Friday, January 28, 2005

How Is a Statue Related to its Constituent Matter?

Our Trinitarian meanderings brought us to the statue/lump analogy as a possible way of making sense of the Trinity. But before we can use the relation of statue S to lump L of matter to understand inter-Trinitarian relations, we first need to understand the S and L relation itself. It became clear from my discussion with Joseph Jedwab that his view of this relation differs from mine. Let’s see if we can clear up this preliminary question.

It seems that there are exactly four combinatorially possible views of the relation of S to L. Before we plunge in, note that ‘S’ and ‘L’ are arbitrary constants, not variables: the first refers to a particular statue, the second to a particular quantity of matter, and indeed the particular quantity of matter of which S is composed.

1. S cannot exist without L, but L can exist without S.
2. Each can exist without the other.
3. Neither can exist without the other.
4. S can exist without L, but L cannot exist without S.

Ad 1. This is what I affirmed earlier. Thus a bust of Socrates cannot exist without being composed of some definite type of matter, say bronze, and indeed, without being composed of some definite parcel of matter. But melt the statue down, and that very quantity of matter will exist without constituting a statue. I took Jedwab to argue against this by saying that S can exist without L. Thus if a vandal removes part of Socrates’ left ear, then S continues to exist, while L does not continue to exist inasmuch as L, having lost a bit of matter, is no longer the very same quantity of matter. Mereological essentialism appears to be an operative assumption here, namely, the thesis that for every material whole W, and part P, if P is a part of W, then necessarily P is a part of W.

Perhaps I can handle the counterexample to the first conjunct of (1) by reformulating (1) as

1*. S cannot exist without some lump of matter M or other, but M can exist without S. (‘M’ is here a variable.)

Ad 2. Given that (1) is false due to the falsity of its first conjunct, then (2) must be true. But (2) is consistent with (1*).

Ad 3. This appears to be Jedwab’s preferred view. His reason seems to be that S and L share all the same proper parts. True, but there is more to S than its matter. S is formed matter. The form is not nothing since without it one does not have a statue but a mere lump of (non-statuesque) matter. Compare a state of affairs (STOA) and its ontological constituents, say, thin particular a, nexus of exemplification EX, and universal U. This STOA is not identical to the set {a, EX, U} or the corresponding mereological sum. And yet there is no further ontological part which, when added to the set, would result in the STOA. And then there is the chariot in which King Milinda rode to his debate with the monk, Nagasena. The chariot is not its parts nor something above and beyond its parts. The chariot is its parts in a particular arrangement, where the latter is not nothing, but also not some further part.

The point of the S/L example is that here we have a two-in-one, a bi-unity, or as I say, a binity. S and L are non-identical as per (1*) above. S and L cannot be strictly identical since S cannot exist without some matter or other, while that matter can exist without constituting S.

Ad 4. This combinatorial possibility is not a metaphysical possibility. A statue cannot exist without some matter or other.

To sum up. We have rejected (1), (3), and (4). This leaves (2). But (2) is consistent with (1*) which I claim expresses the relation of a statue to its constituent matter. This relation is not strict identity. What is it then, loose identity? A sameness relation distinct from identity?

I hope to take up this question tomorrow.