree, and the second premise is almost, but not exactly, true each time, which adds up. Contextualists say the boundary shifts with the conversation. Peter Unger’s nihilism says there are no heaps at all. None of them is free of cost: epistemicism asks you to believe in a boundary you can never find; the others change logic or the meaning of “true”. Interactive · The heap Grains of sand HeapNot a heapCan’t tell Remove grains one at a time, from 200Draw a hidden cut-off The ranges (admissible cut-offs 15 to 80; degree curve centred at 40 grains) are illustrative choices, not facts about sand. Your own verdicts are kept only on this page, only until you leave it. Without JavaScript: on a degree view, removing one grain from 200 changes “heap” by a tiny fraction, but 200 such steps take it from almost fully true to false; that is how a premise that is “almost true” each time can lead to a false conclusion. What a graduate just sees “Same thing” can mean same stuff, same shape, same history or same purpose, and a puzzle usually appears when those pull apart. If a theory of identity says the copy is you, ask what it says when there are two copies. What matters in survival may be a matter of degree: connection fades over years while continuity holds. “No self” is an old claim, argued from India to Oxford, and it is a claim about a deep fact, not about whether people matter. “If it hadn’t happened, the effect wouldn’t have” is a good test of cause, and it fails with a backup, so the lawyer’s “but-for” test is a rule of thumb. “Now” is local: two observers disagree about distant simultaneity, so a universal moving present is hard to define in physics. A paradox is a valid argument with a false-looking conclusion: you must give up a premise, and every choice has a price. Vague words have borderline cases, and sharp lines in law (18 years, 0.08% blood alcohol) are decisions, not discoveries. Where it shows up next Philosophy of Mind (36/05): whether a mind could survive being copied or run on silicon is the teletransporter again. Philosophy of Science (36/06): causation, laws and “because” are what an explanation uses; Hume’s problem is induction’s problem. Law and medicine: “but-for” causation in tort, the brain-death debate about when a person ends, and the legal status of embryos and of corporations (Torts and Civil Liability, 35/05). In the world: sorites arguments in every threshold a regulator sets, and Parfit-style reasoning in debates about future generations. If you want to go deeper 📘 Textbook. Michael Loux and Thomas Crisp, Metaphysics: A Contemporary Introduction (Routledge, 4th edition 2017), is a standard undergraduate text. Theodore Sider’s Four-Dimensionalism (Oxford, 2001) is the best case for the stretched-out view. 📘 Classics. Derek Parfit, Reasons and Persons (Oxford, 1984), Part III; Jay Garfield, The Fundamental Wisdom of the Middle Way (Oxford, 1995), a translation and commentary on Nāgārjuna. 📘 Gentler. Julian Baggini, The Ego Trick (Granta, 2011), a lively tour of personal identity, and Carlo Rovelli, The Order of Time (2018) for time. 🌐 Free text. The Stanford Encyclopedia of Philosophy entries on Personal Identity, Nāgārjuna, Causation, Time and The Sorites Paradox. 🌐 Free course. Shelly Kagan’s PHIL 176 Death (Open Yale Courses) spends lectures 10 to 13 on personal identity and “what matters”. The takeaway Metaphysics tests the assumptions inside everyday words: same, cause, now, heap. The puzzles (the ship, the teletransporter, the preempting rock, the Andromeda walk, the sand) are not tricks; each is a place where two reasonable rules for using a word disagree. Philosophers in 2020 lean one way on most of them, and none is settled. Try this: pick something you own that has had parts replaced, a bike or a guitar, and write down which of the four rules (stuff, continuity, purpose, stages) makes you call it “the same”. Then ask which rule you would use if you sold it. Sources & Further Reading Sources. Plutarch, Life of Theseus 23; Hobbes, De Corpore (1655) 2.11.7; Locke, Essay II.27 (2nd ed. 1694); Reid, Essays on the Intellectual Powers of Man (1785); Parfit, Reasons and Persons (1984); Milindapañha; Nāgārjuna, Mūlamadhyamakakārikā chs. 18, 24 (as in Garfield’s translation); Hume, Enquiry §7; Lewis, “Causation” (Journal of Philosophy, 1973); Pearl, Causality (2000); van Inwagen, An Essay on Free Will (1983); McTaggart, “The Unreality of Time” (Mind, 1908); Putnam, “Time and Physical Geometry” (1967); Penrose, The Emperor’s New Mind (1989); Williamson, Vagueness (1994); Zadeh, “Fuzzy Sets” (1965). Survey figures: the 2020 PhilPapers Survey (Bourget and Chalmers, Philosophers on Philosophy), as tabulated at survey2020.philpeople.org and reported by Daily Nous; percentages are of those who answered each question, and other options exist. Stanford Encyclopedia of Philosophy entries as linked above. 📘 Parfit, Reasons and Persons 📘 Garfield, The Fundamental Wisdom of the Middle Way 🌐 Stanford Encyclopedia of Philosophy Step 6. Modern Philosophy: Descartes to Nietzsche ------------------------------------------------- Why: Descartes, the empiricists, Kant, Hegel, Mill and Nietzsche. In 1641 a French soldier-turned-thinker tried to doubt everything and found one thing left. Over the next 250 years a chain of replies (some from princesses and duchesses nobody put in the textbooks) turned that single point into the problems we still use: mind and body, cause and effect, freedom, and what we can know at all. You are reading this on a screen, and you are sure the screen is there. Now ask the old question: how do you know this is not a dream, or a very good simulation? You will not find a knockdown reply, and that is the point. From the 1630s to the 1880s European philosophers kept looking for one, and the way they failed produced the map of the subject. Between the scientific revolution and the age of mass politics, they asked what the mind brings to experience, what justifies our belief in causes, what makes a society free, and what is left of value once a religious foundation is gone. The usual story calls it a duel: rationalists (reason is the source of knowledge) against empiricists (experience is), settled by Kant. It is a useful map and a bad history. The people on it argued, borrowed and wrote letters, and some of the sharpest letters came from women. The course in one box Who takes itPhilosophy majors, usually in year 2, in most UK and US programmes; history of ideas, politics, literature and law students often take it. Many courses cover the same ten or so authors. What it is forLearning the framework in which later philosophy (including its rebels) writes: the mind as a thing that represents the world, and the world as something science studies. Comes afterAncient & Medieval Philosophy (36/08). Leads toContemporary Philosophy: Analytic, Continental & Beyond (36/12), plus Epistemology (36/03), Philosophy of Mind (36/05), Ethics (36/02) and Philosophy of Science (36/06). What this piece gives youYou will not have read the Critique of Pure Reason. You will know, for each of ten thinkers, the one move that made them matter, with a fair statement of the main objection. Easier first reads: How Do We Know? Epistemology (05/07) and Philosophy of Mind and Consciousness (05/10). Descartes: how much can you doubt? René Descartes (1596–1650) wanted certainty to rest on something unshakeable, as geometry seemed to. In the Meditations (1641) he decided to reject anything that could be doubted, in stages. First, the senses sometimes deceive (a distant square tower looks round). Second, I might be dreaming right now, and nothing marks the difference. Third, an all-powerful deceiver might make me wrong even about "two and three make five". The doubt survives only one thing: in order to be deceived, I must exist. "I think, therefore I am."Descartes, Discourse on Method (1637), part IV; in the Meditations the argument comes in the second meditation Descartes then argued that the mind is a thinking, non-extended thing, and the body an extended, non-thinking thing: dualism. Push the doubt yourself. Interactive · How far does the doubt go? The beliefs are examples in the spirit of Meditations I and II. Which doubt reaches which belief follows Descartes's own order. Without JavaScript: doubting the senses removes beliefs about distant things; doubting by dream removes "I am here by the fire" and the existence of the outside world; the evil-deceiver doubt removes arithmetic. "I am thinking" and "I exist" remain. Two objections shaped the next century. Antoine Arnauld said Descartes argues in a circle: he proves God to guarantee clear ideas, using clear ideas. And in 1643 Princess Elisabeth of Bohemia (1618–1680) asked the question he never answered well: if the mind is not extended, how can it move a body at all? We return to her below. Spinoza and Leibniz: reason takes charge Baruch Spinoza (1632–1677), expelled from the Amsterdam Jewish community in 1656 and earning his living grinding lenses, took dualism's problem and removed it. There is one substance, "God or Nature," and mind and body are two ways of describing it. Everything follows by necessity, as in geometry; the Ethics (published after his death, in 1677) is written as propositions and proofs. Freedom is not choosing against necessity but understanding it. His critics called it atheism; his defenders note that it is a very different God from either a person or a mere pile of matter. Gottfried Wilhelm Leibniz (1646–1716), lawyer, diplomat and co-inventor of the calculus, built on the principle of sufficient reason: nothing is so without a reason. From it he drew the existence of a God who chose "the best of all possible worlds", and a universe of simple, mind-like units, monads. Voltaire's Candide (1759) mocked the optimism; Leibniz's actual claim was that a perfect creator would choose the best total package, evil included. Whether that answers the problem of evil is still argued. Locke, Berkeley and Hume: all knowledge from experience John Locke (1632–1704) opened the Essay Concerning Human Understanding (1689) by denying innate ideas: the mind starts as blank paper and experience writes on it. George Berkeley (1685–1753) then argued that if all we know are ideas, nothing needs matter behind them: to be is to be perceived (esse est percipi), kept in being by God's constant perception. (The famous "tree in the quad" limerick is by Ronald Knox, not Berkeley.) David Hume (1711–1776) pushed hardest. In the Enquiry (1748) he divided all objects of reason into relations of ideas (triangles, arithmetic: denying them is a contradiction) and matters of fact (known only from experience). Then he asked what justifies expecting the future to resemble the past. Not logic, since the sun failing to rise is no contradiction. Not experience, since that would use the very assumption in question. This is the problem of induction. See if you can sort the cases. Interactive · Hume's fork Relation of ideasMatter of factNeither Choose one. Next claim Without JavaScript: "7 × 8 = 56" is a relation of ideas; "the sun will rise tomorrow" is a matter of fact and cannot be proved by logic; a claim that only those two kinds count as knowledge is itself neither, an objection often raised. Hume's other legacies: the self may be a bundle of perceptions with no further owner; "reason is, and ought only to be, the slave of the passions"; and you cannot derive an ought from an is without a step that needs defending. Defenders reply to the induction problem with probabilistic methods (36/06) or by arguing that no justification is needed; no answer has won. Mary Shepherd (1777–1847) is a notable early critic, arguing that we can know by reason that events have causes. Kant: what the mind brings Immanuel Kant (1724–1804) said Hume woke him from "dogmatic slumber". His reply, in the Critique of Pure Reason (1781, revised 1787), was a reversal he compared to Copernicus. Instead of assuming that the mind conforms to objects, suppose objects as we experience them conform to the mind's built-in forms: space, time and categories such as cause. Then some things can be known in advance of experience (that every event has a cause), not because the world in itself must be so, but because that is how any experience we can have is structured. "Thoughts without content are void; intuitions without conceptions, blind."Kant, Critique of Pure Reason, A51/B75, J. M. D. Meiklejohn's translation Kant's key tool is a grid. A judgement is analytic if the predicate is contained in the subject, and synthetic if it adds something; and it is a priori if known independent of experience, a posteriori if not. The hard question, he thought, is how synthetic a priori judgements are possible, since mathematics and physics seem to contain them. Interactive · Kant's grid Analytic a prioriSynthetic a posterioriSynthetic a priori Choose one. Next judgement Without JavaScript: "all bachelors are unmarried" is analytic a priori; "the kettle is boiling" is synthetic a posteriori; Kant held that "7 + 5 = 12" and "every event has a cause" are synthetic a priori. In ethics, the Groundwork (1785) states the categorical imperative: act only on principles you could will as universal law, and treat humanity never merely as a means. The costs: Kant's "things in themselves" are unknowable, which many found unstable; later logicians (Frege) argued that arithmetic is analytic; and Kant's own writings contain racist and sexist claims, which scholars now debate openly when reading him. Women and others the canon left out Women were mostly shut out of universities, so they wrote letters, essays and novels. They were not on the margins of the argument. Elisabeth of Bohemia, exiled princess, corresponded with Descartes from 1643; her mind-body objection was never answered to her satisfaction, and she asked him to explain the passions, which became his last major book. Margaret Cavendish (1623–1673) argued in Observations upon Experimental Philosophy (1666) that matter is self-moving and that peering through instruments is no guarantee of truth, and in the same year published a fantasy, The Blazing World; in 1667 she visited the Royal Society, as a curiosity. Anne Conway (1631–1679) held that all creatures are one substance in different degrees, and Leibniz read her. Émilie du Châtelet (1706–1749) translated and explained Newton and defended the idea that a moving body's energy grows with the square of its speed. Mary Astell (1666–1731) proposed an educational community for women (1694) and asked, in Some Reflections upon Marriage (1700): "If all Men are born free, how is it that all Women are born Slaves?" Mary Wollstonecraft (1759–1797), in A Vindication of the Rights of Woman (1792), argued that women seem inferior because they are badly educated. "I do not wish them to have power over men; but over themselves."Wollstonecraft, A Vindication of the Rights of Woman (1792), chapter 4 Outside northern Europe the argument also went on. In Ethiopia, Zera Yacob wrote his rationalist Hatata (inquiry) in 1667, though scholars disagree over whether it was written by him or by a later hand. Anton Wilhelm Amo, born in what is now Ghana around 1703, taught philosophy in German universities. Both are taken up in Islamic, African & Latin American Philosophy (36/11). Hegel and Mill: history and liberty G. W. F. Hegel (1770–1831) argued that thought and history are one process: ideas develop by running into their own contradictions and moving beyond them. (The tag "thesis, antithesis, synthesis" is not Hegel's; he rarely used it.) His most read passage, from the Phenomenology of Spirit (1807), is the master and the bondsman. Self-consciousness needs another's recognition; the master wins recognition but depends on the bondsman, who, through work, builds a world and a self. Marx took the idea and turned it towards material conditions. Hegel's critics, from Kierkegaard to Popper, called him obscure or dangerous, and his lectures on world history are rightly criticised as dismissive of Africa and Asia. John Stuart Mill (1806–1873) is the clearest voice of liberal utilitarianism: actions are right as they promote happiness, and some pleasures count for more than others. In On Liberty (1859) he gave a rule for when society may interfere with an individual. "The only purpose for which power can be rightfully exercised over any member of a civilized community, against his will, is to prevent harm to others."Mill, On Liberty (1859), chapter 1 He also wrote The Subjection of Women (1869), crediting his wife Harriet Taylor Mill. Apply his rule to a few cases; it is meant to show how the principle works, not to score your morals. Interactive · Does Mill's principle allow interference? Society may interfereLeave the person alone Choose one. Next case Without JavaScript: staying up all night gaming harms only yourself, so Mill says leave it; driving drunk past a school endangers others, so interference is allowed; an unpopular opinion in print is protected, though inciting a mob is not. The critics: communitarians say that no act is purely self-regarding; paternalists argue that some interference helps people; and others ask who counts as harmed (does offence?). Mill himself made exceptions, including that one may not sell oneself into slavery. Nietzsche: after the foundation Friedrich Nietzsche (1844–1900) wrote in short, provocative pieces rather than systems. In The Gay Science (1882, section 125) a madman announces that "God is dead": not a boast but a warning, that the beliefs on which European morals rested had lost their support, and that nobody had reckoned the cost. In On the Genealogy of Morality (1887) he asked where our values came from and who they served, arguing that moralities are historical products with hidden motives. He held that knowledge is always from some perspective (perspectivism), and in section 341 of The Gay Science he posed the eternal recurrence as a test: could you will your life again, exactly as it is, forever? Nietzsche was no nationalist or antisemite and mocked both, but after his collapse in 1889 his sister Elisabeth Förster-Nietzsche, who married an antisemitic agitator, controlled his papers and shaped them for nationalist readers, which is how the Nazis found a "Nietzsche" to quote. The critical edition by Giorgio Colli and Mazzino Montinari (from 1967) restored the texts. What remains debated is how to read him: as a moral sceptic, a perfectionist about individuals, or an artist of provocation. Critics say that his contempt for pity and for "the herd" gives dangerous cover to cruelty. What a graduate just sees The strongest case for any belief is the one that survives a strong doubt, and what survives is often small. If mind and matter are different kinds of thing, you owe an account of how they interact. "The sun will rise" cannot be proved from the past without circular reasoning; induction rests on trust we cannot prove. Some of what we think we learn from the world is the shape our minds give it. Whether a society may override a person's choices for their own good is a live question, and Mill's "only to prevent harm to others" is where it starts. The history of philosophy is a history of letters and objections, and many of the best objections came from people the textbooks omit. Values have histories, and asking whose interests they served is a legitimate question. Where it shows up next Philosophy of Science (36/06): Hume's induction is Popper's and Kuhn's starting point. Philosophy of Mind (36/05): Elisabeth's question is the mind-body problem, which Spinoza, Cavendish and Conway each answered differently. Contemporary Philosophy (36/12): analytic philosophy begins as a rebellion against idealism (Kant and Hegel); the continental line runs through Hegel and Nietzsche. In the world: liberal law and free-speech debate (Mill), human-rights language (Kant), the "is it a simulation?" question (Descartes), and the worry about what a machine knows (Hume, Kant). If you want to go deeper 📘 Textbook. Anthony Kenny, The Rise of Modern Philosophy (Oxford University Press, 2006), volume 3 of his New History of Western Philosophy. A common classroom anthology is Roger Ariew and Eric Watkins's Modern Philosophy: An Anthology of Primary Sources (Hackett); check the current edition. 📘 Gentler. Roger Scruton, A Short History of Modern Philosophy (Routledge); his views are his own and occasionally argued rather than reported. Peter Adamson's later volumes on the podcast cover women of the period. 🌐 Free text. Jonathan Bennett's Early Modern Texts has Descartes, Locke, Berkeley, Hume, Leibniz and others in lightly edited modern English; the Stanford Encyclopedia of Philosophy has entries on every person above, including Elisabeth, Cavendish, Conway, Astell and Shepherd. The takeaway Modern philosophy starts with the attempt to base knowledge on a single certain point and spends 250 years discovering what that costs: the mind-body problem, the problem of induction, a world shaped by the mind, and the question of what is left of value. Its sharpest objections often came from women excluded from the schools, and from places the textbooks seldom visit. Try this: pick one belief you take for granted, such as that tomorrow will resemble today, and write the best argument you can for it without assuming the thing itself. Then compare with Hume. Sources & Further Reading Sources. Descartes, Discourse on Method (1637), Meditations (1641) and the Elisabeth correspondence (from 1643); Spinoza, Ethics (1677); Leibniz, Theodicy (1710) and Monadology (1714); Locke, Essay (1689); Berkeley, Principles (1710); Hume, Treatise (1739–40) and Enquiry (1748); Kant, Critique of Pure Reason (1781/1787, Meiklejohn) and Groundwork (1785); Hegel, Phenomenology of Spirit (1807); Mill, On Liberty (1859), Utilitarianism (1861), The Subjection of Women (1869); Nietzsche, The Gay Science (1882), Genealogy of Morality (1887); Astell (1700); Wollstonecraft (1792); Cavendish (1666); Stanford Encyclopedia of Philosophy entries on Elisabeth of Bohemia and Margaret Cavendish. 📘 Kenny, The Rise of Modern Philosophy 🌐 Early Modern Texts 🌐 History of Philosophy without any gaps Step 7. Chinese & Indian Philosophy: Old Argument Cultures, Read as Philosophy ------------------------------------------------------------------------------ Why: Confucianism, Daoism, Buddhism and the Indian schools, in their own terms. Two civilisations where people argued about human nature, knowledge, causation and the self for two and a half thousand years, with premises, objections, replies and rival schools. Here they are as philosophy, not as a mood of ancient wisdom. Around 300 BCE, a teacher from what is now Shandong called Mencius put a thought experiment to his audience. Suppose you see a small child about to crawl into a well. You feel a jolt of alarm and pity. You do not stop to think of a reward from the parents, or of your reputation, or of how much you dislike the noise of crying. So, he said, the feeling is not a product of calculation: it is a sprout, the beginning of goodness, and every human being has it. A generation later, a philosopher called Xunzi replied that this proves much less than it seems. Feelings are not conduct. Left to themselves, people also quarrel, envy and take what they can; goodness is a skill acquired through teachers, rituals and years of practice, like a warped board straightened with steam and a press. Xunzi's two most famous students then went further: both of them became Legalists, who held that you should not rely on goodness at all. That is a debate, with sides, evidence and counter-examples, not a collection of proverbs. India produced the same thing at the same scale: schools that argued about how we know anything, whether there is a self, and whether the world is real, in texts written for opponents to read and answer. This piece gives you the main positions on both sides, the reasoning behind them, and the places where each is weakest. It is a map, not a tour of everything. The course in one box Who takes itPhilosophy majors, often in year 2, as a core or a required "non-Western" or comparative course. Programmes that put it at the centre include the University of Hawaiʻi's long comparative-philosophy tradition; elsewhere it is an option, or part of East Asian or South Asian studies. Religious studies and history students take it too. What it is forSeeing that the central questions of philosophy were argued out independently in at least three places, and learning to read a text in its own terms before judging it. Comes afterNo prerequisite in the curriculum. Logic & Argument (36/01) helps a lot. Leads toIslamic, African & Latin American Philosophy (36/11), Contemporary Philosophy (36/12), and it feeds Ethics (36/02), Epistemology (36/03) and Philosophy of Language (36/07), which meet the same questions again. What this piece gives youYou will not read Sanskrit or Classical Chinese after this. You will know about eight arguments well enough to state them, and you will be able to tell a real disagreement from a difference of vocabulary. Easier first reads: The Good Life Across Traditions (05/14), What Is a Good Argument? (05/03), and the long reads China and Japan, Hinduism, Buddhism and Jainism and Sikhism in Religions in Depth (33). This piece goes into the arguments those reads only name. Mencius and Xunzi: is goodness grown or built? Confucius (551–479 BCE) left no treatise. His sayings were collected by disciples in the Analects, over a long time. His starting point was practical: society is held together by relationships (parent and child, ruler and minister, friends), and a good person is shaped by how they fulfil those roles, with ren (humaneness, care for others) as the central virtue and li (ritual, courtesy, the forms of respect) as its discipline. The question he left open was the one the next two centuries fought over: where does the capacity for goodness come from? Mencius (c. 372–289 BCE) argued from the well: Anyone seeing a child about to fall into a well feels alarm and compassion (Mencius 2A6). This feeling is not caused by hope of reward, wish for praise or dislike of the child's cries. So the feeling is not produced by self-interest. So people have an innate starting point of goodness: compassion is the sprout of ren, and likewise shame, deference and a sense of right and wrong are sprouts of the other virtues. He added a warning: sprouts can be trampled or starved, and they can be ruined by too much help (his farmer who tugged at his seedlings to make them grow, and killed them). So his claim was that human nature is good in its tendency, not that all people are good. Xunzi (c. 310–c. 235 BCE) used different evidence: Humans are born liking gain and disliking