Change and Identity Over Time

A poker goes into the fire cold and comes out hot. Nothing could be more ordinary, and stating what happened without contradicting yourself turns out to be surprisingly hard. The poker is the same poker. The poker is different from how it was. Both are obviously true, and taken at face value they say that one thing both has and lacks a property.

Two senses of same

The ambiguity has to be cleared before anything else can be said.

Twin sisters can be qualitatively identical and are certainly not numerically identical. There are two of them, and one can be in Oslo while the other is in Lisbon. Conversely, the poker before and after is numerically one thing and is not qualitatively the same, because it was cold and is now hot.

Ordinary English uses "same" for both, and almost every apparent paradox about change is powered by the slide from one to the other. Once the two are separated, the description of the poker stops sounding contradictory: it is numerically one and qualitatively different, and those are compatible.

Persistence and change

The second definition contains the important claim. Change is not two things differing. It is one thing differing from itself, and that requires the thing to be around for both readings. Replace the poker with a different poker and nothing has changed; something has been swapped.

This is why change and identity have to be treated together. An account of change presupposes an account of what makes the later thing the same as the earlier one, and an account that is too strict makes change impossible while an account that is too loose makes it trivial.

The principle that generates the problem

The principle looks unassailable, and it is very close to being so. If there is one thing there, it cannot both have and lack a property, because there is nothing for the difference to be a difference between.

It is also indispensable. Every argument for distinctness in metaphysics runs through it. Show that something is true of the statue and not of the clay, and you have shown that the statue is not the clay. Take that principle away and no such argument works.

The difficulty is that change is exactly a case where something appears to be true of a thing that is not true of it.

Something in that has to go, and each option has been defended.

The responses

The simplest response denies that the properties are what the second premise says. Being cold, on this view, is not a property the poker has full stop; it is a property the poker has at a time. Properly stated, the poker is cold-at-noon and is also not-cold-at-one, and both of those hold of it permanently. Leibniz's law is untouched, because everything true of the thing at noon is true of the thing at one o'clock, once the temporal qualification is written into the property.

The objection to this is that it makes shape and temperature into relations to times rather than ways the poker is in itself, which seems to get the phenomenon wrong. Being bent is not a relation the poker bears to anything. David Lewis pressed this as the problem of temporary intrinsics, and it is the standard test any account has to pass.

A second response qualifies the having rather than the property. The poker has coldness at noon and hotness at one, where the at-a-time attaches to the instantiating instead of to what is instantiated. This preserves the intrinsic character of the properties, at the cost of an account of instantiation that is more complicated than it first appeared.

A third response denies the first premise, but not in the way that would make change impossible. On this view a persisting thing is extended through time as well as through space, and has different parts at different times, in the way a road has different parts in different counties. The poker at noon is one temporal part and the poker at one o'clock is another, and there is no single thing that is both cold and hot, any more than a road that is narrow in one county and wide in another is both narrow and wide.

What has been established

The vocabulary is now precise enough to state the puzzles rather than merely feel them. There is a difference between being one thing and being exactly alike. There is a requirement that change involve one thing across two times. There is a principle about identity that no account can simply discard.

What has not been established is which response to the problem of change is correct. Each survives, each pays a price, and the price is paid in a different currency in each case.

The next article applies all of this to the case that has been used to test it since antiquity.