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TIME CHANGE AND IDENTITY We often say something like the following: “That ship is the same ship we met on ten years ago,” meaning: “That 3-dimensional object is the same thing as the 3-D object we met on ten years ago” Or, more abstractly: Y at T2 is identical to X at T1 Reasons we might give: The ship has the same name Is docked at the same port Looks the same Is run by the same company Etc. 1 Leibniz’s Law Moreover: most of us feel that an object can remain one and the same thing even if it changes a little bit: The foghorn is replaced on the ship. Still, it is the same ship. But consider the following: Leibniz’s Law: If x = y, then every property of x is a property of y and vice versa. This seems obvious: if x and y have different properties, they must be different objects. E.g., two indistinguishable balls except one is heavier than the other. Clearly they are different objects. But: it leads to a problem… 2 Imagine the ship’s planks are replaced until we have all new parts. T1: T2: T3: T4: T5: ABCD (ship 1) ABCE ABEF AEFG EFGH (ship 2) Two options: 1. Ship 2 ship1. Rationale: Leibniz’s Law: Ship 2 has properties that Ship 1 lacks (and vice versa). Consequence: By the same reasoning, ABCE is not identical to Ship 1. Conclusion: loss of a single part destroys identity. 3 Second option 2. Ship 2 = ship 1. Rationale: Forget Leibniz’s Law! Let ship at T1 = X. X-1 plank is a very small change. So, X-1=X. But: X-2 = (X-1)-1 = X-1 = X. And so on… So, the ship we see today is identical to the one we saw 10 years ago. Similarly, each object along the way is identical to the original ship. 4 Problem: Ship of Theseus case. T1: ABCD (ship 1) T2 ABCE D T3: ABEF CD T4: AEFG BCD T5: EFGH ABCD (ship 2) (ship 3) Which is identical to ship 1? Sub-options: I. Ship 3 = Ship 1 Rationale: Only Ship 3 has all the properties of Ship 1(back to Leibniz’s Law?). Result: ABCE is not identical to ship 1. Conclusion: Loss of one part destroys identity. 5 II. Ship 2 = Ship 1 Rationale: Forget Leibniz’s Law (again)! As above: X-1=X. Problem: Ship 3 has all the parts of the original ship. It might even continue to be used to transport people on the same body of water. To favour ship 2 over ship 3 simply seems arbitrary. Conclusion: this position is arbitrary—it has no rational basis. 6 Further problem: Sorites paradox: We know it is possible to destroy a ship by removing planks So it must be false that for all n, X-n equals X. But there is no rational way to determine which n destroys identity—we can’t draw the line at how many planks destroy the ship. Conclusion: Since we know ships can be destroyed, and we know there is no way to determine how many planks will do this, the only rational position is to admit that loss of one plank destroys identity. 7 Grand Conclusion All the rational options lead to the same conclusion: the loss of a single part destroys identity. 8 A solution? “Intactly persisting temporal objects” (IPTO). X is an IPTO if and only if at all times during its existence it has exactly the same parts. So, ABCD, ABCE, etc. are all IPTO’s. They are all distinct: none is identical to any other (still have Leibniz’s Law). 9 How does this help? There is no IPTO that is identical to the original ship. So if we ask: is ship 2 or ship 3 identical to ship 1, the answer is “no”. But there is a non-IPTO that consists of ABCD-EFGH. If we ask: Is EFGH part of the same (nonIPTO) object as ABCD”, the answer is “yes”. Once we make this distinction, all our questions have definite answers. Problem solved? 10 Chisholm We can combine the IPTO’s into at least 10 “objects” Before we thought there were only two. So, which of these “objects” is the original ship—what were we originally referring to? This is an ontological “explosion”! Important questions still can’t be answered. Two positions: Identity realist: there is a definite fact of the matter. One of the two ships is the original. Conventionalist: There is no objective fact of the matter as to which is the original. It depends on the conventions we adopt. 