harm, and envying others. Followed without restraint, these tendencies produce conflict and cruelty. Goodness comes from conscious effort (wei): learning ritual and following teachers. So human nature, taken as what we are born with, is bad, and goodness is made. Note the difference in a word. When Mencius says "nature" he means what a thing grows into when it flourishes; when Xunzi says "nature" he means what is there at birth. A good deal of their disagreement is real, though: Xunzi's view says the ruler's job is to build a moral order; Mencius's says it is to protect one that people already want. Each has an obvious weak point. Mencius must explain why so many people go wrong. Xunzi must explain where the human ability to see that ritual is worth following comes from if we start out merely selfish. His answer is that humans have intelligence and the capacity to learn, which Mencius might fairly say is itself a sprout. Interactive · One case, four Chinese schools Pick a case, and see how the schools in the next section answer it. "Text" means the school's own writings address the case; "reconstruction" means I am working out what its principles imply. Without JavaScript: on the sheep case, the Analects (13.18) has Confucius say that uprightness lies in fathers and sons covering for each other; the Han Feizi uses the story to argue that private loyalty and public law conflict and law must win. On war, Mozi condemns offensive war as crime on a large scale; Mencius allows only a ruler with the people's support to "punish" a tyrant. Mozi, the Legalists and Zhuangzi: three ways to disagree with Confucius Mozi (c. 470–c. 391 BCE) thought Confucian partiality, caring most for kin and less for strangers, was the root of war and waste. His argument was about consequences. The test of any teaching, he said, is whether it benefits the people: what the ancient models did, what people can observe, and whether it works when applied. Wars of conquest fail this test. Stealing a peach is a crime, killing a man a worse one, and conquering a state is the same crime on a larger scale, praised only because the scale is hard to see (Mozi ch. 17). His remedy was jian ai, usually translated "impartial care" or "concern for all": treat strangers' households as you would your own. Mencius thought this was a rejection of the family itself ("to love without distinction is to have no father", Mencius 3B9). Mohist followers also developed canons on logic, argument and defensive warfare, which makes them the closest ancient China came to a school of logic. The Legalists started from the opposite pole. Han Fei (c. 280–233 BCE), a student of Xunzi, argued that a state cannot be built on the hope that rulers and officials will be good, since they mostly won't be. It can be built on a design: clear public law (fa), techniques for controlling officials (shu), and the ruler's authority (shi), run by two "handles", reward and punishment. The strongest part of the argument is practical: it asks for institutions that work with ordinary motives. The weak part is that a ruler can use the same machine on his own subjects, and Han Fei himself died in prison in Qin in 233 BCE, a victim of the court intrigue he had analysed. The Qin dynasty that adopted Legalist methods unified China in 221 BCE and fell in 206 BCE. The Han dynasty that followed kept much of its administrative machinery while making Confucian learning the official curriculum: a long-running scholarly description is "Confucian outside, Legalist inside". Zhuangzi (c. 369–286 BCE) rejected the argument everyone else was having. Rules, rituals and calculations all assume that we can step outside the flow of things and judge. His best-known piece of reasoning is a story. Walking with the logician Huizi on a bridge over the Hao river, he remarked on how happy the fish were. Huizi objected: you are not a fish, so how do you know? Zhuangzi: you are not me, so how do you know I don't know? Huizi: I am not you, so I do not know what you know, and you are not a fish, so you cannot know the fish's joy. Zhuangzi: go back to your first question. You asked how I knew, which assumed I did know. I know it from here, standing on the bridge. It is a joke, and also an argument about what "how do you know" is asking. Interactive · The joy of the fish, step by step BackNext move My paraphrase of Zhuangzi ch. 17 ("Autumn Floods"). The joke is that "how" can mean "by what method?" or "from where?"; translators and scholars still argue about which move wins. Without JavaScript: Zhuangzi says the fish are happy. Huizi: you are not a fish. Zhuangzi: you are not me. Huizi: so neither of us can know the other's mind. Zhuangzi: you asked "how do you know?", so you already took it that I knew; I know it standing on the bridge. The Daodejing, attributed to Laozi (whose historicity is unclear; the oldest excavated manuscripts, from about 300 BCE, were found at Guodian, in a different order from the received text), makes a related move in a calmer voice. Its idea of wu wei, "non-forcing", is not laziness: it is the claim that the best action responds to the situation without strain, like a skilled butcher whose knife never touches bone. The Daoist argument against Confucian virtue is that explicit moral codes only appear once natural care has been lost (Daodejing 18). Neo-Confucianism: Zhu Xi, Wang Yangming and the bamboo When Buddhism entered China (around the first century CE) it brought a metaphysics Confucian thinkers had not worked out for themselves: what the world is made of and what a self is. From about the eleventh century, Confucian philosophers answered with a metaphysics of their own, now called Neo-Confucianism. Zhu Xi (1130–1200) gave it its classic form. Everything has two aspects: li, a pattern or principle (what makes a thing the kind of thing it is, and what makes it good), and qi, the stuff the pattern is realised in. A cracked jar and a perfect one have the same li but different qi. To become wise you should "investigate things" (gewu): study texts, history and the world until the principles in them become clear to you. Zhu Xi selected and commented on the Four Books (the Analects, the Mencius, the Great Learning and the Doctrine of the Mean). From 1313 they were the core of the civil-service examinations, and they stayed there until the examinations were abolished in 1905. Wang Yangming (1472–1529) found the programme did not work, and his story is a good one. As a young man he and a friend decided to investigate the principle in the bamboo in front of the pavilion. The friend gave up on the third day, exhausted. Wang kept at it for seven, fell ill, and concluded that he lacked the ability to become a sage. Years later, exiled to the remote Longchang, he had an insight that became his philosophy: principle is not out there to be found; the mind itself is principle (xin ji li). We have an innate knowing of right and wrong (liangzhi, "good knowing"), and the work is to stop obscuring it. From that came his most quoted claim, the unity of knowledge and action: if you truly know that you should help someone, you are already helping; knowing without acting is not yet knowing. The standard objection is that this makes it hard to say anyone ever knowingly does wrong. Wang's answer is that selfish desire clouds the knowing itself. These two are still taught as a pair: Zhu Xi's cautious, reading-based inquiry against Wang's immediate moral intuition. Neo-Confucianism shaped Korea's Yi Hwang (Toegye, 1501–70) and Japan's Tokugawa-era schools as well. Indian philosophy begins with how we know: Nyāya and Dignāga Indian philosophy has an unusual feature: schools were defined by how they answered the question "what counts as a source of knowledge?" (pramāṇa). The six "orthodox" (āstika) schools are those that accept the authority of the Veda, in some sense; the Buddhist, Jain and Cārvāka schools do not, and are called nāstika. The six are not a list of religions but of research programmes: SchoolBest known for NyāyaLogic and epistemology: four sources of knowledge, and a theory of inference VaiśeṣikaCategories of what exists; atomism SāṃkhyaTwo ultimate realities: puruṣa (awareness) and prakṛti (matter and its three strands) YogaPatañjali's practical psychology, on top of Sāṃkhya's metaphysics Pūrva MīmāṃsāHow to interpret the Vedic texts; a theory of language and of duty (dharma) VedāntaThe nature of brahman and the self: non-dualist (Advaita, Śaṅkara, c. 700 CE), qualified non-dualist (Rāmānuja, 11th–12th c.), dualist (Madhva, 13th c.) Nyāya says there are four sources of knowledge: perception, inference, comparison (analogy) and testimony. Its model of inference is the five-part argument: (1) the hill has fire; (2) because it has smoke; (3) wherever there is smoke there is fire, as in a kitchen; (4) this hill has smoke of that kind; (5) therefore it has fire. The crucial element is the third: the vyāpti, the "pervasion" that links the two. This is where the fight is. How could you know that wherever there is smoke there is fire? You have not seen every case. That is the exact question the Cārvāka or Lokāyata school raised. Their texts are lost, and we know them mainly through opponents' summaries, an important caution. The position reported is that perception is the only reliable source: inference gives only probable guesses, because the universal link cannot be checked in all cases, past and future. A later sceptical text, Jayarāśi's Tattvopaplavasiṃha (around the eighth century), pushes the doubt against every source of knowledge. The Nyāya reply is that the Cārvāka also relies on inference when arguing that inference fails, and that we do establish universal links by repeated co-occurrence with attention to the absence of exceptions. It did not settle the dispute, and the problem of induction in the West is its cousin. The Buddhist logician Dignāga (c. 480–540 CE) turned this into a test that you can run. A reason (hetu) supports a conclusion only if it meets three conditions: (1) it is present in the subject (the hill); (2) it is present in at least some sapakṣa, cases which have the property to be proved (fire); (3) it is absent from all vipakṣa, cases which lack it. Crossing "present in all / some / none of the similar cases" with "present in all / some / none of the dissimilar cases" gives his nine-cell "wheel of reasons". Only two cells pass. Dharmakīrti (c. 600–660) refined the system and defined valid knowledge as "non-deceiving", that is, as guiding action without failing. Interactive · Dignāga's wheel of reasons Choose a reason, or build one. Then check which of the nine cells it lands in. In the similar cases (sapakṣa), the reason is present in In the dissimilar cases (vipakṣa), the reason is present in Assumes the reason is present in the subject. Presets follow the standard textbook examples, which assume the conclusion's opposite-class is as stated; Indian logicians argued about the examples as well as the test. Without JavaScript: a reason is good only if it appears in some similar cases and in no dissimilar ones; smoke for fire passes. "Sound is eternal because it is produced" fails because produced things are all non-eternal. Nāgārjuna: nothing has a nature of its own Nāgārjuna (c. 150–250 CE), the founder of the Madhyamaka ("Middle Way") school, wrote the Mūlamadhyamakakārikā, "Fundamental Verses on the Middle Way". Its target is the idea that things have svabhāva, an intrinsic nature that makes them what they are independent of anything else. His own position is that nothing has one. This is called emptiness (śūnyatā), and it is easily misheard: it does not mean that nothing exists. Things exist, as dependent on causes, parts and the way we name them. He says emptiness is itself dependent arising, and that it is "the middle way" (24.18). The method is a form of argument by elimination. In the first chapter he asks how a thing could arise, and lists the only options: If a thing arises from itself, it must already exist, so arising does nothing. If it arises from something wholly other, then anything could come from anything (darkness from flame). If it arises from both, it inherits both problems. If it arises from neither, it has no cause, and anything could arise anywhere at random. So nothing arises with an intrinsic nature. (What remains is conventional, dependent arising.) The four options are the catuṣkoṭi, or tetralemma. Scholars disagree about how to read it. Some say Nāgārjuna is only showing that a particular view is incoherent while holding no view himself; others, such as Jay Garfield and Graham Priest, argue that he accepts some contradictions as true. The classical objection is: "if everything is empty, so is your argument, so why should I accept it?" Nāgārjuna's reply (Vigrahavyāvartanī) is that an argument does not need intrinsic nature to work; his own claim is empty too, and that is consistent. Interactive · Four ways a thing could arise Take a sprout and a seed. Press each option to see the objection, and watch the options run out. Compressed from the first chapter of the Mūlamadhyamakakārikā and its commentaries. This is a reading; the verse itself is terse. Without JavaScript: from itself, then arising is pointless; from another, then anything from anything; from both, both faults; from neither, anything at random. So nothing arises with a nature of its own. Jain pluralism and the Cārvāka challenge The Jains, whose tradition names Mahāvīra (a contemporary of the Buddha, with dates debated, about the sixth to fifth century BCE) as its last great teacher, drew an epistemological consequence from the thought that reality is complex. Anekāntavāda, "non-one-sidedness", holds that any real thing has endless aspects and that a single statement captures only one. The story of blind men touching an elephant (told in Buddhist, Hindu and Jain sources) is the usual illustration. From it they derived syādvāda, the doctrine of "in some respect": every claim should be made relative to a standpoint. The classical form has seven statements. For a pot: in some respect it is; in some respect it is not; in some respect it both is and is not; in some respect it is inexpressible; and then the three combinations of "inexpressible" with the first three. This is not "everything is true". The "respects" are specific: the pot exists as this clay, here, now, in this shape, and does not exist as cloth, elsewhere, at another time, in another shape. Supporters (the philosopher B. K. Matilal among them) read it as a system for relativising predicates and avoiding contradictions. Critics, from Śaṅkara to Buddhist logicians, said it fails to say anything definite. It is a good test of your own view of what "contradiction" means. Interactive · "In some respect…": the pot The seven statements (saptabhaṅgī) as usually presented in textbooks; the standpoints are the Jain list of own and other substance, place, time and form. Without JavaScript: the pot is, in respect of its own clay, place, time and form; it is not, in respect of anything else; both in turn; and "inexpressible" when both are meant at once, since one word cannot say both. What a graduate just sees "Chinese philosophy" and "Indian philosophy" are not single views. They are families of schools that argued with each other. Mencius and Xunzi differ on what "nature" means before they differ on whether it is good. Mozi's impartial care and Confucian graded care are an old form of the debate between consequentialism and special obligations. A rule-based state, a virtue-based state and a free-flowing one each trade away something the others value. Whether you can know the universal link behind an inference is a question India and the West argued separately. Dignāga's test is a recognisable ancestor of testing a reason for both the cases it should cover and the ones it should exclude. Emptiness is a claim about dependence, not about nothing. A school known mainly through its opponents (Cārvāka) should be read with that in mind. Where it shows up next Ethics (36/02): care for all versus care that starts at home, virtue as cultivated skill (Xunzi, Aristotle), and Wang's claim about knowledge and action. Epistemology (36/03) and Logic & Argument (36/01): the pramāṇa list, the problem of the universal link, and a test for reasons. Philosophy of Mind (36/05): the Buddhist no-self view and the Sāṃkhya puruṣa have counterparts in debates on the self. Islamic, African & Latin American Philosophy (36/11): Indian logic and Buddhist epistemology were part of the same world of trade and translation, and similar questions about causation turn up in al-Ghazālī. In the world: Confucian ethics in East Asian families and schools, Legalist thinking in administrative design, Jain non-violence in Indian diets and law, Buddhist ideas in psychology and medicine. If you want to go deeper 📘 Textbook. Bryan W. Van Norden, Introduction to Classical Chinese Philosophy (Hackett, 2011), a clear survey that treats the thinkers as arguers; pair it with the sourcebook Philip J. Ivanhoe and Van Norden (eds.), Readings in Classical Chinese Philosophy (Hackett, 2nd ed.). For India, Mark Siderits, Buddhism as Philosophy (Hackett, 2007; 2nd ed. 2017). 📘 Gentler. Van Norden, Taking Back Philosophy: A Multicultural Manifesto (Columbia University Press, 2017), and Amartya Sen, The Argumentative Indian (2005). 🎧 Free audio. Peter Adamson's History of Philosophy Without Any Gaps (historyofphilosophy.net) has a long series on India and a sibling series on China. 🌐 Free text. The Stanford Encyclopedia of Philosophy has entries on Confucius, Mencius, Xunzi, Mozi, Han Feizi, Nāgārjuna, Dharmakīrti and Indian logic, written by specialists. 🌐 Free course. HarvardX: The Path to Happiness: What Chinese Philosophy Teaches Us About the Good Life (Michael Puett), adapted from his Harvard course on classical Chinese ethical and political theory. It is a free audit track. The takeaway China and India each built traditions of argument. Mencius and Xunzi disagreed about human nature, Mozi and the Legalists attacked partial loyalty and weak institutions from different sides, Zhu Xi and Wang Yangming split on whether principle is in the world or in the mind, Nyāya and the Cārvāka fought over the universal link in inference, Dignāga turned a reason into a test, Nāgārjuna argued that nothing arises with a nature of its own, and the Jains made relativity of standpoint into a logic. Read them as you would Plato and Hume: state the argument, then look for the weakest premise. Try this: pick one belief you hold firmly and write it as a five-part Nyāya argument (claim, reason, example, application, conclusion). Then ask whether your "wherever…" link is really true of every case. Sources & Further Reading Sources. Analects 13.18; Mencius 2A2, 2A6, 3B9, 7B2; Xunzi ch. 23 ("Human nature is bad"); Mozi chs. 17–19; Han Feizi; Zhuangzi chs. 3 and 17; Daodejing chs. 18 and 31 (Guodian manuscripts, c. 300 BCE); Zhu Xi and Wang Yangming via Chan, A Source Book in Chinese Philosophy (1963) and the Stanford Encyclopedia entries; Four Books in the examinations from 1313 to 1905. Nyāya Sūtras, Dignāga's Pramāṇasamuccaya, Dharmakīrti's Pramāṇavārttika, Jayarāśi's Tattvopaplavasiṃha; Nāgārjuna, Mūlamadhyamakakārikā chs. 1 and 24, trans. Garfield (1995); Matilal on Jain logic. Dates of ancient figures are approximate and disputed. 📘 Van Norden, Introduction to Classical Chinese Philosophy 📘 Siderits, Buddhism as Philosophy 🌐 Stanford Encyclopedia of Philosophy Step 8. Philosophy of Mind: Why There Is Something It Is Like ------------------------------------------------------------- Why: Consciousness, the mind–body problem and machine minds. A brain is wet tissue obeying chemistry, and yet it comes with a point of view. Philosophy of mind asks how those two descriptions fit together, and whether anything else, an octopus, a program, a language model, could have one. In June 2022 a Google engineer, Blake Lemoine, told his managers and then the press that the company’s chatbot LaMDA had become sentient. Google and most researchers disagreed, and he was dismissed that July. Whatever you think of his claim, notice what everyone needed in order to argue about it: some idea of what it would be for a system to have experiences, and some way to tell. We have neither agreed. That is the oldest unsolved problem in philosophy wearing a new coat. Take a simpler case. You stub your toe. A neuroscientist can describe the nerve signals, the spinal reflex and the cortical activity. None of that description contains the throb. The throb is what it is like to be you at that moment, and it is available to you in a way it is available to no one else. Philosophy of mind starts from the gap between what can be described from outside and what is lived from inside, and it asks whether the gap is real. The course in one box Who takes itPhilosophy majors, usually in year 3; cognitive-science, psychology and AI students take it as an elective or as a core course, and it is often the first philosophy course a neuroscientist or computer scientist meets. What it is forStating clearly what minds are, how they relate to bodies, and what would count as evidence that a creature or a machine has one. Comes afterMetaphysics (36/04), which supplies identity and causation, and Cognitive Psychology (35/22), which supplies what the mind does. Biological Psychology (35/20) supplies the brain. Leads toContemporary Philosophy: Analytic, Continental & Beyond (36/12), and it sits beside Philosophy of Language (36/07), since meaning and understanding are the Chinese room’s ground. What this piece gives youYou will not be able to say which theory of consciousness is true, because no one can. You will know the main positions at their strongest, the two famous thought experiments as step-by-step arguments, what the leading scientific theories claim, and a fair map of the debate about machine minds. Easier first reads: Philosophy of Mind: The Hard Problem of Consciousness (05/10) and How Large Language Models Actually Work (29/02). The mind–body problem: from Descartes to functionalism René Descartes (Meditations, 1641) argued that mind and body are two different kinds of thing: the body is extended in space and divisible, the mind is a thinking thing with no parts. The trouble came quickly. In 1643 Princess Elisabeth of Bohemia wrote to him asking how an immaterial mind could push a material body, since pushing seems to need contact. Descartes’ answer, the pineal gland, satisfied neither of them. This is the interaction problem, and it remains the standard objection to substance dualism. Dualism has serious defenders today, but they usually defend a milder claim, that mental properties are not physical ones, and they do not need a soul to push anything. The idea is not only European: Ibn Sīnā’s “flying man” (11th century), an adult floating in the void with no sensation who still knows he exists, was an early argument that the self is not the body, and the Sāṃkhya school in India separated conscious awareness (puruṣa) from matter (prakṛti). The twentieth century tried to dissolve the problem. Behaviourism (Gilbert Ryle, The Concept of Mind, 1949, mocking “the ghost in the machine”) said mental words describe dispositions to behave, not inner events. Objection: a perfect actor behaves as if in pain and isn't, and a stoic is in pain and does not show it. The identity theory (U. T. Place 1956; J. J. C. Smart 1959) said pain simply is a brain process, as lightning is an electrical discharge. Objection, from Hilary Putnam (1967): octopuses and imagined aliens seem able to feel pain with brains built differently, so pain cannot be identical to one type of human neural firing. This multiple realisability led to functionalism: a mental state is defined by what it does, its place in a web of causes and effects. A pain is whatever is caused by damage, causes distress and avoidance, and interacts with beliefs and desires in the right way. The material is irrelevant, as a clock can be brass or quartz. Functionalism is the most popular answer in the profession. In the 2020 PhilPapers survey, among philosophers who answered the question about consciousness, about a third chose functionalism, 22% dualism, 13% the identity theory, 8% panpsychism and 5% eliminativism. On the more general mind question, 52% leaned to physicalism and 32% to non-physicalism. Its critics say it leaves out the feel: two systems with the same organisation might differ in experience. The tool below shows where the theories agree and where they split. Interactive · Is it in pain? What it is made of Human neuronsOctopus neuronsSilicon chip How it behaves when injured Winces, withdraws, says “ow”Shows nothing at all How its insides are organised Same causal pattern as a pained personDifferent pattern (e.g. a giant lookup table) Each verdict applies the position’s own criterion. “Substance dualism” is silent because no outside test could show whether a non-physical mind is attached. Without JavaScript: for a silicon chip with the same causal organisation as a pained person, functionalism says it is in pain; the identity theory and biological naturalism say no; behaviourism says yes only if it behaves as if hurt; substance dualism cannot say. The easy problems and the hard one In 1995 David Chalmers separated two kinds of question. The easy problems are about what the brain does: discriminating and categorising stimuli, integrating information, reporting mental states, focusing attention, controlling behaviour, the difference between waking and sleep. They are “easy” only in that we know what a solution would look like, a mechanism, and neuroscience and psychology are finding them. They are not easy to solve. The hard problem is why any of this is accompanied by experience at all. Explain every function the brain performs and the question remains: why isn’t it all happening “in the dark”? Thomas Nagel (1974) gave the hard problem its slogan. A bat navigates by echolocation. We can learn everything about its sonar and still not know what it is like to be a bat, and Nagel argued that if there is nothing it is like, a creature is not conscious at all. Chalmers added the zombie: a being physically identical to you with no inner experience. If a zombie is even conceivable, he argued, physical facts do not by themselves settle consciousness. Among the professional philosophers surveyed in 2020, 16% called a zombie inconceivable, 37% conceivable but not metaphysically possible, and 24% possible. The replies are a map. Reductive physicalists (the “type-B” family) accept that we can conceive of zombies but say conceivability does not show possibility, as you can conceive of water without H₂O. Illusionists (Daniel Dennett, Keith Frankish) say the hard problem