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.
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).
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.
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.
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.
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.
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 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.
It is valid, so you must give up a premise. Pick your response.
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.
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.
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.
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.
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).
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.
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.
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.
| School | Accepted means of knowing |
|---|---|
| Cārvāka | Perception only (as reported by opponents) |
| Buddhist (Dignāga, Dharmakīrti) | Perception, inference |
| Nyāya | Perception, inference, comparison, testimony |
| Mīmāṃsā (Kumārila), Advaita | Those 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.
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).
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. 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.