PHIL2109 Contemporary Metaphysics
Week 3: Identity and Parthood

Identity

  1. Hesperus is identical to Phosphorus - they stand in the identity relation. We might say that Hesperus is Phosphorus, or that Hesperus and Phosphorus are identical, or that Hesperus is the same thing as Phosphorus, or that Hesperus and Phosphorus are the same thing, or that Hesperus = Phosphorus (technical language). These are different ways of expressing the fact that Hesperus is identical to Phosphorus.
  2. Identity seems to be a 2-place relation. But is it? If it is, then it seems to be a weird one:
  3. Assuming that identity is a 2-place relation, it has the following properties:
  4. Very plausibly we have Leibniz's law, or the the indiscernibility of identicals (I don't like this second name):
  5. We might also have (this is controversial) the converse of this, the identity of indiscernibles (is it the converse?):
  6. It is sometimes said that there are two kinds of identity: numerical identity and qualitative identity:

Parthood

  1. My left hip is a part of me - it stands in the parthood relation to me. Lots of things are a part of something - parthood is a ubiquitous relation.
  2. Since I have parts I am a composite thing. Lots of things have parrts, so lots of things are composite.

Replacement of parts

  1. We naturally think that a composite thing can have some its parts replaced. I might have my left hip replaced by an artificial one, or a watch might have its battery replaced by a new battery.
  2. Is there a limit to how many parts can be replaced? Can I have everything but my left hip replaced? Does the answer depend on how quickly the replacement happens?
  3. Suppose it is suggested that a composite thing can have no more than 10% of its parts replaced. Call this claim LIMIT. Here is an argument against LIMIT:
  4. If LIMIT is not right then we have either (a) a composite thing can have none of its parts replaced (this is mereological essentialism), or (b) a composite thing can have all of its parts replaced.

Disassembly and reassembly

  1. We naturally think that at least some composite things can be disassembled and later reassembled. Examples: Captain Cook's house, a bicycle.
  2. These examples are composite artefacts. What about composite non-artefacts, such as rocks and dogs: can these be disassembled and later reassembled? Does it matter which parts it is disassembled to (e.g. atoms)?
  3. In a case of disassembly and reassembly:

The puzzle of the ship of Theseus

  1. Case 1: renovation. A ship, call it Harbour1, is in the harbour at t1. Its parts are replaced one-by-one until at t2 they have all been replaced. The ship in the harbour at t2, call it Harbour2, is (numerically) identical to Harbour1.
  2. Case 2: moving. A ship, Harbour1, is in the harbour at t1. Its parts are moved one-by-one to a shed and then at t2 reassembled into a ship. The ship in the shed at t2, call it Shed, is identical to Harbour1.
  3. Case 3: combined. A ship, Harbour1, is in the harbour at t1. Its parts are replaced one-by-one and moved to a shed and then at t2 assembled into a ship. Which of the two ships, the ship on the harbour at t2 (Harbour2) or the ship in the shed at t2 (Shed), is identical to Harbour1?

Possible reactions

  1. Both ships are (i.e. Harbour2 = Harbour1 and Shed = Harbour1).
  2. Neither ship is (i.e. Harbour2 ≠ Harbour1 and Shed ≠ Harbour1).
  3. Harbour2 is and Shed is not (i.e. Harbour2 = Harbour1 and Shed ≠ Harbour1).
  4. Shed is and Harbour2 is not (i.e. Shed = Harbour1 and Harbour2 ≠ Harbour1).
  5. Here is another approach. When a part of Harbour1 is detached, it either is or is not still a part of Harbour1 (in the renovation case it is not, in the moving case it is). When a new thing is attached where that part was, it either does or does not become a part of Harbour1 (in the renovation case it does). Then we have the following four possibilities for the combined case:

Composition

  1. Take any bunch of things. Is there some thing of which they and only they are parts (i.e. that they compose)? Or is it only in certain cases? That is, is composition unrestricted or restricted?