rests on a mistake: the brain represents itself as having ineffable inner qualities, and that representation, not a mysterious extra, is what needs explaining. Chalmers calls this the “meta-problem”. Panpsychists (Philip Goff, Galen Strawson) say experience is a basic feature of matter. Advaita Vedānta makes consciousness the basic reality, from the other side. Each pays: illusionism asks you to deny what seems most certain; panpsychism struggles with how small experiences combine; dualism has the interaction problem. Try sorting some questions yourself. Interactive · Easy problem or hard problem? Easy (mechanism)Hard (why experience?) Next question The easy items follow Chalmers’ 1995 list; the hard ones are his hard problem in different words. The score is kept on this page only. Without JavaScript: “How does the brain tell red from green?” and “How do you report what you saw?” are easy problems (mechanisms); “Why is there something it is like to see red?” is the hard problem. Mary’s room: what did she learn? Frank Jackson’s knowledge argument (1982, 1986) is the most-read thought experiment in the subject. Mary is a brilliant scientist who has lived her whole life in a black-and-white room and learned about colour through a black-and-white monitor. She knows all the physical facts about colour vision: wavelengths, retina, visual cortex, what makes people say “red”. One day she steps out and sees a ripe tomato. Jackson’s argument, in short: Before leaving, Mary knows every physical fact about colour vision. On leaving, she learns something new: what red looks like. So there was a fact she did not know, and it was not a physical fact. Physicalism is false. Philosophers have rejected each step. The ability reply (David Lewis, Laurence Nemirow): what she gains is know-how, the ability to imagine and recognise red, not a new fact. The old-fact-in-a-new-guise reply (Brian Loar, David Papineau): she meets a fact she already knew by a different, first-person concept, as one can know that Cicero was Roman and then learn Tully was. The denial of the first step (Dennett): we cannot really imagine knowing everything physical, and if we could, she would not be surprised. Dennett’s version has her shown a blue banana; she would spot the trick. Jackson himself changed his mind, arguing in the late 1990s and in 2003 that the intuition misleads and physicalism is true. Step through it below. Interactive · Mary leaves the room Which step would you reject? Step 1Step 2: nothing newStep 2: new, but not a new factAccept step 3 Without JavaScript: the argument runs from “Mary knows every physical fact” and “she learns something new on leaving” to “so there are non-physical facts”; replies deny the first premise (Dennett), say she gains only an ability (Lewis, Nemirow), or say it is an old fact met in a new way (Loar, Papineau). The Chinese room: can rules add up to understanding? John Searle’s paper “Minds, Brains, and Programs” (Behavioral and Brain Sciences, 1980) targeted a different claim: that running the right program is having a mind (“strong AI”). Imagine Searle in a room with a rulebook in English. Cards with Chinese characters arrive through a slot. The book says which cards to pass back out, by their shapes alone. To someone outside the room the replies are fluent Chinese. Searle, inside, understands none of it. He says a computer is in the same position: syntax (shapes and rules) is not enough for semantics (meaning). The replies are canonical. Systems reply: Searle does not understand, but the whole room might, as no single neuron understands English. Searle: let him memorise the book and do it all in his head; he still does not understand. Robot reply: put the program in a body that sees and acts, so the symbols are tied to the world. Searle: sensor data is more symbols. Brain-simulator reply: simulate every neuron of a Chinese speaker. Searle: a simulated storm does not make anything wet; simulating is not duplicating. Intuition reply (Dennett and others): the argument is an intuition pump, and our intuition about the room may be wrong, because a rulebook that really passed the test would be astronomically large and slow. Try the room. Interactive · Be the clerk in the room A card comes through the slot. Match its shape to the rulebook (which you cannot read as language) and pass back the card it names. Incoming card Respond to Searle SystemsRobotBrain simulatorIntuition Pick a reply to see it and Searle’s answer. The rulebook here has five entries so that you can see it; a real one would have to be astronomically bigger. Searle’s point is meant not to depend on size. The glyphs are invented stand-ins, not real writing. Without JavaScript: in the room, every step is shape-matching (“if this card, pass that card”); the question is whether adding speed, a body or a perfect brain simulation could turn that into understanding. What brains can tell us, and what they can’t The sciences in this major’s neighbours, Biological Psychology (35/20) and Cognitive Psychology (35/22), have turned the mind–body problem into an experimental one: find the neural correlates of consciousness, the minimal brain activity that goes with a given experience. Patients with “blindsight” (Weiskrantz and colleagues, 1974) point accurately at objects in a blind part of their visual field while denying they see anything, so processing and experience can come apart. Under general anaesthesia the brain remains active but experience stops. The cognitive psychology of attention and working memory, a narrow beam that only some information gets through, is where the best-known theories begin. Global workspace theory (Bernard Baars, 1988; Stanislas Dehaene and Jean-Pierre Changeux developed the neuronal version) says information becomes conscious when it wins a competition and is broadcast to many specialist systems at once. Integrated information theory (Giulio Tononi, from 2004) says consciousness is a property of any system that integrates information in the right causal way, measured by Φ, and so depends on the hardware’s physical causal structure, not just its software. Higher-order theories (David Rosenthal) say a state is conscious when the mind represents itself as being in it. Recurrent processing (Victor Lamme) says feedback loops in sensory areas are enough. These theories disagree, and in 2023 and 2025 they were tested against each other. The Cogitate consortium ran an adversarial collaboration in which global-workspace and integrated-information supporters pre-registered what each theory predicts for the same experiments. Its first results (a June 2023 preprint) satisfied none of the workspace theory’s pre-registered predictions and two of three for the information theory; the peer-reviewed version appeared in Nature on 30 April 2025. Neither theory’s predictions were fully borne out. In September 2023 a letter signed by 124 scholars called integrated information theory “pseudoscience”, which others, including the journal’s editors, thought the wrong word for an unfinished science. Read it as a field that has begun to run decisive tests and has not yet had a decisive result. Machine minds: what about large language models? Alan Turing (1950) proposed replacing “can machines think?” with a conversation test, the imitation game. The first chatbot, Joseph Weizenbaum’s ELIZA (1966), already made some users feel understood while following a few text-matching rules; Weizenbaum was alarmed. Today’s large language models (How Large Language Models Actually Work, 29/02) are trained to predict the next piece of text and then tuned to be helpful. They talk fluently about feelings. Does that tell us anything about what they are? The sceptics make four points. A system trained on human writing will produce human-sounding reports of experience whether or not it has any, so its testimony is weak evidence (Emily Bender and Alexander Koller’s 2020 “octopus test” and the 2021 “stochastic parrots” paper make versions of this). Searle’s argument says shape-processing is not meaning. Biological views, such as Anil Seth’s, tie consciousness to a living body that has something at stake. And integrated information theory says digital hardware has negligible Φ however good the software. The open-minded point to evidence and to principle. Models trained only on game moves develop internal board representations (Kenneth Li and colleagues, 2023, on Othello), so “just surface statistics” is too quick. If computational functionalism is true, substrate is irrelevant. In 2023 a team of nineteen researchers (Patrick Butlin, Robert Long and others) derived “indicator properties” from leading scientific theories and checked AI systems against them. They concluded that no current system was conscious and saw no obvious technical barrier to building one that satisfies the indicators. David Chalmers, in a 2023 essay, judged current models unlikely to be conscious but their successors a serious possibility. Jonathan Birch’s The Edge of Sentience (2024) argues for precaution under uncertainty. Everyone agrees on one distinction: intelligence (doing hard tasks), understanding and consciousness (experience) can come apart, so a yes on one is not a yes on the others. Click through the systems below to see what each theory says. Interactive · Who counts as conscious, by theory? These are the verdicts the theories imply, as their defenders state them, not findings. “Open” means the theory leaves the case undecided. Integrated information theory’s statement about digital machines is from Tononi and colleagues (2024 preprint, 2025 commentary). Without JavaScript: for a present-day chat model, computational functionalism says “open, depends on the computation”, global workspace says “unlikely as built”, integrated information theory says no on conventional hardware, and biological naturalism says no. Notice that nothing here depends on today’s models. Whatever 2026’s systems turn out to be, the argument structure is the same, and the dated reports above are where to check what has changed. What a graduate just sees The mind–body problem has a menu: dualism, behaviourism, identity theory, functionalism, illusionism, panpsychism, each with a standard objection. “Same behaviour” and “same inner state” are different claims, and a good test case separates them. Explaining what the brain does (the easy problems) is not yet explaining why it feels like anything (the hard one). Mary is a test for your own premises: which of three steps do you reject, and what does that commit you to? Passing a conversation test is evidence about behaviour; whether it is evidence about experience depends on a theory. Consciousness science now runs adversarial tests between theories, and has not yet produced a winner. Intelligence, understanding and consciousness can come apart, in machines and in animals. Where it shows up next Philosophy of Language (36/07): what understanding is, which the Chinese room is about. Contemporary Philosophy (36/12): phenomenology (Husserl, Merleau-Ponty) and Buddhist philosophy of mind approach the first-person side from other directions. Biological Psychology (35/20) and Cognitive Psychology (35/22): the experiments behind the theories. In the world: how doctors judge consciousness in patients with brain injury, whether farmed animals suffer, the ethics of AI systems, and the law’s idea of a person. If you want to go deeper 📘 Textbook. Jaegwon Kim, Philosophy of Mind (Westview, 3rd edition), is a standard undergraduate text, and Amy Kind’s Philosophy of Mind: The Basics (Routledge) is gentler. Check for the latest edition. 📘 Primary papers. Nagel, “What Is It Like to Be a Bat?” (1974); Chalmers, “Facing Up to the Problem of Consciousness” (1995); Jackson, “Epiphenomenal Qualia” (1982); Searle, “Minds, Brains, and Programs” (1980). All are short. 📘 Gentler. Anil Seth, Being You (2021), a neuroscientist’s case for consciousness as controlled hallucination; Annaka Harris, Conscious (2019), a sympathetic look at panpsychism. 🌐 Free text. The Stanford Encyclopedia of Philosophy entries on Consciousness, The Knowledge Argument, The Chinese Room Argument and Functionalism. 🌐 Free course. MIT OpenCourseWare 24.09 Minds and Machines (Fall 2011) covers dualism, functionalism, qualia and machine minds. The takeaway Philosophy of mind keeps three things apart that ordinary talk blurs: what a system does, what it is made of, and whether it feels like anything. The positions on offer (dualism, functionalism, illusionism, panpsychism) each answer one and pay on another. The same distinctions let you ask about animals and machines without settling the question in advance. Try this: next time someone says an animal or an AI “understands” or “feels” something, ask which of the three they mean (behaves as if, has the right organisation, has experience), and what would count as evidence. Sources & Further Reading Sources. Descartes, Meditations (1641) and the correspondence with Princess Elisabeth (1643); Ryle, The Concept of Mind (1949); Place (1956) and Smart (1959) on the identity theory; Putnam, “Psychological Predicates” (1967); Nagel (1974); Searle (1980); Jackson (1982, 1986, and later retraction, e.g. “Mind and Illusion”, 2003); Lewis, “What Experience Teaches” (1988); Dennett, Consciousness Explained (1991); Chalmers (1995, 1996); Frankish, “Illusionism as a Theory of Consciousness” (2016); Baars (1988); Tononi (2004); Weiskrantz et al. (1974); Turing, “Computing Machinery and Intelligence” (Mind, 1950); Weizenbaum (1966). Survey figures: 2020 PhilPapers Survey (as tabulated by LessWrong/EA Forum posts and Daily Nous; percentages are of those who answered). LaMDA and Lemoine: The Washington Post, 11 June 2022, and Wikipedia’s LaMDA article (Google dismissed him on 22 July 2022). Cogitate adversarial collaboration: Nature, 30 April 2025, and the June 2023 preprint; the 124-signatory letter was posted on PsyArXiv on 15 September 2023 (per the Wikipedia article on IIT). Butlin, Long et al., “Consciousness in Artificial Intelligence” (arXiv:2308.08708, 2023). IIT and digital hardware: Findlay, Tononi et al. (2024 preprint) and a 2025 Nature Neuroscience commentary. Li et al. (Othello-GPT, 2023); Bender and Koller (2020); Bender, Gebru et al. (2021); Mitchell and Krakauer, PNAS (2023); Chalmers, “Could a Large Language Model Be Conscious?” (2023); Birch, The Edge of Sentience (2024). Stanford Encyclopedia of Philosophy entries as linked. 📘 Nagel, “What Is It Like to Be a Bat?” 📘 Seth, Being You 🌐 Stanford Encyclopedia of Philosophy Step 9. Philosophy of Science: What Makes Science Science --------------------------------------------------------- Why: What makes science science, and how theories change. Science is the most reliable way people have found to learn about the world, and nobody has produced a rule that says exactly why. Philosophy of science is the attempt, and its best arguments are now being tested in real laboratories. One year a headline says a daily coffee protects your heart. The next, a headline says it harms it. Then a third study finds nothing. You can respond in three ways: believe the latest, believe none, or ask a better question, which is how a result should change what you think, and when a failed prediction means the theory is wrong rather than the experiment. In 1846 the French astronomer Urbain Le Verrier faced a planet, Uranus, that was not where Newton’s theory said it should be. He did not give up Newton. He proposed an unseen planet, calculated where it must be, and Johann Galle found Neptune that September within about a degree of the spot. Thirteen years later Le Verrier saw the same kind of problem in Mercury’s orbit, used the same move, and proposed a planet called Vulcan. It never existed. The problem was real, about 43 arcseconds of extra turn per century by modern measurement, and the culprit was Newton’s theory, replaced by Einstein’s general relativity in 1915. The reasoning was identical both times, and it succeeded once and failed once. No one can tell you in advance which kind of case you are in. That is the territory of philosophy of science. The course in one box Who takes itPhilosophy majors, usually in year 3; science, history-of-science and science-policy students take it as a core or elective course, and many research-methods courses borrow from it. Departments with a strong history-and-philosophy-of-science tradition, such as the LSE, Cambridge and Pittsburgh, offer whole tracks in it. What it is forUnderstanding what evidence does, how theories are tested and replaced, whether the unseen things they describe are real, and where science ends. Comes afterEpistemology (36/03): knowledge, justification and evidence. Leads toContemporary Philosophy: Analytic, Continental & Beyond (36/12). It underlies Research Methods in Psychology (35/19), Research Methods in Political Science (35/18) and Statistics (34/05), which are the working-science sides of the same questions. What this piece gives youYou will not settle any of these debates. You will have run the central arguments with numbers: the ravens, a blame-sharing calculation, a falsifier who is too strict, a base-rate objection to realism, and a replication simulator. Easier first reads: How Do We Know Anything? Hume, Popper, Kuhn and the Problem of Science (05/16), which tells the story of the thinkers, and Bayesian Thinking for Everyday Life (17/07). This piece goes further by running the arguments. Induction, the ravens and Bayes Science generalises: every raven seen so far was black, so all ravens are. David Hume (1739–48) showed that no argument, deductive or inductive, can justify that step without assuming that the future will resemble the past. The same worry was raised in India by the Cārvāka school, whose rivals report them denying that inference can give knowledge because the universal link it needs can never be checked. Nelson Goodman (1955) made it worse with “grue”: an object is grue if observed before some future date and green, or not observed before then and blue. Every emerald seen so far is both green and grue. Same evidence, different predictions after the date. Which predicates are fit for generalising is not given by logic. Carl Hempel’s ravens paradox (1945) makes the trouble concrete. “All ravens are black” is logically equivalent to “all non-black things are non-ravens”. So a white shoe, which is a non-black non-raven, seems to confirm that all ravens are black. The standard modern reply uses Bayes’ theorem: evidence confirms a hypothesis when it is more likely if the hypothesis is true than if it is false, and how much depends on that ratio. The white shoe does confirm, by a tiny amount, and a black raven confirms far more. Move the sliders to see why. Interactive · How much does each observation confirm? Prior belief that all ravens are black If the hypothesis is false, ravens that are non-black (of 100) Non-black things that are not ravens in the world A toy world: 100 ravens, and the rival hypothesis says exactly the chosen number of them are non-black. Evidence A: pick a raven at random, it is black. Evidence B: pick a non-black thing at random, it is not a raven (a white shoe). Likelihood ratio = chance of the evidence if the hypothesis is true ÷ chance if false. Without JavaScript: with 100 ravens, 10 of them non-black on the rival hypothesis, and 1,000 non-black non-ravens, a black raven multiplies the odds of “all ravens are black” by 1.11 and a white shoe by 1.01. Both confirm; the raven confirms roughly ten times more strongly. This is the Bayesian answer to induction’s problem, as far as an answer exists: evidence shifts degrees of belief, and a sampling plan (looking at ravens, or at non-black things) decides how much. Its critics point to the problem of priors. Where does the starting 50% come from? Subjective Bayesians accept any coherent prior, and argue that enough evidence washes differences out; objective Bayesians look for constraints. The next sections show how much work the priors do. Falsification, and the blame problem Karl Popper (Logik der Forschung, 1934; English edition 1959) saw that no number of black ravens proves “all ravens are black”, but one white raven refutes it. Science, he argued, proceeds by bold conjectures that make risky predictions, and its mark is that they could fail. This is falsificationism, and it is what many scientists mean when they say a claim must be testable. Popper took relativity (whose 1919 eclipse test could have refuted it) as the model, and Freud’s and Adler’s theories, which seemed able to explain any behaviour, as the foil. Pierre Duhem (1906) and W. V. O. Quine (1951) raised the obvious problem. A theory never meets the data alone. A prediction comes from the theory plus auxiliary assumptions: that the instrument works, that no unseen planet is pulling, that the sample is clean. When the prediction fails, logic says only that something in the bundle is wrong. Neptune and Vulcan are the same fork: Le Verrier blamed an auxiliary assumption both times. There is no rule of logic that says which to blame. How do scientists manage? Partly by priors: the part we trust least takes the blame. Compute it. Interactive · Who takes the blame for a failed prediction? Confidence in the main theory (Newton) Confidence in the auxiliary (“no unseen planet”) The anomaly is assumed to be 2% likely if both the theory and the auxiliary are right, and 90% likely if either is wrong. The two beliefs are treated as independent. Those likelihoods are illustrative choices, not historical numbers. Without JavaScript: with 95% confidence in the theory and 70% in the auxiliary, an anomaly leaves the theory at about 86% and drops the auxiliary to about 14%: the blame falls on the assumption you trusted least. Popper’s reply to Duhem was a decision, not a proof: scientists should adopt conventions that keep the main theory open to refutation. A second problem is that a strict falsifier can kill a true theory. Real measurements are noisy, and real tests sometimes fail for dull reasons. The tool below compares a strict rule (drop the theory at the first failed test) with a tolerant rule (drop it after more than k failures), using exact binomial arithmetic. Interactive · A falsifier who is too strict Chance a test of a true theory fails by accident Chance a test of a false theory fails Number of tests Failures tolerated before dropping the theory Tests are treated as independent, each failing with the stated chance. The numbers are illustrative. Without JavaScript: if a true theory fails 5% of tests by accident, a strict falsifier keeps it through 20 tests only about 36% of the time; tolerating two failures keeps it about 92% of the time, while a false theory that fails 40% of tests is still dropped almost every time. Kuhn, Lakatos and Feyerabend: how theories change Thomas Kuhn’s The Structure of Scientific Revolutions (1962) came from history, not logic. Most science, he said, is normal science: puzzle-solving inside a shared paradigm of theories, methods and exemplary solutions. Anomalies pile up and are mostly set aside. If enough accumulate and a rival appears, a crisis follows and sometimes a revolution, after which the field sees its subject differently. Kuhn’s claim of incommensurability, that rival paradigms cannot be fully compared point by point, is the most disputed part, and he later softened it. His real challenge to Popper is that real scientists do not drop a theory at a single failure, and that that is often rational, as the strict falsifier above shows. Imre Lakatos (1970) tried to keep Popper’s rigour with Kuhn’s history. A research programme has a hard core defended by a protective belt of adjustable assumptions. It is progressive while its changes predict novel facts that turn out true, and degenerating when it only patches after the fact. That turns Neptune (new planet, new prediction, confirmed) and Vulcan (patch, no confirmation) into different cases. His critics ask how long a programme may degenerate before it is abandoned; no deadline can be given. Paul Feyerabend (Against Method, 1975) pushed the point to “anything goes”: history shows that every rule of method has been broken to good effect, so no fixed method deserves the name. He meant that no single rule could govern all science, not that all ideas are equal. The history that these arguments draw on is global. Ibn al-Haytham’s Book of Optics (about 1011–21) tested light by designed experiments. Astronomers at the Marāgha observatory and later Ibn al-Shāṭir in Damascus (14th century) built models of planetary motion mathematically equivalent to ones Copernicus later used, and historians still debate how that knowledge travelled. Kuhn’s paradigms and Lakatos’s programmes were meant to describe such work. ThinkerCore ideaMain objection PopperScience is bold, testable conjectureDuhem: tests are of bundles; strictness kills good theories KuhnNormal science, anomalies, revolutionsRelativism; vague “paradigm” LakatosProgrammes are progressive or degeneratingNo deadline for judging FeyerabendNo single method fits all scienceSeems to leave no standard Realism or anti-realism? Does a successful theory describe the world, including things we cannot see (electrons, quarks, genes), or only help us predict what we can? Scientific realists give the “no miracles” argument (Hilary Putnam, 1975): the success of science would be a miracle if its theories were not at least approximately true. Anti-realists reply with the pessimistic induction (Larry Laudan, 1981): the history of science is full of successful theories, such as caloric, phlogiston and the luminiferous ether, that were later rejected as not referring to anything real. Bas van Fraassen’s constructive empiricism (The Scientific Image, 1980) says science aims only at theories that are empirically adequate, and accepting one does not require believing in unobservables. Structural realists (John Worrall, 1989) look for a compromise: what survives theory change is mathematical structure, as Fresnel’s equations for reflected light survived the fall of the elastic ether into Maxwell’s theory. In the PhilPapers survey of 2009, about three quarters of professional philosophers (75.1%) accepted or leaned to scientific realism and 11.6% to anti-realism; the 2020 survey asked again, and its figure for this question is not given here. A neat objection to the no-miracles argument is that it ignores base rates. Success is a likely result of truth, but if most theories are false the posterior can still be low, which is the logic of a medical test with many false positives. Try it. Interactive · The no-miracles argument and the base rate Share of theories that are approximately true Chance a true theory is successful Chance a false theory is successful This is