Friday, September 14, 2012

Can two objects be in the same place at the same time?

To: Pearl K.
From: Geoffrey Klempner
Subject: Can two objects be in the same place at the same time?
Date: 1st May 2008 11:03

Dear Pearl,

Thank you for your email of 1 May, with your University of London Metaphysics essay in response to the question, 'Can two objects be in the same place at the same time? Justify your answer.'

This is really a question, as I read it, about the notion of 'identity under a covering sortal concept' as discussed by David Wiggins in his book 'Sameness and substance', which is based on his earlier monograph, 'Identity and spatio-temporal continuity'. You wouldn't have heard of the latter (which I studied as a student) but the other book is quite well known.

There is an issue about 'strict' identity, with some philosophers refusing to allow that ANY identity over time can be strict but this seems to defeat the purpose of having a notion of identity in the first place.

I agree with the way you pose the problem: there is a prima facie clash between the criterion of 'being in the same place at the same time' and satisfying Leibniz Law.

First major howler, two red balls which have all their attributes in common are still two red balls not one! (There is a story about how Leibniz got the courtiers at Hanover to search through the garden to 'prove' his thesis of the identity of indiscernibles by failing to find two perfectly identical leaves. Leibniz knew full well that his theory didn't require this.)

The point is it all depends whether you include spatial relation amongst the properties quantified over. If so, then Leibniz Law holds, but not otherwise. If being at a certain place IS a property of red ball A then this is a property that red ball B can't have.

Oops, but now it looks as though our two original criteria are collapsing into one another, as 'being in the same place' is now one of the properties considered in Leibniz Law!

However, there is still a tension here as demonstrated by the example of the clay and the statue. The question is whether being in the same place is *sufficient* for identity or only necessary but not sufficient.

Second major howler: we are not considering the lump of clay before it was made into a statue (when it looked like a lump!) but only after. In that case the lump of clay is exactly the same shape as the statue, how could it not be? So what are the grounds for saying that the lump of clay and the statue are not identical?

The grounds for saying this is that the lump of clay and the statue have different *criteria of identity*. Their identity comes under different sortal concepts, 'material' and 'artifact'.

Proof that they are different (by Leibniz Law) is that the material existed when the statue did not yet exist, and will exist after the statue is destroyed.

(There was a dispute between Peter Geach and Wiggins over the question of so-called 'relative identity'. Geach held that this example showed that the very same objects could be 'the same X' but not 'the same Y': e.g. A and B are the same material but not the same statue. There is general agreement that Geach was wrong about this: either A is identical to B or it isn't.)

What there can't be, according to Wiggins' account of 'identity under a sortal concept' is two objects which both fall under the same sortal in the same place at the same time.

What are your intuitions on this? I was at a lecture by Wiggins where he gave the example of two pennies. I have one in each hand, moving them backwards and forwards until they touch. Then, magically, they merge and part again. Is that logically possible? During the time when they merged (let's say completely) were there two pennies or only one? Does it matter if the weight is different?

As for the ship of Theseus, I think that this is a red herring (sorry about the mixed metaphor). It illustrates the point about identity under a sortal concept, which reinforces what Lowe says: the concept 'same artifact' supports the process of continuous repair and replacement, but not storage of parts and reassembly.

What one would say about the reassembled ship is that according to the criteria of identity for the sortal concept 'artifact', the ship came into existence when it was assembled. This does grind against our intuitions somewhat, because you don't want to say that your computer which was taken to bits while you were having your room decorated is a 'new computer' when it is reassembled (even if it does work better). The difference, however, seems to depend on the smallness of the 'bits'. If the plastic and metal were recycled and the material used to build a computer, then you would definitely say it was a 'new computer', even if it was exactly the same construction as the old one.

All the best,