PHIL2109 Contemporary Metaphysics
Week 5: Problems with Coincidence

The puzzle of the statue and the lump of bronze

  1. Suppose that a lump of bronze is formed into a statue. At the end of the process we have (a) a lump of bronze, and (b) a statue. Question: Are the lump of bronze and the statue (numerically) identical, or are they (numerically) distinct?
  2. Here is a reason to think that they are identical: If they were not identical then there would be two distinct things in exactly the same region of space (and composed from the same bronze particles); but this is not possible; so they are identical.
  3. Here is a reason to think that they are distinct: There are properties that one has but the other lacks; so, by Leibniz's law, they are distinct. Here are some such differentiating properties:
  4. So there is reason to think that the lump of bronze and the statue are distinct, but also reason to think that they are identical. This is the puzzle.

A response: Deny any difference in properties

  1. This is a tough response to make, because we must deny that there is any property that differentiates the lump of bronze and the statue.
  2. Here is one way to do it:

A response: Relativize identity

  1. As well as saying things like 'Superman is the same as Clark Kent', we say things like 'Superman is the same person as Clark Kent'.
  2. Here 'person' is a sortal term - it stands for a sortal. A sortal is a kind of substance: tree, planet, tiger, statue, lump of bronze, and so on. (So 'tree', 'planet', 'tiger', etc., are all sortal terms.)
  3. The fact that we say such things might show that identity is actually a 3-place relation (rather than a 2-place one), one of whose relata is a sortal. One thing is not identical to another thing, simpliciter, but only relative to a sortal. Proponents of relative identity claim that this is so.
  4. Moreover, they claim:

    It is possible that: for some substances x and y and sortals f and g: x is the same f as y but x is not the same g as y.

  5. That is, they deny the following:

    Necessarily: for all substances x and y and sortals f and g: if x is the same f as y, then x is the same g as y.

  6. Here is an example they might give: Suppose that the lump of bronze is melted down and made into a statue of a different kind. Then the first statue is the same lump of bronze as the second statue, but the first statue is not the same statue as the second statue.
  7. But:
  8. How is this supposed to help with the puzzle of the statue and the lump of bronze?

A response: Appeal to temporal parts

  1. Some appeal to temporal parts to respond to the puzzle of the statue and the lump of bronze.
  2. According to this response, the statue and the lump of bronze are 4D worms which have 3D temporal parts - one for each moment at which they exist. The statue and the lump of bronze are distinct 4D worms, but for a period of time they share temporal parts. Thus there is never a time at which two distinct things are wholly and exactly colocated.
  3. But here is a problem for this response. Suppose the lump of bronze and the statue come to exist at the same time, and cease to exist at the same time. So they have exactly the same temporal parts and are thus one and the same 4D worms (can they deny this?). But it seems that they still have different modal properties and thus must be distinct things. It also seems that they have different aesthetic properties.

One more response

  1. There is no such thing as the lump of bronze and the statue - all we have is bronze particles that become arranged statue-wise.
  2. This might ultimately lead to the view that all there are are simple (non-composite) things, such as the elementary particles of physics - there are no chairs, plants, humans and so on.

Constitution

  1. Suppose that the statue and the lump of bronze are numerically distinct objects that exactly coincide. Some say that although the lump of bronze is not identical to the statue, it constitutes the statue.
  2. Constitution is said to be an asymmetric relation: Necessarily: for all x and y: if x constitutes y then y does not constitute x.

    (A relation R is sometimes said to be non-symmetric just in case it is neither symmetric nor asymmetric. So it is possible that there are x and y such that x stands in R to y, and it is possible that there are x and y such that x does not stand in R to y. Note that being non-symmetric is different from being not symmetric.)

  3. Here is a proposed account of the constitution relation:

    Necessarily: for all x and y: x constitutes y at time t iff x and y exactly coincide at t, and every part of x at t is a part of y at t, but not every part of y at t is a part of x at t. (Does this assume that both x and y are complex - i.e. have parts?)

    It follows from this account that constitution is asymmetric - thought to be a point in favour of the account.

  4. According to this account, does the lump of bronze constitue the statue? We need the following three things to be true:

    Anyone who thinks that the statue is not identical with the lump of bronze but is constituted by it, will probably also think that the head of the statue is not identical with the part of the lump with which it coincides, but is constituted by it.

The problem of Tibbles and Tib

  1. Here is a case that is potentially more puzzling than that of the statue and the lump of bronze:
  2. Tibbles is a cat. Tib is that part of Tibbles which is everything but Tail, Tibbles' tail. Tibbles is not identical to Tib, because Tibbles has Tail as a part but Tib does not. Suppose that Tibbles loses Tail (which it can do, and still be Tibbles). Tib still exists. But now Tibbles and Tib exactly coincide.

  3. Why might this be more puzzling? Because it seems that some of the possible responses to the puzzle of the status and the lump of bronze are not possible repsonses here:
  4. Note that there seem to be fewer candidates for differientiating properties. Tibbles and Tib seem to be things of the same kind, and thus can equally well survive the loss of parts.
  5. One common objection is that although there is such a thing as Tail, there is no such thing as Tib (and hence no problem here). One difference between Tail and Tib might be that Tail could exist without Tibbles, but Tib could not.
  6. Note that if we accept that Tibbles and Tib are distinct things that are exactly colocated, then it seems that we have to accept that there could be any number of distinct things that are exactly colocated. Let Ti be that part of Tib which is everything except Ear, Tib's ear. Suppose that Tibbles and Tib both lose Ear. Then we have three distinct things that are exactly colocated: Tibbles, Tib, Ti.