the base-rate objection (Howson 2000; Magnus and Callender 2004) in its simplest form. Realists reply that “success” means precise novel predictions, which false theories almost never make, so the third slider should be near zero. Without JavaScript: if 10% of theories are true, true ones succeed 95% of the time and false ones 10%, a successful theory is true with probability about 51%; if false theories succeed only 1% of the time, it rises to about 91%. What counts as science? The demarcation problem Popper’s falsifiability was a criterion of demarcation: a line between science and pseudo-science. Courts have wanted such a line. In McLean v. Arkansas (1982) Judge William Overton listed essential characteristics of science, including being guided by natural law and testable. In Kitzmiller v. Dover Area School District (2005) Judge John E. Jones III ruled that intelligent design is not science and cannot be taught as such in US public-school science classes. Philosophers have been less sure that one criterion works. Laudan (1983) called the problem dead: any proposed mark, falsifiability, testability, or being supported by evidence, either excludes real science or includes junk, since astrology makes testable claims that were tested and failed. Paul Thagard (1978) proposed instead that astrology is unscientific because it has been stagnant for centuries and its practitioners do not try to explain its failures, which is Lakatos’s degeneration under another name. Most philosophers now treat science as a cluster of features, which family-resemble one another without any one being necessary: public evidence, error-correction, openness to criticism, a track record of novel predictions, and a community that checks its own work. This is less tidy than a single test. It also describes the working lesson better, which is that you judge a field by how it behaves when it is wrong. That leads straight to the live case. A live case: the replication crisis Every argument above is now being tested on psychology, medicine and economics. How Do We Know Anything? (05/16) tells the story and gives the main replication table; here are the numbers that bear on the philosophy. In 2015 the Reproducibility Project: Psychology tried to repeat 100 studies: 97 of the originals had significant results, 36% of the repeats did, and the effects were about half as large. In 2018 a project on 28 findings across 60 labs found about half failed. In a 2016 survey by Nature of 1,576 researchers, more than 70% had failed to reproduce another scientist’s results and more than half their own. In medicine, a 2012 report from the company Amgen said only 6 of 53 landmark preclinical cancer studies (11%) could be confirmed, and the Reproducibility Project: Cancer Biology (2021) found effect sizes about 85% smaller than the originals where experiments could be redone. The philosophy shows in the diagnosis. John Ioannidis’s 2005 paper “Why Most Published Research Findings Are False” is Bayes at work: the chance that a significant result is true depends on how plausible the hypothesis was, on statistical power, and on how many ways the data were analysed. Duhem appears when failed replications are blamed on hidden moderators. Kuhn appears in the incentives: journals rewarded novel, positive results. In 2021 Anne Scheel and colleagues found 96% of hypotheses in a random sample of standard psychology papers came out positive, against 44% in Registered Reports, where the method is accepted before the data exist. Play with the base-rate arithmetic yourself. Interactive · How many “findings” are true? Share of tested hypotheses that are true Statistical power (chance to detect a true effect) Analyses tried before reporting the best p < 0.05p < 0.005 Expected counts for 1,000 tested hypotheses, with independent analyses; the chance that at least one of k analyses of a false hypothesis passes is 1 − (1 − α)k. The “replication” line assumes repeats of 80% power at p < 0.05. Numbers are illustrative, not an estimate for any field. Whether to lower the threshold to 0.005 is argued: Benjamin and colleagues proposed it in 2018, and Lakens and colleagues replied that each field should justify its own threshold. Without JavaScript: if 10% of hypotheses are true, power is 35% and α is 0.05, then of 1,000 hypotheses about 35 true and 45 false ones come out significant, so only about 44% of significant results are true; with ten analyses tried per false hypothesis, only about 9% are. What has changed since: preregistration, Registered Reports, larger samples, open data and code, and a research field, metascience, that studies science itself. The crisis is a reason to ask how a result was obtained, not to give up on science. In that it is Popper’s point in practice: a community that finds and publishes its own failures is behaving as one that can learn. What a graduate just sees Induction cannot be proved, and “which predicate to generalise” (green or grue) is part of the problem. A white shoe does confirm “all ravens are black”, by a tiny amount; how much depends on how the evidence was sampled. A failed prediction blames a bundle, and the blame falls on whichever part you trusted least. A strict rule for dropping theories would have dropped many true ones. Anomalies are normal; the question is whether the programme is predicting new things or only patching. A theory’s success is evidence of truth only given a base rate of true theories, which is why realists stress novel predictions. There is no single mark of science; judge a field by how it handles being wrong. A significant result is a probability statement whose meaning depends on priors, power and how many analyses were run. Where it shows up next Research Methods in Psychology (35/19) and Statistics (34/05): significance, power and preregistration are the working side of Bayes and Popper. Philosophy of Mind (36/05): the theories of consciousness are being tested by adversarial collaborations, a method straight from this debate. Contemporary Philosophy (36/12): social epistemology, feminist philosophy of science and the sociology of knowledge. In the world: evidence-based medicine and regulation, science journalism, climate and public-health communication, and court rulings on expert evidence. If you want to go deeper 📘 Textbook. Peter Godfrey-Smith, Theory and Reality (University of Chicago Press, 2003), is the widely used survey; A. F. Chalmers, What Is This Thing Called Science? (Hackett, 4th edition 2013) is a clear classic. 📘 Primary texts. Popper, The Logic of Scientific Discovery; Kuhn, The Structure of Scientific Revolutions (50th anniversary edition 2012); Feyerabend, Against Method. Ioannidis (2005) is free to read online. 📘 Gentler. Samir Okasha, Philosophy of Science: A Very Short Introduction (Oxford, 2nd edition 2016); Stuart Ritchie, Science Fictions (2020), on the replication crisis. 🌐 Free text. The Stanford Encyclopedia of Philosophy entries on The Problem of Induction, Karl Popper, Imre Lakatos, Scientific Realism and Science and Pseudo-Science. 🌐 Free course. The University of Edinburgh’s Philosophy and the Sciences: Introduction to the Philosophy of Physical Sciences (Coursera, with Michela Massimi and colleagues) opens with scientific knowledge, method and underdetermination, then applies them to cosmology; check the enrolment options for a free route. MIT OpenCourseWare 24.09 Minds and Machines is a good companion on the mind side (36/05). The takeaway Science works without a proof that it should. Evidence moves belief by an amount that depends on priors; a failed prediction implicates a bundle; theories are dropped when a rival is progressing, not at a single failure; and a field is scientific to the extent that it finds and fixes its own mistakes. The replication crisis is those lessons arriving in practice. Try this: the next time a headline reports a new finding, ask three things: how plausible was it before, how big and how many were the studies, and has anyone repeated it. Sources & Further Reading Sources. Hume, Treatise (1739) and Enquiry (1748); Hempel, “Studies in the Logic of Confirmation” (Mind, 1945); Goodman, Fact, Fiction, and Forecast (1955); Popper, Logik der Forschung (1934); Duhem, La théorie physique (1906); Quine, “Two Dogmas of Empiricism” (1951); Kuhn (1962); Lakatos, in Lakatos and Musgrave (eds.), Criticism and the Growth of Knowledge (1970); Feyerabend (1975); Putnam, Mathematics, Matter and Method (1975); van Fraassen (1980); Laudan, “A Confutation of Convergent Realism” (1981) and “The Demise of the Demarcation Problem” (1983); Worrall (1989); Thagard, “Why Astrology Is a Pseudoscience” (1978); Howson (2000); Magnus and Callender (2004). Neptune and Vulcan: Le Verrier 1846 and 1859; Galle’s observation of 23 September 1846; Mercury’s anomaly about 43 arcseconds per century (modern value). Survey: Bourget and Chalmers, “What Do Philosophers Believe?” (2014; the 2009 survey: scientific realism 75.1%, anti-realism 11.6%). Replication: Open Science Collaboration, Science (2015); Klein et al., Many Labs 2 (2018); Baker, Nature (2016; 1,576 researchers); Begley and Ellis, Nature (2012); Errington et al., Reproducibility Project: Cancer Biology (eLife, 2021; effects about 85% smaller, per Wikipedia’s summary); Ioannidis, PLoS Medicine (2005); Scheel, Schijen and Lakens, Advances in Methods and Practices in Psychological Science (2021; 96% v. 44%); Benjamin et al., Nature Human Behaviour (2018); Lakens et al. (2018). McLean v. Arkansas (E.D. Ark. 1982); Kitzmiller v. Dover (M.D. Pa. 2005). Stanford Encyclopedia of Philosophy entries as linked. 📘 Godfrey-Smith, Theory and Reality 📘 Kuhn, The Structure of Scientific Revolutions 🌐 Stanford Encyclopedia of Philosophy Step 10. Philosophy of Language: What Words Mean and What They Do ----------------------------------------------------------------- Why: Meaning, reference and what words do. "The Morning Star is the Evening Star" told astronomers something. "The Morning Star is the Morning Star" told them nothing. Yet both name the same planet. A century of philosophy grew from that puzzle, and from the stranger fact that we mean far more than we say. Someone asks, "Can you pass the salt?" and you do not answer "Yes." Someone says, "Some of the students passed," and you hear that not all did, although nobody said so. A friend says, "Great weather," in a storm, and you hear the opposite. In each case the words on the page are not what is communicated, and in each case you got it right without thinking. Philosophy of language asks how that is possible. How can a sound or a mark be about something? Why can a true statement be informative or empty depending on which name you use? What are we doing when we promise, or name a ship, or say "I do"? The questions are old, but the modern subject begins in the 1890s with Gottlob Frege, and the tools it built (sense, reference, presupposition, rigid designation, implicature) are now used in linguistics, law, computer science and the study of language models. The course in one box Who takes itPhilosophy majors, usually in year 3, at programmes in the analytic tradition (MIT's philosophy department, for one, teaches it as 24.251). Linguistics majors take its formal cousin, semantics and pragmatics, and it sits on both routes. What it is forSeeing exactly what a sentence says, what its speaker meant, and what each of them has to do with the world. Comes afterLogic & Argument (36/01), for the quantifiers and the idea of validity. Leads toSemantics & Pragmatics (36/24), the linguist's version; Philosophy of Mind (36/05), where meaning and thought are one question; Contemporary Philosophy (36/12); and Computational Linguistics (36/30), where "meaning" meets statistics. What this piece gives youYou will not be able to defend a theory of reference in a seminar. You will know the six or seven moves that every such theory is built from, why each was made, and what its critics say. Easier first reads: How Children Learn Language (26/06) and How Language Changes (26/05). Sense and reference: Frege and the two stars The obvious theory says a name means the thing it names. "Venus" means Venus. Then "Hesperus" (the evening star) and "Phosphorus" (the morning star) mean the same thing, because both are Venus, and the sentence "Hesperus is Phosphorus" should say no more than "Venus is Venus." But the first was a discovery, and the second is a triviality. In "Über Sinn und Bedeutung" (1892) Frege put it plainly: statements of the form a = a and a = b differ in what they tell you. His answer is that an expression has two things attached. Its reference is the object it picks out. Its sense is the way it picks it out, the route by which a thinker gets to the object. "The bright point at dawn" and "the bright point at dusk" are two routes to one planet. Frege then did the same for whole sentences: the sense of a sentence is the thought it expresses, and its reference is its truth-value. That explains why swapping co-referring names keeps a sentence true (the reference is unchanged), yet can change what a thinker believes (the sense is changed). sense → referencesense is the route; reference is where the route ends. Two routes can end at one place. Interactive · Which identity teaches you something? Pick the left-hand and right-hand expression of "A is B". A B Reference: Venus is the planet seen both at dawn and dusk; the Moon is a separate body. The verdict follows Frege's test (cognitive value), not a full theory. Without JavaScript: "The Morning Star is the Evening Star" is true and informative (one reference, two senses); "The Morning Star is the Morning Star" is true and trivial; "The Morning Star is the Moon" is informative and false. Sense does extra work. Ancient sailors did not know that the two stars were one, so "the sailors believed the Morning Star rose at dawn" is true while "the sailors believed Venus rose at dawn and again at dusk" may not be. Frege said that inside a belief report an expression refers to its usual sense, not to its usual object. Critics found this heavy, and the next two sections are attempts to do without it. Descriptions: Russell and the king of France Bertrand Russell's "On Denoting" (1905) attacked a different puzzle. Take "The present King of France is bald." France has no king. If the phrase must refer to something for the sentence to mean anything, the sentence is meaningless. But it is not: it is plainly false, or so Russell thought. His fix was to say that "the F is G" is not a subject and predicate at all. It is a hidden claim in three parts: there is an F  ·  there is only one F  ·  it is G"The King of France is bald" is false because the first part fails. This also exposes an ambiguity. "The King of France is not bald" can deny the whole claim (true: there is no such king) or say of the king that he lacks hair-loss (false: there is no king). Logicians call this a difference of scope. Peter Strawson replied in "On Referring" (1950) that the sentence has a presupposition, that there is a king, and when that fails the sentence is neither true nor false. Keith Donnellan (1966) added that "the man drinking a martini" can pick out a particular man even if he is drinking water, which Russell's account does not allow. Play with the scenarios below. Interactive · Who is right about the king? Computed from Russell's three clauses for "the King is bald". Strawson's column gives "no truth-value" whenever there is not exactly one king. Without JavaScript: with no king, Russell makes "the King is bald" false and "it is not the case that the King is bald" true; Strawson makes both lack a truth-value. Names: Kripke and the rigid designator Russell extended his analysis to ordinary names: "Aristotle" is short for a description such as "the teacher of Alexander". Frege agreed on something like it. In three lectures at Princeton in January 1970, later the book Naming and Necessity (1980), Saul Kripke argued that this is wrong. His arguments, in order: Modal. Aristotle might never have taught Alexander (his father was a court physician; he might have become one). If "Aristotle" meant "the teacher of Alexander", "Aristotle taught Alexander" would be necessary. It is not. A name is a rigid designator: it picks the same person in every possible world, while a description picks whoever fits in each. Epistemic. Most of us know little that is uniquely true of the people we name, and we still refer to them. Semantic. Suppose "Gödel" is associated only with "proved incompleteness", and the proof was actually done by a man called Schmidt. A description theory says that you are talking about Schmidt. Almost no one thinks so (Kripke's case is hypothetical; Gödel's proof was his own). Interactive · Names and descriptions across possible worlds Three invented worlds, labelled as such: in w1 Aristotle became a physician and Isocrates tutored Alexander; in w2 Alexander had no tutor. Everything outside w0 is a thought experiment. Without JavaScript: "Aristotle" picks Aristotle in every world; "the tutor of Alexander" picks Aristotle in w0, Isocrates in w1 and nobody in w2. So "Aristotle tutored Alexander" is true in w0 only, while "the tutor of Alexander tutored Alexander" is true in all three. What fixes reference instead? Kripke's picture is causal-historical: a baptism ties a name to a person, and each speaker who hears it and means to use it as others do passes the link along. Predict first, then look. Interactive · Predict, then reveal Suppose the only thing you know about "Gödel" is that he proved the incompleteness theorem, and (contrary to fact) Schmidt had proved it. Who are you talking about when you say "Gödel was a genius"? Schmidt, the man who fits the descriptionGödel, the man at the other end of the chain Pick one, then read the answer. Without JavaScript: the description theory says Schmidt; Kripke says Gödel, because your use of the name is linked back to Gödel by a chain of speakers. The critics have good cases. Gareth Evans (1973) noted that "Madagascar" began as a name of part of the African mainland and came, through a chain of speakers' mistakes, to name the island, so the chain alone can't be all of it. And Kripke left an old puzzle open: if a name just stands for its bearer, why is "Hesperus is Phosphorus" informative? Defenders of the Millian view reply with pragmatics; Fregeans keep sense. The PhilPapers Survey of 2020 asked professionals exactly this ("Proper names: Millian or Fregean?"); see its results page for the split, which I do not reprint here. Meaning as use: Wittgenstein's two philosophies Ludwig Wittgenstein held both a view of language and its sharpest critique. The Tractatus Logico-Philosophicus (German 1921, English 1922) said that a sentence is a picture of a possible fact, names stand for simple objects, and what can't be pictured can't be said. "The limits of my language mean the limits of my world."Wittgenstein, Tractatus 5.6, C. K. Ogden's 1922 translation Later he rejected the picture. Philosophical Investigations (published 1953, after his death in 1951) starts with a scene: a builder calls "Slab!" and an assistant brings a slab. Here a word is not a label for a thing; it is a move in a language-game, tied to what people do. For a large class of cases, he wrote, the meaning of a word is its use in the language (section 43). He also argued that "game" has no single feature common to all games, only overlapping family resemblances (section 66), and that a language only one person could ever understand is incoherent (the private language argument, from about section 243). Each claim has opponents, and the last has produced shelves of books. What most readers keep is a change of question: not "what does this word stand for?" but "what are people doing with it?" Doing things with words: Austin and Searle J. L. Austin's William James Lectures at Harvard in 1955, published in 1962 as How to Do Things with Words, began with an observation. Some sentences are not true or false; saying them does something. "I name this ship," "I promise," "I bet you," "I do." Austin called these performatives, and noticed that they can go wrong in different ways from statements. They can be unhappy rather than false. Each needs a recognised procedure, the right people in the right circumstances, correct execution, and (for some) sincerity. The tool below lets you break them. Interactive · "I now pronounce you married" Speaker has the authority The couple are eligible and willing It is a stage play Speaker means it Austin's categories: misfire (a condition on the procedure fails, so the act is void) and abuse (the act is done but insincerely). Stage use he called "etiolated". Marriage law differs by country; this is Austin's idea, not a legal test. Without JavaScript: if the speaker has no authority the act misfires and no marriage results; if everything is in order but the speaker is insincere the marriage still happens (an abuse); on stage nothing is done. Austin's second step was to say that every utterance is several acts at once: the locutionary act (uttering words with a sense), the illocutionary act (what you do in saying it: warn, ask, order) and the perlocutionary act (what you bring about by it: scare, persuade). "There's a bull in that field" can be a warning, whether or not it frightens anyone. John Searle's Speech Acts (1969) developed rules for them, and his later scheme sorts illocutions into five kinds: assertives, directives, commissives, expressives and declarations. "Can you pass the salt?" is the case that shows why this matters: it is literally a question about ability, and in practice a request. What you mean beyond what you say: Grice Paul Grice, in the William James Lectures of 1967 (the essay "Logic and Conversation" appeared in 1975), explained the salt case with one idea. Conversation is cooperative, and we assume a speaker is following four maxims: say as much as is needed (Quantity), say what you believe true (Quality), be relevant (Relation), be clear and orderly (Manner). When a speaker visibly breaks one, we infer that something else is meant: an implicature. A reference letter that praises a student's handwriting and nothing else says very little; the hearer concludes there is nothing good to say. Sort the cases yourself. Interactive · Which maxim is being flouted? Pick a maxim. Next case Invented cases in the spirit of Grice's. Score is kept on this page only. Without JavaScript: the vague letter flouts Quantity; "Great weather!" in a storm flouts Quality; a reply that seems off-topic flouts Relation; an absurdly roundabout phrase flouts Manner. Implicatures differ from what a sentence strictly entails by a test. They can be cancelled: "Some of the students passed; in fact all did" is not a contradiction, so "not all" was never part of the meaning of "some", only something we read in. Rivals disagree on how many maxims there are. Dan Sperber and Deirdre Wilson's relevance theory (1986) reduces them to a single principle of relevance, and the neo-Griceans (Larry Horn, Stephen Levinson) keep a short list. India's argument about words: Nyāya, Mīmāṃsā and Buddhist apoha None of this was invented only in Europe. Indian philosophers argued about meaning for well over a thousand years, often more precisely than the West did for most of that time. The main schools were the Nyāya logicians (the Nyāya Sūtra, compiled in the early centuries CE), the Mīmāṃsā interpreters of the Vedic texts (Jaimini's Sūtra, with Śabara, and later Kumārila Bhaṭṭa and Prabhākara, about the 7th century CE), the Buddhist logicians Dignāga and Dharmakīrti, and the grammarians led by Bhartṛhari. Four debates are worth knowing. What does a word denote? The Nyāya answer, in the Sūtra: a word denotes an individual together with its form and its universal (a cow, the shape of a cow, cowness). Others stressed the universal alone; Buddhists denied universals exist. Where does word-meaning come from? Mīmāṃsā held that the link between word and meaning is eternal and not made by anyone; this protected the Veda as authorless. Nyāya held that it is conventional, set by divine will (the later Navya-Nyāya school, from Gaṅgeśa in the 14th century, kept and refined that view). How do we learn it? By watching elders. If one elder says "Bring the cow" and another does it, a child links the words to the act, then isolates "cow" by changing one word. Many scholars note the likeness to Wittgenstein's builders; it is an echo, not an influence. Do words mean on their own, or only in sentences? Kumārila: words first denote their meanings, then the sentence's meaning is put together from them. Prabhākara: words convey meanings only as already related, which he took to be what children learn from commands. Bhartṛhari went further: the sentence is a whole (sphoṭa), understood in a flash. The Buddhist apoha theory says a word like "cow" works by excluding what is not a cow, so it needs no real universals. Nyāya textbooks also list conditions for a string of words to give an understood sentence: ākāṅkṣā (expectancy: the words need each other to complete a sense), yogyatā (compatibility: the meanings can sensibly combine) and sannidhi (proximity: said together, not hours apart). This is a surprisingly modern checklist, and you can run it. Interactive · Does this string become a sentence? The "sprinkles with fire" example is the standard classical illustration of failed compatibility. The verdicts are the traditional ones, applied to simple examples. Without JavaScript: "Bring the cow" meets all three; a bare list of nouns lacks expectancy; "he sprinkles with fire" lacks compatibility; words said an hour apart lack proximity. What a graduate just sees Two expressions can refer to the same thing and still not mean the same, and the proof is that one identity is news and the other is not. A sentence that sounds like it is about someone may secretly be a claim that "there is exactly one such person", and where "not" goes can change the truth. A name is not a hidden description; it is a tag that stays on the person across the ways things could have gone. Ask what people are doing with a word before asking what it stands for. Some sentences are acts: they can misfire without being false. What is meant often outruns what is said, and the extra can be cancelled, which shows it was never part of the sentence. The theory of meaning has been argued across traditions, and the Indian debates are not footnotes. Where it shows up next Semantics & Pragmatics (36/24): the linguist's formal versions of sense, scope, presupposition and implicature. Philosophy of Mind (36/05): whether thoughts are meaningful in the way words are, and what a machine that handles words understands. Computational Linguistics (36/30) and How Large Language Models Actually Work (29/02): models learn meaning as use, in Wittgenstein's sense, and whether that is all of meaning is exactly the debate above. In the world: contracts and statutes (a promise is an act; "the" in a statute may bring a presupposition); advertising and politics (implicature lets a speaker mislead while saying only true things); and courtroom questions about what a defendant "meant". If you want to go deeper 📘 Textbook. William Lycan, Philosophy of Language: A Contemporary Introduction (Routledge, 3rd edition, 2019), clear and organised by problem; Alex Miller, Philosophy of Language (Routledge, also in later editions), similar in range. Check the current edition. 