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 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.
original plank new plank
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).
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.
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.
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.
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.
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.
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).
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.
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).
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”.
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.
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. 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.