11 Chisholm’s Identity conventionalism X at T1 is identical to Y at T2 if: Y evolved from X = at each step, common parts; not too much change. Every object that evolved from X and into Y was used for the same purpose as X (sailing). If other objects evolved from X, their function was different from those that became Y. I.e., only one “chain” continued along the same way – nonbranching clause. So: Strictly speaking, an object (ship) never retains its identity when it loses a part. What we call a particular ship, X, is really a collection of non-identical objects. We pragmatically decide to group them together into “X”. 12 Vagueness There may be borderline cases where it is not clear whether X and Y are identical. E.g.: two ships, Y and Z, evolve from X, i.e. at each stage, some parts overlap. Y and Z are each used to sail the same route on similar schedules. There is no clear answer as to which is the same ship: we must adopt a useful convention. T1 T2 T3 ABCD ABEF AIEF GHCD GHJD If both AIEF and GHJD have the same function, it is a matter of choice which to identify with ABCD. 13 Summary of Chisholm’s view X can be the same as Y even if strictly speaking X and Y aren’t identical. Strictly speaking, nothing remains identical when it loses a part. Identity over time is a matter of convention and overlapping of some parts. 14 Problem What defines a “good” rule? There is no philosophical ground for calling one good and another not good. Alternate conceptions have equal philosophical justification. E.g. tomorrow someone tries to steal your car. Your say, hey that’s my car. Reply: no, it’s not identical to the object you purchased. If Chisholm is right, this is just as correct as the view that it is your car. He favours the view that would call it your car, but there is no metaphysical ground for this. 15 Moreover, Chisholm’s view presupposes something, namely: That some things retain their strict identity across time, i.e. some things are IPTO’s In order to say one object is the same ship as another, we had to assume the parts of the ship remained the same across time. Otherwise, there could be no overlap and wouldn’t make sense to say one evolved from the other. So some things must retain their strict identity if conventionalism is going to work. Perhaps things without parts, such as elementary particles? Everything else, built out of them, is only “loosely” identical, i.e. by convention? Do you agree with this? 16 An Alternate Solution: 4-Dimensionalism Common view: Objects undergo changes in time, but remain self-identical: T1 T2 T3 T4 T5 Objects are three-dimensional They endure through time: i.e., the object is permanent from T1-T5 (so it retains its identity) but it also changes Smart, Quine and Lewis all reject this view. What’s the problem? 17 The problem with 3-dimensionalism Objects gain/lose properties all the time. So, only IPTO’s retain their identity. But things like wooden planks, metal bars aren’t actually IPTO’s – they can gain or lose atoms, molecules, etc. It seems that only elementary particles retain their identity over time. But that seems unnecessarily harsh. Why not alter our concept of objects instead of our concept of identity? 18 Four-dimensionalism Objects are spread out in time: they occupy four dimensions; they don’t endure through them (they perdure) Change isn’t remaining identical yet changing Change = time-slices of a 4-D object differing from each other Space Time T0 Birth T1 T2 T3 T4 P1 (x’ tall) P2 (y’) P3 (z’) Death 19 A solution? On this view, the ship at T1 is simply a (temporal) part of a 4-D object that stretches out over time. So, the ship at T2 is a different temporal part of a 4-D object. Such objects may even have “branching” structures such as the boat whose planks are replaced. So, what retains its identity is a 4-D object spread out in space and time. This entity never changes. Different parts have different properties. But this doesn’t violate Leibniz’s Law (no more a change than a plank being green at one end, red at the other). The whole 4-D structure never changes (no gain/loss of properties). 20 Problems 1. There are no objects in this room, only (temporal) parts of objects. 2. There is no “you” that survives one moment to the next. You are the collection of parts from birth to death. We’ll look at this more in the case of personal identity. 3. The parts of a 4-D object may reach back and forward in time infinitely. Are “objects” eternal? Quine: where you decide to draw the line and call something an “object” is simply the result of pragmatic considerations. There is no fact of the matter. 21