📘 Primary and gentler. Bertrand Russell's The Problems of Philosophy (1912), chapter 5, free at Project Gutenberg, for the idea of knowledge by description; then Saul Kripke, Naming and Necessity (Harvard University Press, 1980), which is short and readable. 📘 India. Bimal Krishna Matilal, The Word and the World: India's Contribution to the Study of Language (Oxford University Press, 1990). 🌐 Free course. MIT OpenCourseWare 24.251 Introduction to Philosophy of Language (Fall 2011), with lecture notes. The Stanford Encyclopedia of Philosophy has free entries on descriptions, implicature and speech acts. The takeaway Words have a route (sense) and a destination (reference); sentences can hide structure; names tag people rather than describe them; words are moves in activities; some utterances are acts; and speakers mean more than they say. Each of these was introduced to solve a particular puzzle, and each still has live critics. Indian philosophers worked on the same puzzles from different starting points. Try this: for one day, catch three things people communicate without saying them (a reply that skips the question, a "fine", a "some"), and name the maxim that makes you hear it. Sources & Further Reading Sources. Frege, "Über Sinn und Bedeutung" (1892); Russell, "On Denoting", Mind 1905; Strawson, "On Referring", Mind 1950; Donnellan, "Reference and Definite Descriptions", Philosophical Review 1966; Kripke, Naming and Necessity (lectures January 1970; book 1980); Evans, "The Causal Theory of Names", 1973; Wittgenstein, Tractatus (1921; Ogden 1922) and Philosophical Investigations (1953); Austin, How to Do Things with Words (lectures 1955; book 1962); Searle, Speech Acts (1969); Grice, "Logic and Conversation" (William James Lectures 1967; published 1975); Sperber and Wilson, Relevance (1986); Stanford Encyclopedia of Philosophy entries on these topics; Matilal (1990) for the Indian theories. The PhilPapers Survey 2020 (philpapers.org) asks about proper names. 📘 Lycan, Philosophy of Language 📘 Kripke, Naming and Necessity 🌐 MIT OCW 24.251 Step 11. Islamic, African & Latin American Philosophy: Arguments With the Ancients and With Power ------------------------------------------------------------------------------------------------- Why: Falsafa, African and Latin American philosophy. A philosopher in Baghdad asks what is left of you when your senses are gone. One in Córdoba defends reason against the man who said fire does not burn. One in a Mexican convent asks to be allowed to read. These are three traditions that were pushed to the edge of the standard syllabus, and they ask questions every course asks. In the 1090s, in Baghdad, a man at the peak of his career wrote a book against philosophers. Al-Ghazālī held the leading teaching post of his day. He accused the Greek-trained thinkers of his own world of three errors serious enough to count as unbelief, and he chose his examples so that you could test them in a kitchen: the cotton and the flame. Everyone says the fire burns the cotton. What have you actually seen? About eighty-five years later, a judge in Córdoba, Ibn Rushd, wrote the reply. A few centuries after that, in Mexico City's convent of San Jerónimo, Sor Juana wrote a letter defending a woman's right to study. In 1550 in Valladolid, in Spain, two men argued before judges over whether the people of the Americas were "natural slaves". In the Ethiopian highlands, a man who had fled persecution and hidden in a cave reasoned his way to a God of reason and to the equality of all people. This piece follows the arguments, not the biographies. It also tries to be fair to religion: several of these thinkers were devout, some were charged with unbelief, and their reasoning does not depend on whether you share their faith. The course in one box Who takes itPhilosophy majors, usually in year 3, as an option or part of a "world philosophy" strand. Islamic philosophy is taught in philosophy and Middle Eastern studies departments; African philosophy is a core field in universities in Ghana, Kenya, South Africa and Nigeria; Latin American philosophy is a standard field in Mexico, Argentina, Brazil and Colombia and a growing one elsewhere. What it is forHearing the philosophical conversation as it actually happened: with its sources, translators, objections and political stakes, in more than one language and continent. Comes afterAncient & Medieval Philosophy (36/08), since falsafa continues Aristotle and Neoplatonism. Leads toContemporary Philosophy (36/12), and it feeds Metaphysics (36/04), Epistemology (36/03), Ethics (36/02) and the political subjects of the major (35/12, Political Theory). What this piece gives youYou will not read Arabic, Ge'ez or Akan afterwards. You will be able to state six arguments in their strongest form and say what each is up against. Easier first reads: Islam: From Mecca to Two Billion People in Religions in Depth (33/09, Part 9 on law, theology and philosophy), The Good Life Across Traditions (05/14), and How Do We Know Anything? (05/16). This piece goes into the arguments those pages only name. Falsafa: Ibn Sīnā and the man who floats In the ninth century the Abbasid court in Baghdad paid for a vast translation of Greek science and philosophy into Arabic. Out of it came falsafa, the Arabic word for philosophy in the Greek manner, as distinct from kalām, the dialectical theology that defended Islamic doctrine by argument. Al-Kindī (c. 801–873) is called the first philosopher of the Arabs; he argued that the world cannot have existed for an infinite past, because an actual infinity cannot be completed by successive addition. Al-Fārābī (c. 872–950), known as the "Second Teacher" after Aristotle, built on logic and wrote on the ideal city and on how a prophet and a philosopher can both grasp truth. The most original of them is Ibn Sīnā, known in Latin as Avicenna (980–1037). He is famous for medicine (the Canon, finished around 1025) and for two arguments. The first is the "flying" or "floating man", a thought experiment about the soul. Imagine you are created fully formed, suspended in empty air, eyes covered, limbs apart so that you touch nothing and feel nothing. The floating person would still be aware that she exists. She would not be aware of having a body: she senses none. What you are aware of and what you are not aware of cannot be the same thing. So the self is something other than the body. The step doing the work is 3, and objectors go for it. That I can conceive of myself without a body does not show that I could exist without one (a person can think of water without thinking of H₂O). Avicenna replied that the experiment is meant to make you notice a direct self-awareness that does not come through the senses, not to run a proof. Descartes's "I think" argument came six centuries later, and whether Avicenna influenced it is debated. Interactive · The floating man, one step at a time BackNext step A paraphrase of the argument in Avicenna's Kitāb al-Shifā' ("The Healing"), On the Soul, with the standard objection and reply added. Without JavaScript: imagine a person made fully formed, floating with no sensation. She would still be aware of herself, though not of any body, so (says Avicenna) the self is not the body. Objection: being able to conceive it does not show it could happen. His second argument concerns God, and it is a good example of how an argument can be examined without anyone's faith being the test. Avicenna separates a thing's essence (what it is) from its existence (that it is). For anything whose essence does not include existence, existence has to come from something else. A chain of such things must end in a being whose essence is its existence, which he calls the Necessary Existent. Critics ask why the chain must end, whether "existence" is the kind of property that can be part of an essence at all, and whether such a being must be a god or a person. Believers reply that the argument gets the structure of the world right, and defenders and critics alike still use it as a model of how a metaphysical argument is built. Al-Ghazālī: does fire really burn the cotton? Al-Ghazālī (1058–1111) taught at the Niẓāmiyya in Baghdad, then went through a crisis in 1095, left his post and travelled, and came back to write. His Incoherence of the Philosophers (Tahāfut al-falāsifa, c. 1095) attacks the philosophers, mainly Avicenna and al-Fārābī, on twenty points. Three, he said, put them beyond the pale: that the world is eternal, that God knows only universals and not particulars, and that bodies will not be resurrected. On the rest he thought they were wrong but not unbelievers. The part that interests philosophers today is the seventeenth discussion, on causation. The philosophers held that causes necessitate their effects: the fire's nature makes the cotton burn. Al-Ghazālī's argument is about evidence: What we observe is that the cotton burns when it meets the fire, and that this happens every time. We do not observe a "making" that connects them. We see one event after the other, "with" it, not "by" it. So observation does not show that fire necessitates burning. Therefore the claim of necessary causation goes beyond what we know. Al-Ghazālī adds that God can do what He wills, so a miracle (Abraham in the fire) is possible. His own positive view is close to occasionalism, the Ash'arite kalām position that God directly brings about every event on the occasion of the preceding one. This is not a scientific scepticism: it protects the possibility of miracles. But the argument stands apart from the use he made of it. In 1739 David Hume made a similar point about "constant conjunction" from the opposite direction, to cast doubt on our grip on necessity, with no God in the picture. Whether Hume knew of al-Ghazālī is not established. Interactive · Why did the cotton burn? Four positions on one scene. The fourth (Ibn Rushd) is taken up in the next section. Without JavaScript: we observe cotton burning after contact with fire (Ghazālī: "with", not "by"). He concludes necessity is not shown; God can act otherwise. Hume (1739): we see conjunction, not necessity. Ibn Rushd: denying that natures cause their effects destroys knowledge. Al-Ghazālī also gave a famous argument for God's existence, the kalām cosmological argument: whatever begins to exist has a cause; the world began to exist; so the world has a cause. Both premises are disputed. Some philosophers and physicists question whether the first premise applies to the universe as a whole; others question whether the universe had a beginning in the relevant sense, or whether an infinite past is impossible; and many theists think the argument works while others prefer different ones. Present-day philosophers of religion still debate it with the same premises. Ibn Rushd: can reason and revelation disagree? Ibn Rushd (Averroes, 1126–1198) was a judge in Córdoba and Seville, a physician, and the author of commentaries on Aristotle so thorough that Latin scholars called him simply "the Commentator". He answered al-Ghazālī twice. In the Decisive Treatise (Faṣl al-maqāl, c. 1179–80) he asked whether philosophy is permitted by Islamic law. His argument: The Qur'an repeatedly urges people to reflect on the world and its structure. The best reflection is demonstration, as in philosophy. Truth does not contradict truth, so a demonstrated conclusion cannot truly conflict with revelation. Where a text seems to conflict with a demonstration, the text is to be read allegorically (ta'wīl). But only those trained in demonstration should do so; the public should receive teaching in simpler forms. Premises 4 and 5 are the contested ones, and Ibn Rushd's "elitism" is a fair criticism, as is the question of who decides when a text is to be read allegorically. He is often said to have taught a "double truth", one for philosophers and one for the people. He did not: the doctrine was attributed to thirteenth-century Latin "Averroists" at the University of Paris and condemned in 1277. His claim was that there is one truth with more than one way of reaching it. In the Incoherence of the Incoherence (Tahāfut al-Tahāfut, c. 1180) he replied on causation: to deny that fire has a nature that causes burning is to deny that anything can be known through its causes, which is what knowing means in science. God remains the ultimate cause, acting through created causes. It is one of the great exchanges in the history of philosophy, and it was not won decisively by either side. The picture of Ibn Rushd as the end of Islamic philosophy and the start of European rationalism is a simplification: his Latin influence was large, but the tradition continued in Persian-speaking lands, in Iran and India, for centuries. Ibn Khaldun and Mulla Sadra: dynasties and becoming Ibn Khaldun (1332–1406), born in Tunis, served rulers across North Africa and Spain, and wrote his Muqaddimah ("Introduction") in 1377 in an Algerian fortress, in about five months by his own account. Its aim was a new science, 'ilm al-'umrān, the science of civilisation: to explain history by causes, not by anecdote. Its central concept is 'aṣabiyya, group solidarity (cohesion, "team spirit"). Tribes at the edge of a settled state have it strongly, because they depend on one another for survival; this lets them conquer a rich but divided state. Their children grow up in comfort, taxes rise, solidarity fades, and a new, tougher group arrives. He reckons the cycle at about three generations, roughly 120 years. Interactive · A dynasty's solidarity, generation by generation Founders' solidarity Share kept each generation Challenger's solidarity at the frontier A toy model of one idea in the Muqaddimah. The numbers are invented for illustration; they are not Ibn Khaldun's, and real dynasties lasted from a few years to centuries. A generation is taken as 40 years, following him. Without JavaScript: with founders at 100, a generation keeping 65% and a challenger at 30, solidarity runs 100, 65, 42, 27: the dynasty falls to the challenger in the fourth generation, after about 120 years. Critics note that his model fits the Maghrib best, that "tribe versus city" is a simplification, and that it is not obvious how solidarity is measured. Admirers point to how early it asks for causes in climate, economy and group structure. Sociologists (see Classical Social Theory, 35/75) treat him as a founder of the field. In Safavid Iran, Mulla Sadra (c. 1572–1640), working in Shiraz and Isfahan, reworked Avicenna. Where Avicenna held that essence and existence are two aspects of a thing, Mulla Sadra argued that existence is the fundamental reality (aṣālat al-wujūd) and essence a mental abstraction from it; existence comes in degrees of intensity, like light. His most original thesis is substantial motion (ḥaraka jawhariyya): not only the accidents of a thing (its colour, place) change, but its substance is in constant becoming. A thing is a process, not an object with changes added on. He applied it to the soul, which begins bodily and is perfected by development. His major work is the Four Journeys (al-Asfār al-arba'a). The tradition of reading it is alive today in Iran's seminaries and philosophy departments. African philosophy: Zera Yacob, ubuntu, Wiredu and the sages In the late 1660s, in the Ethiopian highlands, Zera Yacob (born around 1600 near Aksum) wrote the Hatata ("Inquiry"). According to the text he had fled persecution during the Jesuit-backed attempt to convert Ethiopia to Catholicism, hid for a couple of years in a cave, and reasoned from scratch. His arguments are plain: the world has a creator whose existence is shown by order and causation; the different religions (Orthodox, Catholic, Muslim, Jewish) each claim revelation but contradict one another, so human reason must be the test; whatever contradicts creation's evident purposes, such as slavery and the claim that celibacy is holier than marriage, cannot come from God. Whether Zera Yacob wrote it is itself an argument: in 1920 the Italian scholar Carlo Conti Rossini suggested that the Italian missionary Giusto da Urbino forged it, and Claude Sumner answered in 1976 with arguments from the text's language and ideas. Most present-day scholars accept the text as Zera Yacob's, though a minority are not persuaded. If it is authentic, it is a seventeenth-century African argument against religious coercion and for human equality, written about two decades before Locke's Letter Concerning Toleration (1689). Ubuntu is a family of ideas, from the Nguni proverb umuntu ngumuntu ngabantu, "a person is a person through other persons". John Mbiti's 1969 formulation, "I am because we are, and since we are, therefore I am", became widely quoted. Ifeanyi Menkiti argued (1984) that personhood is achieved: you become a full person through your relations and duties, not at birth. Kwame Gyekye replied with a "moderate communitarianism", giving rights to individuals alongside duties to community. Thaddeus Metz has tried to state ubuntu as a moral theory: roughly, an action is right insofar as it honours relationships of identity and solidarity. In South Africa, judges cited ubuntu in S v Makwanyane (1995), when the Constitutional Court struck down the death penalty. The critics' question is the standard one: does a theory that grounds persons in community leave enough room to dissent from it? Kwasi Wiredu (1931–2022), a Ghanaian philosopher, argued for "conceptual decolonization": examining which of the concepts in African philosophy come from colonial languages and which from the speakers' own, and keeping what survives argument. He also proposed that the Akan tradition of deciding by consensus is a model for democracy without party competition. And he argued that some puzzles in European metaphysics, about "being", reflect the grammar of Greek and English; Gyekye and others dispute this. Behind these lies a dispute about what African philosophy is. In Bantu Philosophy (1945) the Belgian missionary Placide Tempels set out what he took to be a shared Bantu worldview centred on "vital force". Paulin Hountondji, from Benin, answered in the 1970s that this "ethnophilosophy" treated Africans as a single collective mind. Philosophy, he said, is argument by individuals who can be wrong, and one written down for criticism. Henry Odera Oruka (Kenya, 1944–1995) proposed an in-between: in the 1970s he interviewed Kenyan villagers with reputations as thinkers, and found some who reasoned critically, sometimes against the community's own views. He called this sage philosophy, and argued it showed that oral cultures have individual philosophers. Interactive · Who would say this? Match each claim to a thinker, then see what the others would add. Next claim Without JavaScript: Tempels described a shared Bantu philosophy of vital force; Hountondji objected that philosophy needs individual argument; Oruka interviewed Kenyan sages and found critical thinkers; Wiredu worked on clearing colonial confusions from concepts and defended consensus politics. Latin America: Las Casas, Sor Juana and the philosophy of liberation Philosophy in Latin America begins with a political question. In 1550–51 Charles V had a committee of theologians and jurists meet at Valladolid to hear Bartolomé de las Casas against Juan Ginés de Sepúlveda. The issue was the justice of the Spanish conquest, and the argument turned on Aristotle, who had said that some people are "natural slaves", lacking the faculty of deliberation. Sepúlveda applied that to the peoples of the Americas. Las Casas, who had been a landowner in the Caribbean before becoming a Dominican, answered that they had cities, laws and arts and could be persuaded, not compelled. The judges issued no clear verdict, and the conquests went on. Las Casas also earlier had proposed bringing Africans to work in the colonies, and later repudiated this, a fact that complicates the usual picture of him. Interactive · Valladolid, 1550: the argument in four moves BackNext move Reconstructed from the two men's published arguments and standard accounts of the debate. Without JavaScript: Sepúlveda says some people are natural slaves (Aristotle), so subduing them is just; Las Casas says the Aristotelian category fits few if any, that the Americas' peoples have cities, laws and religion, and that only persuasion is legitimate. Sor Juana Inés de la Cruz (1648 or 1651–1695), a self-taught nun in New Spain, wrote a long philosophical poem on the mind's striving to know the world at a glance (Primero sueño, published 1692). Her Response to Sister Filotea (1691) answered a bishop who told her to stop secular study. Her argument is that every kind of knowledge serves understanding of the sacred, that women have the same intellects, that the church's own saints and women scholars show it, and that studying is not a defiance. In 1693–94 she gave up her library and writing; why is debated. In the twentieth century the question became: is there a Latin American philosophy? José Vasconcelos (1882–1959), in La raza cósmica (1925), argued that the mixing of peoples in the Americas would produce a "cosmic race". The book is a landmark in how Latin America saw itself, and also, in its hierarchy of peoples, a source of criticism from Indigenous and Afro-descendant writers. In 1940 he edited a magazine sympathetic to the Axis, which harmed his reputation. In 1968 the Peruvian Augusto Salazar Bondy wrote that Latin American philosophy had been imitative because it reflected underdevelopment and dependence, and could only become authentic by overcoming them. Leopoldo Zea (Mexico, 1912–2004) replied in 1969 that Latin American philosophy should be "philosophy without more": philosophy does not need to be unique to be real, and gains authenticity by taking its own circumstances seriously. Enrique Dussel (1934–2023), born in Argentina and later based in Mexico, developed the philosophy of liberation (Filosofía de la liberación, 1977). Its starting point is the person excluded by the existing order: the poor, the colonised, women, the indigenous. Drawing on Emmanuel Levinas's ethics of the Other, Dussel argues that a philosophy built in the centres of power takes the "totality" (the system) as given, and that the first ethical fact is the face of the person it leaves out. It sits alongside Paulo Freire's Pedagogy of the Oppressed (1968 in Portuguese, English 1970), the liberation theology of Gustavo Gutiérrez (1971) and Aníbal Quijano's notion of "coloniality of power". Critics ask whether "the Other" is a precise enough category to build a normative theory on, and whether the approach can be tested. What a graduate just sees Philosophy in Arabic was not a footnote to Aristotle: it asked new questions about existence, the self and God. The argument about whether fire "makes" cotton burn is one of philosophy's classic debates, and it began as a dispute about miracles. Ibn Rushd did not teach a "double truth"; the view was pinned on others later. Explaining history by social causes is an old idea with a famous author: Ibn Khaldun. "Ubuntu" is not one slogan but a set of rival philosophical theories about persons. The question "is it philosophy?" is itself a philosophical debate, with sides, in Africa and Latin America. Arguments about equality and toleration were made in seventeenth-century Ethiopia and sixteenth-century Spain, as well as eighteenth-century France. When a source's authorship is disputed (the Hatata), say so and read the arguments anyway. Where it shows up next Metaphysics (36/04): essence and existence, causation and necessity, substance and process. Epistemology (36/03): Ghazālī and Hume on inference, and what counts as knowing a cause. Ethics (36/02) and Political Theory (35/12): ubuntu and relational ethics, liberation, Wiredu on consensus. Contemporary Philosophy (36/12): the demand to "decolonize" curricula, the continuing debate about the canon, and the Levinas behind Dussel. In the world: South Africa's constitutional jurisprudence, Iran's philosophical seminaries, Latin American education and liberation movements, and the histories of science and sociology. If you want to go deeper 📘 Textbook. Oliver Leaman, An Introduction to Classical Islamic Philosophy (Cambridge University Press, 2nd ed. 2002); Kwasi Wiredu (ed.), A Companion to African Philosophy (Blackwell, 2004); Susana Nuccetelli, Ofelia Schutte and Otávio Bueno (eds.), A Companion to Latin American Philosophy (Wiley-Blackwell, 2010). 📘 Gentler. Peter Adamson, Philosophy in the Islamic World (Oxford University Press, 2016), and Kwame Anthony Appiah, In My Father's House (1992), on what "African" means in African philosophy. 🎧 Free audio. Peter Adamson's History of Philosophy Without Any Gaps (historyofphilosophy.net) has long series on the Islamic world and on Africana philosophy. 🌐 Free text. The Stanford Encyclopedia of Philosophy has entries on Avicenna, al-Ghazālī, Averroes, Ibn Khaldun and Mulla Sadra, each by a specialist. The takeaway Three traditions carried on the central arguments of philosophy under their own conditions. Ibn Sīnā asked what is left of the self without the body and what makes existence necessary. Al-Ghazālī asked what we actually observe when we say one thing causes another, and Ibn Rushd answered that knowing means knowing causes. Ibn Khaldun and Mulla Sadra treated history and substance as processes. In Africa the question became who counts as a philosopher and what persons owe each other, and in Latin America whether the conquered are fully human and whether philosophy can be both local and real. Try this: take any statement of the form "X causes Y" you heard today. Write down what you actually saw, and then what you added. Is the added part a law, a habit of the mind, or a guess? Sources & Further Reading Sources. Avicenna, The Healing (floating man; Necessary Existent); al-Ghazālī, Incoherence of the Philosophers, discussion 17, trans. Marmura (1997/2000); Ibn Rushd, Decisive Treatise, trans. Hourani (1961) or Butterworth (2001), and Incoherence of the Incoherence, trans. Van den Bergh (1954); the 1277 Paris condemnation; Ibn Khaldun, Muqaddimah, trans. Rosenthal (1958); Mulla Sadra, al-Asfār al-arba'a. Zera Yacob and Walda Heywat, The Hatata, ed. Sumner (1976), and Conti Rossini (1920). Mbiti, African Religions and Philosophy (1969); Menkiti (1984); Gyekye, Tradition and Modernity (1997); Wiredu, Cultural Universals and Particulars (1996); Tempels, La philosophie bantoue (1945); Hountondji, African Philosophy: Myth and Reality; Oruka, Sage Philosophy (1990); S v Makwanyane (1995). Las Casas and Sepúlveda at Valladolid, 1550–51; Sor Juana, Respuesta a Sor Filotea (1691); Vasconcelos (1925); Salazar Bondy (1968); Zea (1969); Dussel (1977). Dates of early figures are approximate. 📘 Adamson, Philosophy in the Islamic World 📘 Wiredu (ed.), A Companion to African Philosophy 🌐 Stanford Encyclopedia of Philosophy Step 12. Contemporary Philosophy: Analytic, Continental & Beyond ---------------------------------------------------------------- Why: Analytic, continental and global philosophy since 1900. The twentieth century began with a hope that logic could clean up philosophy and ended with philosophers still arguing about almost everything. What changed, what split, what crossed over, and what a 2020 survey says the profession now thinks. "The present King of France is bald." Is that true, false, or neither? France has had no king since 1848, so you might say it is false. But then "the present King of France is not bald" sounds false too, and a logic in which a sentence and its denial are both false is in trouble. In 1905 Bertrand Russell published a short paper that solved this, and it is often called a paradigm of philosophical analysis. Forty-five years later, Peter Strawson said Russell had misunderstood what ordinary speakers do with such a sentence. That is the twentieth century's philosophy in miniature: a precise tool, a clever result, a reply that says the tool changed the question. Across the same decades, on the other side of the Channel and the Rhine, others argued that the question should start with lived experience, or with history, or with power. And from about 1950 the picture widened again: Japanese, African, Latin American and feminist philosophers joined the conversation in their own voices. The labels "analytic" and "continental" are shorthand, and they blur. Analytic philosophy is a tradition (not a method) that grew from Frege, Russell, Moore and Wittgenstein and prizes clarity and argument; "continental" is a catch-all for a set of European traditions with different methods, from phenomenology to critical theory. Plenty of philosophers cross the line. This piece tours six places where the argument went, and ends with what philosophers say they believe. The course in one box Who takes itPhilosophy majors, typically in year 4 or the end of year 3, as a survey of recent philosophy or as a capstone. In British programmes it is covered by the "history of philosophy since Kant" and "twentieth-century philosophy" strands of the QAA benchmark; in American ones, by courses on analytic philosophy and on continental philosophy. What it is forKnowing the positions behind present arguments in logic, language, mind, ethics and politics, and seeing how they depend on each other. Comes afterModern Philosophy: Descartes to Nietzsche (36/09). Leads toThe rest of the major's final year: Political Theory (35/12), Medical Ethics & Law (35/60) and Foundations: Sets, Logic & Infinity (34/71). It draws on Philosophy of Language (36/07), Philosophy of Science (36/06) and Philosophy of Mind (36/05). What this piece gives youYou will not be able to read Heidegger or Quine unaided. You will know a position, an argument and an objection from each of six areas, and you will be able to place a new philosopher on the map. Easier first reads: Existentialism: Freedom, Responsibility, and the Absurd (05/08), The Veil of Ignorance (05/09), Justice: From Plato to Rawls, Nozick and Sen (05/13) and Philosophy of Mind: The Hard Problem of Consciousness (05/10). This piece goes into the arguments those pages only mention. Frege, Russell and Wittgenstein: logic, descriptions and language-games Gottlob Frege's Begriffsschrift (1879) invented modern logic with quantifiers ("for all", "there is"), which let him write arguments that the old syllogisms could not. In "On Sense and Reference" (1892) he asked a puzzle: "the Morning Star is the Evening Star" is informative, though both names refer to the planet Venus. So a name has a sense (a way the object is given) as well as a reference. In 1902 Russell wrote to Frege that his system contained a contradiction (about "the set of all sets that are not members of themselves"). Frege replied with grief; set theory had to be rebuilt. Russell's own tool was the theory of descriptions. "The present King of France is bald" is, he said, not a subject-predicate claim about a king; it is shorthand for three claims: (1) there is a present King of France; (2) there is at most one; (3) whoever it is is bald. If (1) fails, the whole sentence is false, no mystery needed. His analysis explains the puzzle about negation by scope: "the King is not bald" can mean "there is exactly one king and he is non-bald" (false) or "it is not the case that there is exactly one king who is bald" (true). Strawson (1950) answered that ordinary speakers presuppose a king exists; if none does, the sentence misfires and is neither true nor false. Philosophers still divide on which is right. Interactive · Three sentences, two theories Choose a situation (the "world"). See how Russell and Strawson each treat the sentences. Without JavaScript: if there is no king, Russell makes "the King is bald" false, "the King is non-bald" false and "it is not the case that the King is bald" true. Strawson says all three lack a truth value, since the presupposition fails. Ludwig Wittgenstein (1889–1951) shaped the field twice, against himself. His Tractatus Logico-Philosophicus (German 1921, English 1922) held that a proposition is a picture of a possible state of affairs; what cannot be pictured cannot be said ("whereof one cannot speak, thereof one must be silent"). The Vienna Circle of the 1920s–30s took him up: only claims that are verifiable by experience or true by logic have meaning (A. J. Ayer, Language, Truth and Logic, 1936). The standard objection is that the principle itself is neither, and today most philosophers reject naive verificationism. Wittgenstein's later work, published after his death as Philosophical Investigations (1953), turned away from pictures. Meaning, he said, is use in a practice: words belong to "language-games" in which they have jobs. The famous example is the word "game". There is no one feature all games share; there are overlapping similarities, like the resemblances among members of a family (§§66–67). He also argued (§§243 ff.) that a purely private language, whose words refer to sensations only the speaker can know, could not have a standard of correctness. Interactive · Is there a feature all games share? Press a feature to see which games have it. Then pick two games to compare. My own illustrative table of six games and five features, in the spirit of Investigations §66; a different table would give different overlaps, but the point is how often a universal feature is missing. Without JavaScript: in a table of chess, poker, football, patience, ring-a-ring-o'-roses and a ball thrown at a wall, no feature is shared by all six, though neighbouring games overlap. Wittgenstein calls this a family resemblance. Quine and the web of belief: what to revise when the evidence disagrees In "Two Dogmas of Empiricism" (1951), W. V. O. Quine attacked the Vienna Circle's two supports: the clean split between claims true by meaning ("bachelors are unmarried") and claims true by fact, and the idea that each sentence can be tested alone. Our beliefs, he said, face experience together, as a web: a clash between prediction and observation tells you that something in the web must change, not what. We can revise a physical theory, an auxiliary assumption, a measurement, or even a law of logic. We usually revise what costs least. This is holism, and it goes back to Pierre Duhem; it is often called the Duhem–Quine thesis. History supplies a clean test. In the 1840s the orbit of Uranus did not match Newton's predictions. The French astronomer Urbain Le Verrier (and, independently, John Couch Adams) concluded that an unseen planet was pulling on it, and calculated where. Johann Galle in Berlin found Neptune on 23 September 1846, within about a degree of the prediction. In 1859 Le Verrier found that Mercury's orbit also did not match Newton: its closest point to the Sun advances faster than the theory allows (the modern value is about 43 arcseconds per century). He did the same thing, proposing an unseen planet, Vulcan, inside Mercury's orbit. No one found it. In 1915 Einstein's general relativity explained the excess exactly. Interactive · What would you revise? Without JavaScript: Uranus's anomaly was resolved by a new planet (Neptune, 1846). Mercury's anomaly, treated the same way (Vulcan), was resolved by revising Newtonian gravity (general relativity, 1915). The logic was the same in both cases. Only further evidence could say which move was right. Thomas Kuhn's The Structure of Scientific Revolutions (1962) built a larger story on this, and Karl Popper's falsifiability (The Logic of Scientific Discovery, 1934/1959) is the main alternative. Philosophy of Science (36/06) takes them up. Meanwhile Saul Kripke (Naming and Necessity, lectures 1970) argued that some truths are necessary yet known only through experience (water is H₂O), another blow to the old neat categories. And Edmund Gettier's three-page paper of 1963 showed that justified true belief is not enough for knowledge. Phenomenology and existentialism: Husserl, Heidegger, Sartre and Beauvoir On the European continent the start was different. Edmund Husserl (1859–1938) wanted a rigorous science of experience. His key idea is intentionality: consciousness is always consciousness of something. His method is the epoché, "bracketing" the question of whether the world exists in order to describe how things show up. Martin Heidegger (1889–1976), in Being and Time (1927), turned this into a study of the being who asks about being (Dasein): we are always already in a world of tools, other people and projects, "thrown" into a situation we did not pick, and finite. It is among the most influential and most difficult books of the century. Heidegger joined the Nazi Party in 1933 and was rector of the University of Freiburg in 1933–34. The Black Notebooks, published from 2014, contain antisemitic remarks. How far this affects his philosophy is disputed, and scholars of all positions have written on it. Jean-Paul Sartre (1905–1980) took the method into freedom. In Being and Nothingness (1943) and the lecture Existentialism Is a Humanism (1945), he held that "existence precedes essence": a person has no fixed nature to follow and is responsible for what they make of themselves. Bad faith is the attempt to deny this, either by treating yourself as a thing with a fixed nature (a waiter who is nothing but his role) or by pretending your situation doesn't limit you at all. Simone de Beauvoir (1908–1986) was a philosopher in her own right, not Sartre's disciple. In The Ethics of Ambiguity (1947) she argued that we are both free and situated, and that freedom is only real when others are free too. In The Second Sex (1949) she applied it to gender: "one is not born, but rather becomes, a woman". Her point was that what a woman is has been made by a history of situations in which men were treated as the universal and women as the Other. Her account of oppression differs from Sartre's: she said that having far fewer options is not a failure of will. Maurice Merleau-Ponty's Phenomenology of Perception (1945) put the body at the centre, and Frantz Fanon's Black Skin, White Masks (1952) described what racialised experience does to the sense of self. Interactive · Is this bad faith? Next case Short sketches of Sartre's discussion. He gave the waiter example; the others are my illustrations of the two ways he described. Without JavaScript: bad faith means denying either your freedom (I'm just made this way) or your situation (nothing limits me). Deliberating and accepting the costs of a choice is not bad faith. Beauvoir adds that real constraints are not self-deception. Critical theory, Arendt and Rawls: the political turn The Frankfurt School grew from the Institute for Social Research, founded in 1923 and directed by Max Horkheimer from 1930; the Nazi takeover sent its members into exile. Horkheimer and Theodor Adorno's Dialectic of Enlightenment (written 1944, published 1947) argued that the Enlightenment's drive to master nature turned into domination of people, and that the "culture industry" of film, radio and advertising trained people to accept it. Herbert Marcuse's One-Dimensional Man (1964) said similar of consumer society. Critics called this elitist and pessimistic. Jürgen Habermas (born 1929) answered with a more hopeful theory: language contains a built-in demand for reasons, and a legitimate society is one where laws could be accepted by all through free discussion (The Theory of Communicative Action, 1981). Hannah Arendt (1906–1975) is hard to place. In The Origins of Totalitarianism (1951) she described the new form of rule that destroys the public sphere. In The Human Condition (1958) she distinguished three activities: labour (the cyclic work of staying alive), work (making a durable world of objects) and action (speaking and acting with others, starting something new). Politics is action. Reporting on Adolf Eichmann's trial in 1961, she coined "the banality of evil": the evil lay not in a monstrous character but in a failure to think. It is among the most debated phrases of the century. Critics said she underrated Eichmann's active antisemitism, and later research (Bettina Stangneth, 2011) supports that; defenders say she meant that his motives lacked depth, not that he was ordinary. In the English-speaking world, John Rawls's A Theory of Justice (1971) revived political philosophy. His argument: a just society is one you would choose from an "original position" in which you do not know your own place in it (the veil of ignorance). He argued that the parties would choose two principles: equal basic liberties, and inequalities only if they open to all and benefit the least advantaged (the difference principle). John Harsanyi had argued earlier that a rational chooser behind the veil would maximise average utility. The tool below does the arithmetic of the dispute: how a choice among four invented societies depends on how much you fear ending up at the bottom. Interactive · Behind the veil: four societies How much you dislike risk (0 = only the average matters) Each society has five equally likely positions with the incomes listed. The score is a certainty equivalent: the guaranteed income you'd swap for the gamble, using a standard risk-aversion curve. The incomes are invented. Rawls himself did not argue "just be very risk-averse"; he argued from ignorance of probabilities and from the strains of commitment. This only shows how the choice moves. Without JavaScript: if you only care about the average, the unequal society with a very rich top wins. As you fear the bottom more, a gentle inequality that lifts the worst-off beats it; at the extreme, the society with the highest minimum wins, which is the difference principle's choice. Critics came from every side. Robert Nozick (Anarchy, State, and Utopia, 1974) said redistribution violates individual rights over what one has legitimately acquired. Communitarians such as Michael Sandel said the "unencumbered self" behind the veil ignores that we are formed by our communities. Susan Okin pointed out that Rawls left the family out of the scope of justice. Charles Mills (The Racial Contract, 1997) argued that actual social contracts have been contracts among a racial few. Amartya Sen (The Idea of Justice, 2009) argued for comparing real situations instead of describing a perfect one. Rawls's later Political Liberalism (1993) tried to find principles that people with different comprehensive views could share. The Kyoto school and philosophy beyond the West Nishida Kitarō (1870–1945) is often called Japan's first modern philosopher. His An Inquiry into the Good (1911) began with "pure experience", the moment before the split between knower and known, drawing on William James, Zen practice and German idealism. Later he built a "logic of place" (basho) and a concept of "absolute nothingness": the place in which things appear without itself being a thing. His colleagues Tanabe Hajime (1885–1962) and Nishitani Keiji (1900–1990, Religion and Nothingness, 1961) carried the project on at Kyoto University. The echo of Nāgārjuna's emptiness (see 36/10) is not a coincidence: they were talking with Buddhism and with Hegel, Nietzsche and Heidegger together. This is philosophy done across traditions, not a Western method applied to Eastern material. The school's wartime record is contested. In 1941–43 several members took part in discussions on "the world-historical standpoint and Japan" published in a leading journal, which critics read as giving philosophical cover to Japanese imperial expansion; others read parts of them as attempting to criticise militarism from inside. Historians and philosophers disagree on how far each person went, and some members were barred from public posts after the war. Nishida himself died in June 1945. The case is a useful warning that a profound philosophy and a compromised politics can sit in the same person. The wider "beyond" in this course includes women who changed analytic philosophy (G. E. M. Anscombe's "Modern Moral Philosophy" in 1958, Philippa Foot, Iris Murdoch), philosophy of race (W. E. B. Du Bois, Fanon, Mills), African and Latin American philosophy (36/11) and the Chinese and Indian traditions (36/10). The demand to widen the canon is a live argument, and it comes with a methodological one: whether a text is read for what it said then, or for what it can still do now. What philosophers think now: the PhilPapers 2020 survey In 2020 David Bourget and David Chalmers ran the second PhilPapers Survey, after the first in 2009. Results were first reported in November 2021 from "target" respondents: professional philosophers, mostly at departments in English-speaking countries, with anywhere from a few hundred to about 1,800 answering each question. It is the best snapshot of the profession's opinions, with real limits: it samples mainly Anglophone philosophers, and a majority is not a proof. Interactive · What the profession said Figures for the "target" group as reported on the survey's results pages (survey2020.philpeople.org), rounded, with the number answering. Some questions allow choosing more than one answer, so percentages may overlap or sum to under 100. Without JavaScript: about 19% of those answering accept theism; 52% accept physicalism about the mind against 32% non-physicalism; 62% are moral realists against 26% anti-realists; 63% would switch the trolley, and 56% would not push the man. Some fair readings. On most questions no answer is a large majority: on normative ethics, the three big families sit within a few points of each other (virtue ethics 37%, deontology 32%, consequentialism 31%). On a few, a position leads clearly: more philosophers accept moral realism than reject it, and most say they would switch the trolley but not push the man. Compatibilism about free will has been the leading view in both surveys. In 2009 the proportion of those who accepted theism was close to 15% among faculty at leading departments; in 2020, among the broader target group, it was about 19%, so a slight rise should not be over-read, because the groups differ. The survey also tells us what philosophers think of philosophy: when asked how much progress philosophy has made, 42% said a lot and 47% said a little. What a graduate just sees Many philosophical problems can be recast as a question about the logical form of a sentence, and sometimes that dissolves them. Sometimes it only moves them. "Meaning" is not a thing in the head: look at how a word is used, and be suspicious of a demand for a definition that covers every case. When a prediction fails, logic says something is wrong, not what; the choice of what to revise is a judgment, and history can go either way. Freedom and situation go together: you choose within a body, a past and a society, and denying either is a way of dodging responsibility. A theory of justice is a theory of what you could defend to someone in the worst-off position. A thinker's brilliance and a thinker's politics are two separate things to be weighed, as with Heidegger and the Kyoto school. "Analytic" and "continental" are historical labels. Good philosophy in both shows its work. The profession agrees much less than you would think. Check the survey before saying "most philosophers believe". Where it shows up next Political Theory (35/12) and Medical Ethics & Law (35/60): Rawls's veil, Habermas on legitimacy, and consent and autonomy in clinical ethics. Foundations: Sets, Logic & Infinity (34/71): Frege's quantifiers, Russell's paradox and the road to Gödel. Philosophy of Language (36/07) and Philosophy of Mind (36/05): sense and reference, use, and the Chinese room. In the world: debates on AI and understanding, on gender, on justice in health care and tax, on whether a history of colonisation requires rewriting what universities teach. If you want to go deeper 📘 Textbook. Scott Soames, Philosophical Analysis in the Twentieth Century (Princeton University Press, 2 vols., 2003), and Simon Critchley, Continental Philosophy: A Very Short Introduction (Oxford University Press, 2001). John Rawls, A Theory of Justice (rev. ed. 1999), is the primary text for that section. 📘 Gentler. Sarah Bakewell, At the Existentialist Café (2016), a lively group portrait of Sartre, Beauvoir, Heidegger, Husserl and the rest. 🌐 Free text. The Stanford Encyclopedia of Philosophy has entries on every thinker named here. 🌐 Free course. MIT OpenCourseWare 24.00 Problems of Philosophy (Fall 2019, Miriam Schoenfield). 🌐 The survey. The PhilPapers Survey 2020, with full results and methods. The takeaway Twentieth-century philosophy is a set of arguments, not a set of slogans. Frege and Russell gave it new logic, and Wittgenstein twice changed what it takes meaning to be. Quine showed that evidence tests a whole web of belief. Husserl, Heidegger, Sartre and Beauvoir put experience, freedom and situation at the centre. Arendt, the Frankfurt School and Rawls turned the questions to politics, and the Kyoto school and other traditions showed the map is larger than Europe. The 2020 survey shows a profession that agrees on some things and divides on most. Try this: pick one question from the survey (free will, God, the trolley) and write down your answer before you look at the profession's. Then write the strongest objection to your own answer. Sources & Further Reading Sources. Frege, Begriffsschrift (1879) and "Über Sinn und Bedeutung" (1892); Russell, "On Denoting", Mind (1905) and letter to Frege (1902); Strawson, "On Referring", Mind (1950); Wittgenstein, Tractatus (1921/22) and Philosophical Investigations (1953); Ayer (1936); Quine, "Two Dogmas of Empiricism" (1951); Kuhn (1962); Kripke (1980); Gettier (1963). Le Verrier, Adams and Galle (1846); Le Verrier on Mercury (1859); Einstein (1915). Husserl; Heidegger (1927); Sartre (1943, 1945); Beauvoir (1947, 1949); Merleau-Ponty (1945); Fanon (1952). Horkheimer and Adorno (1947); Habermas (1981); Arendt (1951, 1958, 1963); Stangneth, Eichmann Before Jerusalem (2011); Rawls (1971, 1993); Harsanyi; Nozick (1974); Okin; Sandel; Mills (1997); Sen (2009). Nishida (1911); Nishitani (1961). Bourget and Chalmers, "Philosophers on Philosophy: The 2020 PhilPapers Survey", Philosophers' Imprint (2023), and the results at survey2020.philpeople.org. 📘 Bakewell, At the Existentialist Café 📘 Soames, Philosophical Analysis in the Twentieth Century 🌐 Stanford Encyclopedia of Philosophy Step 13. Political Theory: Justice, Power, Legitimacy and Liberty ----------------------------------------------------------------- Why: Justice, power and legitimacy. Four questions every society answers whether it knows it or not: who rules, why anyone obeys, how free people should be, and what a fair share looks like. Thinkers from Athens, Qufu, Pataliputra and Tunis gave different answers, and each is still in use. select{font-family:-apple-system,sans-serif;font-size:.9rem;min-height:44px;max-width:100%;min-width:0;border:1px solid var(--line);border-radius:10px;background:var(--hi);color:var(--ink);padding:6px 8px} .row{display:flex;flex-wrap:wrap;gap:8px;align-items:center;margin:6px 0} .row>*{min-width:0} .chips button{min-width:0} A traffic light turns red at 3 a.m. on an empty street, and you stop. Nobody is watching. Why? Because it is the law, because it is sensible, because everyone else stops, because someone could be coming. Now scale that up: why do millions of people hand over a slice of their pay every year, accept a verdict from a stranger in a robe, or send their sons and daughters to fight when an official signs a paper? Political theory is the study of that ordinary miracle, and of whether it is justified. It is not the same as political science that counts votes. It asks what a government is for, when it has the right to command, and what we owe each other. The strongest answers come from every continent, and a good course reads them side by side rather than treating Europe as the default. The course in one box Who takes itPolitical science, philosophy and law students, usually in year 1 or 2. It is the opening course of Oxford's PPE politics paper, MIT's Course 17 and Sciences Po, and the heart of Oxford's Jurisprudence. English majors meet the same ideas in novels. What it is forGiving you the concepts to say why a law, a tax or a regime is fair or unfair, rather than only that you like it. Comes afterNothing. It is the starting point. Leads toComparative Politics (35/13), and for law students Constitutional Law (35/03) and International Law & Human Rights (35/10). The ideas here also feed Political Economy (35/17). What this piece gives youYou will not settle the debates; nobody has. You will recognise six big answers, who gave them and what each one's critics say. It takes no side on today's partisan fights. Easier first reads: The Social Contract: Why Obey a State at All? (18/14), What Is Freedom? (18/11) and Justice: From Plato to Rawls, Nozick and Sen (05/13). This piece goes further and lets you test the arguments. Why have a state at all? Nature, contract and the fish Start from a thought experiment: no government. What would life be like? Thomas Hobbes, writing during the English civil war, said in Leviathan (1651) it would be a "war of all against all", with life "solitary, poor, nasty, brutish, and short". Not because people are wicked, but because they fear each other, and the safest move against a fearful neighbour is to strike first. The only escape is to give up your freedom to a sovereign strong enough to keep everyone in awe. The same worry appears elsewhere. The Indian tradition of statecraft speaks of matsya-nyaya, "the law of the fishes", where the big fish eat the small. Kautilya's Arthashastra (attributed to the Mauryan minister of about 300 BCE; Patrick Olivelle's 2013 translation argues the text took its present shape around the first century CE from older material) makes the king, and his rod of punishment, the cure. Ibn Khaldun, in the Muqaddimah (1377), argued that people need a restraining authority because aggression is natural to them. Aristotle in his Politics disagreed in a different way: humans are by nature political animals who flourish only in a community, so the state is not an invention but a fulfilment. The social contract tradition says a state is justified by an agreement, real or imagined. John Locke (Second Treatise, 1689) thought people in nature already have rights to life, liberty and property, and form governments to protect them, so a government that violates them may be resisted. Jean-Jacques Rousseau (The Social Contract, 1762), opening with "Man is born free, and everywhere he is in chains", argued legitimacy comes only from the general will of the people governing themselves. Hobbes wanted a strong sovereign; Locke a limited one; Rousseau a self-governing one. Hobbes's logic is a game you can run. Each person chooses to keep the peace or to grab. If everyone keeps the peace each gets 3; a grabber facing a peaceful person takes 4 and leaves them 0; two grabbers fight and each get 1. Grabbing wins in every pairing, so peace collapses. Now add a sovereign who punishes grabbers. How much punishment is enough? Interactive · Hobbes's trap Penalty on a caught grabber Chance a grab is caught Share keeping the peace at the start Payoffs: peace–peace 3 each; grab vs peaceful 4 and 0; grab–grab 1 each. Expected penalty = penalty × chance. Strategies spread in proportion to their advantage (a replicator model, 200 rounds). A toy: it ignores the cost of the sovereign, and who watches the watcher. The answer is neat: an expected penalty above 1 is enough, whatever the starting mix, because it removes the temptation exactly. But notice what the toy leaves out. Who punishes the sovereign? That is Locke's question, and the reason constitutions limit power. Who should rule, and for whose sake? Plato's Republic (about 375 BCE) answered: those who know. Rule should belong to philosopher-guardians trained to see the good, as a ship should be steered by a navigator, not by a vote of the crew. Aristotle's Politics asked two more practical questions of every regime. How many rule: one, few or many? And for whose benefit: the common good, or the rulers' own? Combine them and you get six constitutions, three good and three corrupted. Interactive · Aristotle's six regimes One rules A few rule The many rule For everyone's good For the rulers' own gain Aristotle, Politics III. His term for rule of the many in their own interest is "democracy", which he saw as rule of the poor majority; "polity" is his name for the good form of rule by the many. Notice the question under Aristotle's grid: not "who is in charge?" but "is power used for everyone?" Other traditions ask the same. Confucius (551 to 479 BCE) held that government begins with the ruler's own conduct; a leader who is himself upright needs few orders. Mencius, his follower, said the people matter most, the state next, the ruler least, and that a ruler who abuses the people loses the Heaven-given mandate to rule, an idea that justified rebellion in Chinese history. Kautilya's king serves the welfare of his subjects, whose happiness is his, though the Arthashastra is frank about spies, deception and war in a way that Confucian texts avoid. Machiavelli, centuries later, separates what rulers should be from what they must do to keep power. Each of these is a view about the same two variables. Why people obey: power, legitimacy and the tipping point Power is the ability to make others do things. Legitimacy is the belief that the power is rightful. Max Weber, in lectures of 1919 (Politics as a Vocation), defined the state as the body that claims the monopoly of legitimate force within a territory, and gave three sources of legitimacy: tradition ("it has always been so"), charisma (a leader's personal appeal) and legal-rational rules (offices and procedures). Ibn Khaldun added a cycle: a dynasty rises on asabiyya, the solidarity of a tight group, then its rulers grow comfortable, solidarity fades, and after about three generations, which he counted as roughly 120 years, a hardier group replaces it. Legitimacy is not only a feeling. It works as a prediction about everyone else. Mark Granovetter's threshold model (1978) says each person has a threshold: they will join a protest if enough others already have. Some people join first at nothing; some join at ten others; some need half the street. Whether a crowd tips depends on the whole distribution, not the average. The economist Timur Kuran used this idea to explain why East Germany's regime seemed stable until the autumn of 1989 and then fell. Interactive · Who joins the crowd? Thresholds 0, 1, 2 ... 99 Same, but the "1" needs 2 Bell-shaped (use sliders) Average threshold Spread of thresholds 100 people. Each joins when the number already in the crowd reaches their threshold. The first mode is Granovetter's own example: nudging one person's threshold from 1 to 2 turns a full riot (100) into a crowd of one. Bell-shaped thresholds are spaced by the normal distribution. A model, not a forecast. The moral of the model is that a regime's support can be much thinner than it looks, and also that a crowd's size can hide how fragile it is. Legitimacy lives in expectations about other people, which is why regimes work hard at appearing strong, and why sudden changes surprise even the people living through them. Liberty: where does my freedom end? John Stuart Mill's On Liberty (1859) gave the most famous rule: the only purpose for which power can rightfully be used against a member of a community, against their will, is to prevent harm to others. Their own good, physical or moral, is not a sufficient warrant. This is the harm principle. Isaiah Berlin (1958) sorted freedom into negative liberty (freedom from interference) and positive liberty (the capacity to run your own life), warning that talk of the "real self" can excuse tyranny. Philip Pettit and the republican tradition, from Rome to Madison, defined freedom as non-domination: you are unfree if someone merely can interfere at will, even if they are kind. Confucian thought sees the person as made by relationships and duties, so freedom detached from role and community seems thin. Nozick treats each person as the owner of their body and property. These lenses give different answers to concrete questions. Choose a case below. The answers are how a thinker in each tradition would typically reason, our extrapolation, not quotations. Interactive · Five lenses on one law Case Lenses: Mill (harm principle), Nozick (self-ownership and property), Rawls (equal basic liberties, fair terms), Confucian (roles, virtue and harmony), republican (freedom as non-domination, after Pettit). Each lens is a family of views, with internal disagreements. The point is not to find the winning lens but to see that people who agree on "freedom is important" can disagree on a helmet law for honest reasons: they are counting different things. Justice: the veil, the entitlement and the flute John Rawls (A Theory of Justice, 1971) asked what rules we would choose for society if we did not know our place in it: rich or poor, clever or slow, man or woman, believer or not. Behind this veil of ignorance, he argued, we would choose equal basic liberties and allow inequalities only if they work to the benefit of the least advantaged: the difference principle. He thought a cautious chooser would follow the "maximin" rule, maximising the worst outcome. John Harsanyi replied that a rational chooser would maximise the average instead. The truth may lie between, and your own fear of the bottom sets where. Interactive · Behind the veil Four invented societies, each with five income groups (thousands per year). You will be placed in one group at random. How much you fear landing at the bottom Average only (Harsanyi) Worst case (maximin) Incomes are illustrative. "Equal-share value" is the sure income you would swap for the gamble, using constant-risk-aversion utility: fear 0 is the plain average, 1 is the geometric mean (log utility), 10 or more is treated as the pure minimum. Robert Nozick, in Anarchy, State, and Utopia (1974), objected from another direction. Justice is not a pattern of shares but a history of how they came about: if holdings were acquired fairly and transferred freely, the result is just, whatever it looks like. His example: start from any distribution you like, and suppose a million fans each freely pay 25 cents to watch the basketball star Wilt Chamberlain play. He ends up rich. To keep the pattern you would have to keep stopping free exchanges. Critics replied that markets rest on rules the community sets (Rawls's "background justice"), and that G. A. Cohen argued the freedom of the poor is also reduced by the property system. Interactive · Wilt Chamberlain in a village Fans who pay Each fan's payment (out of 100 coins) A village of 100 people, each starting with 100 coins (perfect equality, Gini 0). The Gini coefficient runs from 0 (equal) to 1 (one person has all). Amartya Sen (The Idea of Justice, 2009) came at it from a third angle. We do not need a perfect blueprint of a just society to know that famine or slavery is unjust; we need ways to compare real options. He asks what people are actually able to do and be (their capabilities), not only what they own. His example: three children quarrel over a flute. The first can play it, the second is poor and has no toys, the third made it. A utilitarian, an egalitarian and a libertarian each have a good reason to pick a different child, and none is simply wrong. Sen's moral is that plural, reasoned argument matters more than a single formula. Whose voices were left out of the contract? Great theories have blind spots, and some of the best political theory is the critique of the blind spots. Mary Wollstonecraft's A Vindication of the Rights of Woman (1792) argued that women's supposed unfitness for citizenship was produced by an education built to make them pleasing instead of rational, so the argument for equal rights applied to them too. Mill's The Subjection of Women (1869) made the same case from liberal premises. Karl Marx and Friedrich Engels (Communist Manifesto, 1848) argued that the question "what is a fair contract?" hides that workers must sell their labour to survive, so political equality can coexist with deep economic unfreedom; defenders of markets reply that Marx's predictions failed and that voluntary exchange raises the poorest. (31 Political Economy covers that debate.) Carole Pateman (The Sexual Contract, 1988) and Susan Moller Okin (Justice, Gender, and the Family, 1989) asked why theories of justice rarely examined the household. Charles Mills (The Racial Contract, 1997) argued that the social contract was in practice a contract among whites that excluded others. Communitarians such as Michael Sandel (Liberalism and the Limits of Justice, 1982) said Rawls's chooser, stripped of identity, is not a real person. Gandhi's Hind Swaraj (1909) questioned whether modern states, even self-governing ones, deliver freedom. These challenges did not end the older traditions, which have replies; they widened the conversation about who counts. What a graduate just sees Every government answers four questions (who rules, why we obey, how free, how fair), whether it says so or not. A state can be justified as nature's fulfilment (Aristotle), a bargain (Hobbes, Locke), a general will (Rousseau), or a protector (Kautilya). Each carries a different limit on power. Ask "how many rule, and for whom?" before arguing about names. Aristotle's two questions still sort most regimes. Legitimacy is a belief about what others believe. Regimes can look stable and be brittle, as in a threshold cascade. "Freedom" has at least three meanings (no interference, capacity, no domination), and people can honestly disagree while using the same word. Justice theories answer differently: a fair procedure (Rawls), a fair history (Nozick), or fair real options (Sen). Ask which one an argument is using. A thought experiment is a tool for isolating a variable, and its strength depends on what it assumes away. Who is left out of a theory is as informative as who is in it. Where it shows up next Comparative Politics (35/13): Aristotle's grid becomes the study of presidential and parliamentary systems, democracies and autocracies; Weber's legitimacy becomes the question of why some regimes last. Constitutional Law (35/03) and International Law & Human Rights (35/10): Locke's limits and Mill's harm principle live on in bills of rights and proportionality tests. Political Economy (35/17): Rawls, Nozick and Marx are the three poles of the argument about markets and fair shares. In the world and in books: every constitutional debate, every tax argument, and every novel about a tyrant or a rebellion. Literature students find these arguments in dystopias and in epics from the Mahabharata to Orwell. If you want to go deeper 📘 Textbook. Will Kymlicka, Contemporary Political Philosophy: An Introduction (Oxford, 2nd edition, 2002). The classic survey of utilitarianism, liberal equality, libertarianism, communitarianism, feminism and multiculturalism. 📘 Textbook. Adam Swift, Political Philosophy: A Beginners' Guide for Students and Politicians (Polity; later editions). Clear and problem-led. 📘 Gentler. Michael Sandel, Justice: What's the Right Thing to Do? (2009). Everyday dilemmas leading into the big theories. 🌐 Free course. Yale Open Courses, PLSC 114 Introduction to Political Philosophy (Steven B. Smith): Plato to Rawls, with lectures and transcripts. Also Sandel's Justice course from Harvard. The takeaway Political theory gives names to the questions every society answers: why a state, who should rule and for whom, why people obey, how free we should be, and what is fair. No single tradition has the last word, and the best answers have been argued across Athens, China, India, the Islamic world and modern Europe; the best critics asked who was left out. Try this: next time you hear an argument about a law, name what it assumes. Is it about harm to others, about fairness of procedure, about a fair history, or about what people can actually do? Then ask which of the other three it leaves out. Sources & Further Reading Sources. Primary texts are in the public domain: Plato's Republic, Aristotle's Politics (III), the Analects and Mencius, Hobbes's Leviathan (1651, ch. 13), Locke's Second Treatise (1689), Rousseau's Social Contract (1762), Wollstonecraft (1792), Marx and Engels (1848), Mill (On Liberty 1859; Subjection of Women 1869). Later works are described, not quoted: Weber (Politics as a Vocation, 1919), Berlin, "Two Concepts of Liberty" (1958), Rawls (1971), Nozick (1974), Pettit (1997), Sen (2009), Granovetter, "Threshold Models of Collective Behavior" (American Journal of Sociology, 1978), Kuran, "Now Out of Never" (World Politics, 1991), Pateman (1988), Okin (1989), Mills (1997), Sandel (1982). Arthashastra: Olivelle, King, Governance, and Law in Ancient India (Oxford, 2013), which dates the finished text to the early centuries CE; the traditional attribution to a Mauryan minister about 300 BCE is contested. Ibn Khaldun's dynastic cycle: Muqaddimah (1377), with the three-generation, 120-year figure as he gave it. Every number in the interactives was computed in node (the Hobbes toy, the threshold cascade, the equal-share values and the Gini coefficients); incomes and populations are invented for illustration. 🌐 Yale Open Courses: PLSC 114 Introduction to Political Philosophy 🌐 Harvard: Justice with Michael Sandel 📘 Kymlicka, Contemporary Political Philosophy Step 14. Medical Ethics & Law: Whose Body, Whose Decision --------------------------------------------------------- Why: Ethics where it is hardest: consent, life and death. Every clinic runs on a few quiet promises: that you decide what happens to you, that what you say stays private, that the research behind your treatment was fairly done, and that scarce care is shared by rules. Medical ethics is the study of those promises and of what to do when they collide. A man in his seventies is told his scan shows a cancer. His daughter takes the doctor aside: "Please don't tell him. It will destroy him." Whichever way the doctor goes, she is answering a question that no blood test can answer: whose information is this, and who decides? Medical ethics is what a graduate learns to see in a moment like that. It is a small set of ideas for looking at a hard case, plus a history of what went wrong when they were ignored. This piece explains how medical ethics and law work. It is not medical or legal advice; laws differ by country and change, and for a health question you should see a clinician. In an emergency, call your local emergency number. The course in one box Who takes itMedical, nursing and allied-health students, usually woven through the years of training and examined late (year 3 onward). Philosophy, law and public health students meet it as bioethics. What it is forGiving clinicians and patients a shared language for decisions where the medically best option, the person's wishes, the law and fairness pull in different directions. Comes afterPolitical Theory (35/12), for the ideas of liberty, justice and legitimacy it borrows. Leads toPublic & Global Health (35/61), where the same questions apply to populations, and Surgery, Anaesthesia & Emergency Care (35/62), where consent is asked in a hurry. It also sits behind Epidemiology & Evidence-Based Medicine (35/58) and Clinical Psychology (35/27). What this piece gives youYou will not be able to say what the law allows in a particular case; it differs by place and changes. You will see the four principles and their critics, what capacity really tests, why confidentiality has edges, how research scandals wrote the rules, how end-of-life law differs across countries, and why rationing is unavoidable. Easier first reads: Justice: Plato to Rawls, Nozick and Sen (05/13), Moral Philosophy, Seriously (05/15) and Rights, Constitutions and the Rule of Law (18/04). The four principles, and the people who push back In 1979 two American philosophers, Tom Beauchamp and James Childress, published Principles of Biomedical Ethics. It proposed four principles as a common vocabulary for clinicians who disagree about theory: respect for autonomy (people decide about their own lives), beneficence (act for the patient's good), non-maleficence (avoid causing harm) and justice (distribute benefits and burdens fairly). The book is in its eighth edition (2019) and is the most-used framework in medical teaching. The authors are clear that the principles do not rank themselves. Each is a strong reason that can be outweighed; you must specify what a principle means in a context and then balance it against the others. That is where the argument starts. Critics say this gives no way to settle conflicts: Danner Clouser and Bernard Gert (1990) called the principles a checklist of unconnected slogans, a "pick and mix" of different moral theories. Virtue ethicists say it ignores the character of the person acting; casuists say reasoning from paradigm cases beats principles. Defenders such as Raanan Gillon reply that the four principles are common ground between people of many moral views, which is exactly why they are useful at a bedside. Interactive · Same facts, different weights Refuses bloodDon't tell himOne bed left Weight on autonomy Weight on beneficence Weight on non-maleficence Weight on justice Illustration only. Each option is scored 0 to 3 on how well it honours each principle, by the author, to show that the answer moves with the weights. Beauchamp and Childress themselves reject a formula like this; real cases are settled by argument about facts, not arithmetic. With equal weights of 5, respecting a competent adult's refusal of blood scores 40 against 30 for transfusing anyway. Put the weight on welfare (beneficence and non-maleficence at 10, autonomy and justice at 2) and transfusion edges ahead, 44 to 40. The sliders do not give the right answer; they show where the disagreement lives, usually in how much a person's choice should count, not in the facts. Consent and capacity: whose decision is it? The legal core of autonomy is informed consent. In 1914 Judge Benjamin Cardozo wrote in Schloendorff v. Society of New York Hospital that every adult "of sound mind has a right to determine what shall be done with his own body"; an operation without consent is a wrong even if it is skilful. Since then the question has been what must the patient be told. The older English answer was what a responsible body of doctors would say (Bolam, 1957); Montgomery v Lanarkshire Health Board (UK Supreme Court, 2015) made it the risks this patient would want to know. A consent only counts if the person can make the decision. Capacity is not a label on a person; it is decision-specific and time-specific. In England and Wales the Mental Capacity Act 2005 (in force 2007) starts from five rules: assume capacity; give all practicable help first; an unwise decision is not proof of incapacity; if someone lacks capacity, act in their best interests; choose the least restrictive option. Its test asks whether the person can understand the relevant information, retain it long enough, use or weigh it, and communicate a choice. Other systems word it differently but ask something very similar. capacity = understand + retain + use or weigh + communicatefor one decision, at one time; failing any part means the person lacks capacity for that decision Interactive · Does she have capacity? Invented vignettes for illustration; capacity assessments belong to trained clinicians and, in the last resort, courts. If an eating disorder or any mental-health struggle touches you, findahelpline.com lists services in your country. The third case is where the field itself is unsettled. Clinicians and courts disagree about when a belief that comes from an illness stops a person from weighing the facts, even though they can repeat them. That is a live debate, not an error in the test. Confidentiality and where it stops "Whatever I see or hear in the lives of my patients ... I will keep to myself": the line is from the Hippocratic tradition, and some version of the promise appears in oaths from ancient Greece to the Indian Charaka Samhita to modern declarations. The reason is practical: people who fear exposure hide symptoms. But no legal system treats it as absolute. Disclosure is usually allowed or required in four kinds of situation: the patient agrees; the law requires a report (notifiable infectious diseases in most countries, certain injuries, suspected child abuse); a court orders it; or there is a serious risk to someone else that cannot be avoided otherwise. The best-known case for the last is Tarasoff v. Regents of the University of California. In 1976 the California Supreme Court held (17 Cal. 3d 425) that a therapist who reasonably believes a patient is a serious danger to an identifiable person has a duty to take reasonable steps to protect that person. US states have since followed it in different ways, from mandatory to merely permitted; elsewhere, professional bodies such as the UK's General Medical Council allow disclosure in the public interest. Interactive · Who may be told? General patterns only; the exact rule depends on the country, the profession and the facts. Not legal advice. Research ethics: the rules were written after the scandals At the Doctors' Trial in Nuremberg, American judges tried Nazi physicians for lethal and torturous experiments on camp prisoners. The 1947 judgment set out ten principles, the Nuremberg Code; the first begins, "The voluntary consent of the human subject is absolutely essential." In 1964 the World Medical Association adopted the Declaration of Helsinki, which put research ethics in doctors' own hands; it has been revised many times, most recently in October 2024, which added emphasis on global inequities and scientific integrity. Rules written by doctors did not stop the next scandal. From 1932 to 1972 the US Public Health Service, with Tuskegee Institute, followed about 600 poor Black men in Macon County, Alabama: 399 with syphilis and 201 without. By 1947 penicillin was the standard treatment, and the men were still not given it. Whistleblower Peter Buxtun went to the press; the story broke on 25 July 1972 and the study ended that November. A 1974 class action brought a $10 million settlement, and President Clinton apologised on 16 May 1997. Congress passed the National Research Act in 1974, which led to ethics review boards, and in 1979 the Belmont Report named three principles for research: respect for persons, beneficence, and justice (who bears the burden and who gets the benefit). A different kind of case is Henrietta Lacks. In 1951, at Johns Hopkins Hospital in Baltimore, doctors took samples of her cervical cancer without asking her; she died on 4 October 1951, aged 31. Her cells became the first human cell line that kept dividing, HeLa, used worldwide for decades. Her family learned of it in 1975; the HeLa genome was published without their consent in 2013, after which the NIH and the family agreed on controlled access to the data. Rebecca Skloot's 2010 book told the story, and in July 2023 the family settled a claim against a biotech supplier on undisclosed terms. At the time, permission was neither required nor customarily sought; in Moore v. Regents (1990), the California Supreme Court later held that discarded tissue is not a person's property. Law and ethics did not move together. Interactive · Scrub through the years Year Red dots are wrongs and revelations; blue dots are rules and rulings. The end of life: refusing, withdrawing, dying with help Three things are often run together. Refusing or stopping treatment is allowed for a person with capacity in most legal systems, even when death follows; it is why advance directives exist. Euthanasia means a clinician gives a drug that ends the person's life; assisted suicide means the clinician prepares or prescribes and the person takes it. Pain relief that might hasten death as a side effect is judged under the older "double effect" idea. The laws on euthanasia and assisted suicide differ widely and are changing quickly. The Netherlands and Belgium (2002) were the first to legalise euthanasia by statute. Switzerland never legalised it but has not punished assisting a suicide unless the motive is selfish since 1942. Colombia's Constitutional Court decriminalised it in 1997, and Canada, Spain, New Zealand and every Australian state have passed laws since 2016. Arguments for the laws stress autonomy and relief from suffering. Arguments against stress risks to disabled and vulnerable people, the quality of palliative care, and the role of doctors as healers. Table · Some laws, with how they came about AllStatuteCourt rulingNot yet in force PlaceWhat it allowsSince SwitzerlandAssisted suicide, self-administered; not a crime unless the motive is selfishPenal Code art. 115, in force 1942 NetherlandsEuthanasia and assisted suicide, with review committees1 April 2002 BelgiumEuthanasia2002 LuxembourgEuthanasia2009 ColombiaEuthanasia; the court decriminalised it, rules followed, widened in 2021Court 1997 CanadaMedical assistance in dying2016 (Royal Assent 17 June) SpainEuthanasia and assisted suicide25 June 2021 AustraliaVoluntary assisted dying, state by state: Victoria first, then WA, Tasmania, Queensland, South Australia, NSW2019 to 2023 New ZealandAssisted dying7 November 2021 Oregon (US)Assisted suicide only; euthanasia illegal; several other US states have similar laws1997 GermanyFederal Constitutional Court struck down the ban on organised assisted suicide; active euthanasia stays illegalCourt 2020 EcuadorConstitutional Court decriminalised euthanasia under conditionsCourt 5 Feb 2024 IndiaSupreme Court: withdrawing life support allowed; active euthanasia illegalCourt 2018 UruguayEuthanasia for adults with terminal illness; law passed Oct 2025, decree reported April 20262025 to 2026, check PortugalLaw 22/2023 passed but not in force as of May 2026Pending FranceAssembly gave final approval on 15 July 2026; reported promulgated in August after constitutional review; check implementationPending England and WalesAssisting suicide remains a crime; a bill was reintroduced in 2026, second reading scheduled 11 September; outcome not verifiedPending Checked on 1 November 2026 against Wikipedia's "Legality of euthanasia" and news reports; the 2026 entries may have moved. Always check current law. Scarce resources: who gets the last bed No health system can give everyone everything. Rationing is not a question of whether but how: by price, by waiting, by clinical rules, by lottery, or by a body that decides what the public purse will fund. Norman Daniels's "accountability for reasonableness" says a fair process publishes its reasons, lets people appeal, and revises. In the first waves of COVID-19, hospitals in many countries wrote ventilator triage protocols, and the criticism that a rule favouring likely survivors quietly discriminates against disabled people showed how hard it is to be efficient and fair. Health economists use the quality-adjusted life year (QALY): a year in full health counts 1, a year in a worse state counts less, death 0. Dividing the extra cost of a treatment by the extra QALYs it gives yields a cost per QALY, compared with a threshold a health system is willing to pay. England's NICE has long used a range around £20,000 to £30,000 per QALY (check the current figure). Critics say QALYs undervalue life with disability; defenders say that without some measure, the loudest case wins. cost per QALY = extra cost ÷ extra QALYsQALYs = years × quality of life (0 to 1) Interactive · A fictional treatment against a threshold Years of life with treatment Quality of life with treatment (0 to 1) Extra cost (thousand units) Threshold (thousand units per QALY) Fictional drug. Without treatment, 2 years at quality 0.5 (1.0 QALY). Money units are arbitrary. Not a funding decision. With the sliders at their starting values the treatment gives 4 × 0.6 = 2.4 QALYs against 1.0, a gain of 1.4, for 60 thousand units: about 43 thousand per QALY, above a threshold of 30. Raise the quality to 0.8 and the gain is 2.2, the cost per QALY drops to about 27, and the answer flips. The number is only as good as the quality weights, which are value judgments. Other ways to think about it The four principles grew from American liberal thought, and they travel unevenly. Scholars in other traditions have asked what a bedside looks like when the unit is not the lone chooser. In ubuntu thinking, widely discussed in southern Africa and summed up in the Nguni saying that a person is a person through other people, decisions are shared with family and community, and a diagnosis may belong to the family before the patient. Confucian bioethics, discussed by scholars in China, Korea, Japan and Taiwan, often places the family at the centre and sees a decision made together as a form of respect, not a loss of autonomy. Care ethics, from Carol Gilligan and Nel Noddings, starts from dependence. Islamic medical ethics draws on the aims of the law (protecting life, faith, intellect, lineage and property) and on fatwas. Latin American bioethicists, including the Brazilian school around Volnei Garrafa, argue that bioethics must start from inequality and poverty, not only consent forms. UNESCO's 2005 Universal Declaration on Bioethics and Human Rights tried to find common ground across these. These are broad traditions, not national stereotypes: within every country, patients and doctors differ, and many families abroad want what the Anglo-American texts call autonomy. The lesson: ask the patient how they want to decide, and with whom. What a graduate just sees Any hard case becomes four questions: whose choice, what helps, what harms, what is fair. The answer is in how they are weighed. Capacity belongs to one decision at one time; an unwise choice is not an incapable one. Confidentiality is a strong default with known edges: consent, the law, a court, a serious danger to others. Almost every research rule is a scar from an earlier scandal. Withdrawing, withholding, helping and doing are not the same act in law, and the line moves by country and decade. Rationing always happens; the question is whether it is done openly and with reasons. Autonomy as drawn in textbooks is one culture's emphasis; ask patients how they want to decide. Where it shows up next Epidemiology & Evidence-Based Medicine (35/58): trials need consent and review boards; the Belmont principles decide who may be enrolled. Public & Global Health (35/61): quarantine, vaccination mandates and rationing apply the same principles to populations. Surgery, Anaesthesia & Emergency Care (35/62): consent in a hurry, and in emergencies with no one to ask. Genetics (35/46) and Clinical Psychology (35/27): shared genes and compulsory treatment raise the hardest confidentiality and capacity questions. In the world: hospital ethics committees, the courts, research ethics boards, health-data law, and every conversation about a living will. If you want to go deeper 📘 Textbook. Tom Beauchamp and James Childress, Principles of Biomedical Ethics (8th ed., Oxford University Press, 2019). The framework itself and the objections to it. 📘 Gentler. Tony Hope, Medical Ethics: A Very Short Introduction (Oxford University Press). A short, readable tour of consent, capacity and rationing. Also Rebecca Skloot, The Immortal Life of Henrietta Lacks (2010). 📘 On dying. Atul Gawande, Being Mortal (2014), a surgeon on what matters at the end of life. 🌐 Free reading. The Declaration of Helsinki and UNESCO's Universal Declaration on Bioethics and Human Rights; free online health-ethics and research-ethics courses are also hosted at OpenWHO. The takeaway Medical ethics is four old questions (whose choice, what helps, what harms, what is fair) asked again with the facts of each case, and a body of law that records what societies decided after learning the hard way. The answers move with place and time, so the useful habit is to ask the questions out loud. Try this: this week, think of the last time you or someone you know had a medical decision to make. Who was told? Who decided? Was it a choice or an instruction? Notice which of the four questions was missing. (This is reflection, not advice.) Sources & Further Reading Sources. Beauchamp and Childress (1979, 8th ed. 2019); Clouser and Gert (1990); Gillon. Mental Capacity Act 2005 (England and Wales; royal assent 7 April 2005, in force 2007). Schloendorff (1914), Bolam (1957), Montgomery (2015), Moore v. Regents (1990) and Tarasoff (1976, 17 Cal. 3d 425) as standard legal references; Tarasoff variations from an encyclopaedia summary. Tuskegee: US Public Health Service 1932 to 1972, 600 men, 399 with syphilis; AP story 25 July 1972; settlement of $10 million in 1974; Clinton apology 16 May 1997; Belmont Report 1979 (encyclopaedia summaries of primary sources). Lacks: 1951, 1975, 2013, 2023 (encyclopaedia summary). Declaration of Helsinki: 1964, eighth revision October 2024. End-of-life laws: Wikipedia "Legality of euthanasia" (read 1 November 2026) and news reports for France and England. NICE range as widely reported (check current). The interactives' numbers were computed in node. Not medical or legal advice. 🌐 WMA Declaration of Helsinki 🌐 UNESCO bioethics 📘 Beauchamp and Childress, Principles of Biomedical Ethics 📘 Gawande, Being Mortal Step 15. Foundations: What Mathematics Stands On ------------------------------------------------ Why: Sets, logic and infinity: where philosophy meets mathematics. Sets, logic and infinity: the three things every proof leans on, how they let you reach certainty about the endless, and the famous places where they run out. Ask a child for the biggest number they know, then say "plus one". You have just done mathematics. You did not check every number. You gave a short argument that works for all of them, and no list could ever match it. That move, certainty about something endless from a few steps of reasoning, is what a first mathematics course is really about. It is also a little frightening, because it asks what the steps are allowed to be. What counts as a legal move? What are numbers made of? Is there a largest infinity? Around 1900 mathematicians found that the loose answers they had used for centuries produced actual contradictions, and rebuilt the ground floor. What they built, and the discovery in 1931 that the building can never be finished, is what this course teaches. A graduate does not carry the axioms around. A graduate carries a feel for what a proof is, for which statements are slippery, and for the fact that "infinite" is not one thing. The course in one box Who takes itEvery mathematics major, in year 1 or early year 2, usually as an "introduction to proof" course (Cambridge's first-year Numbers and Sets is a classic shape). Computer science majors meet a lighter version as discrete mathematics. Logic and set theory then return as electives for people who want to go further. What it is forLearning the rules of the game (sets, logical statements, proof) so that every later course can be trusted, and learning where the rules stop. Comes afterDiscrete Mathematics (34/08). Leads toReal Analysis (34/72) and Abstract Algebra (34/73), and through them Topology (34/76), Number Theory (34/75) and Complex Analysis (34/74). What this piece gives youYou will not be able to write a formal set-theory derivation. You will know what a proof by contradiction feels like, why Cantor's diagonal argument works, why "the set of all sets" is not allowed, and what Gödel actually showed. Easier first reads: Infinity Comes in Sizes (12/16) and Gödel's Incompleteness Theorems (12/08). This one has you build the arguments yourself. Everything is a collection: sets A set is a collection of things, and the only question you may ask about a set is which things are in it. Order does not matter, repeats do not matter. {1, 2, 3} and {3, 2, 1, 1} are the same set. That sounds too thin to build anything on, yet by 1900 almost all of mathematics had been rewritten in the language of sets: a function is a set of input-output pairs, a number can be a set (zero is the empty set, one is the set containing the empty set, and so on), a shape is a set of points. The first surprise is how fast sets multiply. A subset is a collection you can form by picking some of a set's elements. For each element there are two choices, in or out, and the choices are independent. So a set with n elements has 2n subsets Five elements give 32 subsets; ten give 1,024; a mere 30 give over a billion. The collection of all subsets of S is the power set of S, and it will matter again when we reach infinity. Switch elements in and out below; each choice of in/out is a binary number, which is why the count is a power of two. Interactive · Build a subset Elements in the full set Without JavaScript: a set with 4 elements has 2 × 2 × 2 × 2 = 16 subsets, including the empty set and the whole set. With 6 elements there are 64. Logic: "for all" and "there is" do not commute A proof is a chain of statements, so the first skill is reading one exactly. Two phrases carry most of the weight. "For all" (∀) claims something about every member; one counter-example kills it. "There exists" (∃) claims at least one member works; one example proves it. And the order you write them in changes the meaning. "Everybody loves somebody" is: for every person, there is someone they love. "Somebody is loved by everybody" is: there is one person, whom all love. The first can be true while the second is false, if everyone loves a different person. The reverse never happens. This is the exact trap in the definition of a limit (next course): "for every ε there is a δ" is not the same as "there is a δ that works for every ε", and confusing them is how false proofs happen. Two more habits. To negate a statement, flip the quantifiers and negate the end: the opposite of "everybody loves somebody" is "somebody loves nobody". And an implication "if P then Q" is only broken by P true and Q false; it is equivalent to its contrapositive, "if not Q then not P" ("if the grass is dry, it did not rain"). Many proofs are easier backwards. Make your own relation below. Interactive · Who loves whom? Everyone loves the next person Everyone loves Dee Nobody loves anybody Rows love columns. Press a cell to change it. Without JavaScript: if Ann loves Bo, Bo loves Cy, Cy loves Dee and Dee loves Ann, then everybody loves somebody, but nobody is loved by everybody. If all four love Dee, both statements are true. Proof by contradiction: the biggest prime does not exist The most powerful single move in mathematics is to assume the opposite of what you want and watch it fall apart. Two proofs, both over 2,000 years old, show how it feels. Euclid gave the first in his Elements; the second is traditionally credited to the early Greek mathematicians. Infinitely many primes. Suppose, for contradiction, you had a complete list of primes. Multiply them all together and add 1; call it N. Divide N by any prime on your list and the remainder is 1, because the product part divides evenly. So no prime on the list divides N. But every number above 1 has some prime factor (that is the quiet fact the proof leans on), so a prime outside your list exists. The list was not complete. The trick is the "+1": it manufactures a number your list cannot reach. Note that N itself need not be prime; the proof only says a new prime divides it. The square root of 2 is irrational. Suppose √2 = p/q in lowest terms. Then p² = 2q², so p² is even, so p is even, say p = 2r. Then 4r² = 2q², so q² = 2r² and q is even too. Both even contradicts "lowest terms". The trick is choosing lowest terms first, so that a shared factor of 2 is forbidden. Interactive · Try to complete the list of primes Pick the primes on your "complete" list. The page multiplies them, adds 1, and factors the result. Without JavaScript: the primes 2, 3, 5, 7, 11, 13 multiply to 30,030, so N = 30,031. It is not divisible by any of them; it equals 59 × 509, two primes your list missed. Infinity comes in sizes: Cantor's diagonal Two sets are the same size if you can pair their elements one to one, with none left over on either side. That is how a child checks that every guest has a chair. Applied to infinite sets it gives strange results: the even numbers pair with all the counting numbers (2n with n), so there are "as many" evens as numbers. A set you can list as a first, second, third... item is called countable. The whole numbers, the integers and even the fractions are countable. In 1891 Georg Cantor published a short argument that the real numbers are not. Take any supposed list of infinite sequences of 0s and 1s (think: which numbers are in each set). Build a new sequence by going down the diagonal and flipping each entry: it differs from the first sequence in the first place, from the second in the second place, and so on. It cannot be anywhere on the list. The trick is making the new object disagree with the n-th item at the n-th place, so it differs from everything at once. Read each row of the grid as a subset of {1, ..., n}, and the argument becomes Cantor's theorem: no list of subsets of S, indexed by the elements of S, can contain every subset. The missing one is D = {x : x is not in its own row}. That works for any set at all, so the power set is always strictly bigger, and there is no largest infinity. The proof is the same one you can run on a finite grid. Interactive · The diagonal always escapes Size of the grid Shuffle the rows Each row is a subset of {1..n}: a filled cell means that number is in it. Press cells to edit. The bottom row is the diagonal, flipped. Without JavaScript: write any 3 rows of 3 bits. Flip the diagonal. The new row differs from row 1 in column 1, from row 2 in column 2, from row 3 in column 3, so it is not any of them, however you filled the rows. Cantor's names for the sizes: the countable infinity is ℵ0 ("aleph-null"); the reals have size 2ℵ0, which is bigger. Whether anything sits between them is the continuum hypothesis, and we will get to what happened to that question. Russell's paradox and the axioms Early set theory allowed any rule to define a set: "the set of all things that are red", "the set of all sets". Around 1901 Bertrand Russell asked about the set R of all sets that do not contain themselves. Is R a member of itself? If yes, then it is a set that contains itself, so by its own rule it should be out. If no, it is a set that does not contain itself, so it should be in. Either way, a contradiction. It is the barber who shaves exactly those men who do not shave themselves: who shaves the barber? Interactive · Who shaves the barber? The rule: the barber shaves every man who does not shave himself, and nobody else. Guess, then test. The barber shaves himself The barber does not Pick one. Without JavaScript: if the barber shaves himself, the rule says he shaves only men who do not, so he must not. If he does not, the rule says he must. There is no such barber, and there is no such set. Gottlob Frege, who had just finished the first great attempt to base arithmetic on logic, received Russell's letter at the worst moment. The repair that most of mathematics now uses is Zermelo–Fraenkel set theory (ZF, or ZFC with the axiom of choice). Zermelo's 1908 system replaced "any rule makes a set" with a safer one, separation: given a set A you may carve out the members satisfying a rule, but you cannot conjure a set out of thin air. Then {x in A : x not in x} is fine; it just turns out not to be a member of A. Fraenkel and Skolem sharpened the system in 1922 and added replacement. Its main ingredients, in plain words: AxiomWhat it lets you do ExtensionalitySets with the same members are the same set. Pairing, UnionForm {a, b}; gather the members of members. Power setAll subsets of a set form a set. InfinityAn infinite set exists (the counting numbers). Separation, ReplacementCarve out by a rule; swap members for their images. FoundationNo set contains itself, and no endless descending chain of memberships. ChoiceFrom any family of non-empty sets you can pick one from each. The axiom of choice is the one that has history. It is needed for many theorems (every vector space has a basis) and also gives weird ones, like the Banach–Tarski paradox of 1924, which cuts a ball into pieces that reassemble into two balls the same size. The pieces are not measurable, so nothing physical is violated. Most mathematicians accept it; constructive mathematicians, who insist on explicit constructions, do not. A graduate knows which of their proofs use it. What the rules cannot settle: Gödel and the continuum David Hilbert hoped for a single formal system strong enough for all of mathematics, provably free of contradiction, and able to decide every statement. In 1931 Kurt Gödel showed that this cannot be had. His first incompleteness theorem: any consistent system that can express basic arithmetic, and whose axioms can be listed by a computer program, has true statements it cannot prove. His second: such a system cannot prove its own consistency. The sketch has three steps, and the first is the one to see. The trick is to turn statements into numbers. Give each symbol a code, and encode a formula by raising successive primes to those codes. Now a statement about formulas is a statement about numbers, which the system can express. Second, with some work, "this number codes a proof of that formula" becomes an arithmetic statement. Third, build a sentence G that says, via the coding, "I am not provable". If the system proves G, it proves something false (assuming it is sound). If it does not, then G is true and unprovable. Try the coding yourself. Interactive · Turn a formula into one number UndoClearTry: S0 = S0 Without JavaScript: with the codes 0→1, S→2, +→3, =→4, the formula "0=0" is 21 × 34 × 51 = 810. Factor 810 and you can read the formula back. Gödel's result did not make mathematics unreliable. It said the foundations are never "finished". And it has a concrete sibling. The continuum hypothesis says nothing lies between the size of the counting numbers and the size of the reals. Gödel showed in 1940 that ZFC cannot disprove it (assuming ZFC is consistent); Paul Cohen showed in 1963, with a new method called forcing, that ZFC cannot prove it either. Set theorists still disagree about what that means: some hope a compelling new axiom will settle it, and others think it has no single true answer. As far as anyone can tell, the answer is not in the axioms we have. Two more statuses so you can tell open from closed. Closed: the incompleteness theorems and the independence of CH are proved. Open: whether any natural new axiom decides CH. And the earliest question we asked, whether ZFC itself is consistent, cannot be proved inside ZFC (if it is consistent), by Gödel's second theorem. What a graduate just sees A statement with "for all" is killed by one counter-example; one with "there exists" is proved by one example. The order of the two changes the meaning. To prove "if P then Q" you may prove "if not Q then not P"; to prove something never happens, assume it does and chase the consequence. A subset is an in/out choice for each element, so a set of n things has 2n subsets. "Infinite" is not one size. Pairing things one to one is the test, and the diagonal beats any list. "The set of everything satisfying X" is dangerous. Carve from a set you already have. Every proof starts from something assumed. The honest questions are which axioms, and what follows. There are statements, true or not, that a given system cannot settle, and that is a theorem, not a failure of effort. Where it shows up next Real Analysis (34/72): the ε–δ definition is nested quantifiers, and the real numbers are built from sets of rationals. Abstract Algebra (34/73): a group is a set with an operation, and everything is proved from axioms in the style you just met. Topology (34/76): a space is a set with a chosen family of subsets, and the axiom of choice shows up as a real theorem (Tychonoff's). Computer science: the diagonal argument reappears as Turing's proof that no program can decide whether every program halts. The same trick, applied to programs rather than numbers. Practice: proof assistants like Lean and Coq check proofs against a fixed foundation, exactly the "legal moves" idea made mechanical. If you want to go deeper 📘 Textbook. Richard Hammack, Book of Proof. The standard free first text on proof, sets and logic, offered online by the author. 📘 Textbook. Herbert Enderton, Elements of Set Theory (Academic Press, 1977). The classic next step into axiomatic set theory, if you want the real ZF development. 📘 Gentler. Agustín Rayo, On the Brink of Paradox (MIT Press, 2019). Puzzles from infinity to Gödel's theorem, with almost no formal prerequisites. 🌐 Free course. MIT OpenCourseWare 24.118 Paradox and Infinity (Spring 2019, taught by Agustín Rayo): infinities, paradoxes, computability and Gödel, built on his book. The takeaway Mathematics rests on three things you can now see: sets as the raw material, logic with its careful "for all" and "there exists", and proof as the only way to reach certainty about the endless. They explain the surprises (more than one infinity, a set that cannot exist) and the limit (no finite list of rules decides everything). Try this: this week, take any "always" or "never" claim you hear ("nobody reads anymore") and negate it exactly. Notice that the negation only needs one example. Sources & Further Reading Sources. Set counting, quantifier logic, Euclid's primes argument, the √2 proof and Cantor's diagonal/Cantor's theorem are standard textbook mathematics (Hammack; Enderton). Cantor's diagonal paper: 1891. Russell's paradox c. 1901, Zermelo's 1908 axioms using separation, and Fraenkel and Skolem's 1922 addition of replacement: Stanford Encyclopedia of Philosophy and the MacTutor biographies. Gödel 1931 (incompleteness); Gödel 1938–40 (CH consistent with ZFC); Cohen 1963 (CH independent, forcing): standard accounts; sources differ slightly on Gödel's exact year (announced 1938–39, monograph 1940). Banach–Tarski 1924. Course: MIT OCW 24.118 (Spring 2019). Every number the interactives show was computed in node: 2n subsets for n=1..6; 2·3·5·7·11·13+1 = 30031 = 59×509; 810 = 2×34×5. 🌐 MIT OCW 24.118 Paradox and Infinity 📘 Rayo, On the Brink of Paradox 📘 Hammack, Book of Proof