Tuesday, February 08, 2005

Jedwab on Wholes, Parts, Composition, Identity, and Trinity

What follows are Joseph Jedwab's comments on yesterday's post, Another Ride on the Chariot. My remarks, per usual, are in blue. Jedwab's comments may be taken as a model of how philosophical discussion ought to be conducted.

1. I still think nothing is both one whole and many parts. Suppose there are two simples that compose one whole. How many entities are there here? Three. ExEyEz [x is a simple & y is a simple & ¬x=y & x is a proper part of z & y is a proper part of z].

BV: Although this makes sense, I find it counterintuitive. Suppose Sam Sixpack is at the supermarket to buy a sixpack. The fast checkout lane displays a sign that reads, "Six items or less." Sam may wonder whether he has one item or six items, but he surely will not think that he has seven items: the six cans plus the sixpack. Now suppose that each can when purchased singly costs one dollar. Sam will expect to pay six dollars for the sixpack or less, not 6 + 6 for the sixpack = 12 dollars total. But if he were buying seven items, the cost would be 12 dollars. Since the cost is not 12 dollars, Sam is not buying seven items. (Cf. D. Baxter, "Many-One Identity," Phil Papers, 1988, p. 200)

So I don't see that in your simpler example there are three entities. I think this is especially clear if 'entity' is being used univocally across 'x is an entity,' 'y is an entity' and 'z is an entity,' where z is the whole of which x and and y are proper parts. For z depends for its existence on x and y, but not vice versa. What you are implying is that x, y, and z are equally real. But they cannot be if z depends for its existence (reality) on x and y.


There are four possibilities:

A. A whole and its parts are equally real in one of two ways. Either (Aa) the whole is identical to its parts, or (Ab) the whole is distinct from its parts.
B. A whole and its parts are equally unreal.
C. A whole is real, while its parts are unreal.
D. A whole is unreal, while its parts are real.


I take you to be opting for (Ab): the whole and its parts are equally real -- which is why you count them as three entities -- but the whole is distinct from its parts.

But I have already argued against (Ab). A whole cannot possibly be something over and above its parts, something wholly distinct from them. A whole is composed of its parts, and thus existentially dependent on them. Although a whole of two parts is more than its parts, it is not a third thing. But you are taking the whole to be a third thing -- and that strikes me as a mistake, the same kind of mistake as when one takes a sixpack to be seven items.

2. Identity is reflexive and forces indiscernibility. And it is one-one: it is a two-place relation that holds between one entity and one entity. Perhaps it is many-many: perhaps it is a multigrade relation that holds between n entities and n entities, where n>1. For example, perhaps this is an identity claim: Locke, Berkeley, and Hume are the British Empiricists. But identity is not one-many or many-one: it is not a multigrade relation that holds between one entity and n entities, or between n entities and one entity, where n>1. Here are three more arguments. I shall assume there are composites.

BV: But I didn't say that a whole is identical to its parts, but that a whole is identical to its parts properly connected. You are making me out to be a reductionist, one who reduces a whole to its parts, but I'm not a reductionist. To reduce a whole to its parts is to eliminate the whole. Here, reductionism entails eliminativism.

3. Suppose composition is identity. Identity is permanent. So no whole can have different parts at different times at which the whole exists. But this is false. So composition is not identity.

BV: Again, I'm not saying that composition is identity. I am not saying that for z to be composed of x and y is for z to be identical to x and y. I am saying that both your hypostatization of z -- your treating of z as a tertium quid -- AND reductionism are to be rejected. Both of these are false: the whole and its parts are equally real; the whole is unreal, the parts alone are real.

4. Suppose again composition is identity. Identity is essential. So no whole can have different parts at different worlds at which the whole exists. But again this is false. So composition is not identity.

BV: Again you commit an ignoratio elenchi against me.

5. Finally, suppose there are simples that compose more than one whole, e.g. both a statue and a lump. And suppose composition is identity. Then the statue is identical to its simple parts and the simple parts are identical to the lump. So the statue is identical to the lump, contra the assumption that the simples compose more than one whole. So if there are simples that compose more than one whole, composition is not identity.

BV: Ditto.

6. If the chariot is identical to its parts when these are properly connected, it is identical to its parts and so the claim implies that composition is identity. I take it that you do not want to say that the chariot and its parts are temporarily or accidentally identical to its parts.

BV: The first sentence involves a non sequitur. If the chariot is identical to its-parts-properly-connected, it is precisely NOT identical to its parts.

7. Back to the Trinity. There are at least two ways to read your defence. Question: which way should I read your defence?

8. First, common sense says there are chariots and so I am entitled to believe in chariots. There is an apparent contradiction about chariots that I can't answer. But I trust common sense here more than I trust the reasons that lead, on the assumption that there are chariots, to contradiction. Scripture and tradition say that God is triune and so I am entitled to believe God is triune. There is an apparent contradiction about God as triune that I can't answer. But I trust scripture and tradition here more than I trust the reasons that lead, on the assumption of God as triune, to contradiction.

BV: This is the way I intended it. Mundane partite entities are apparently self-contradictory, but they exist. So the triune God, though apparently self-contradictory, might still exist despite its apparent contradictoriness. In other words, it is not irrational to accept the existence of the triune God even though it is apparently contradictory just as it is not irrational to accept the existence of chariots and the like even though they are apparently self-contradictory entities.

Part of what I am suggesting is that we are not forced into making Zenonian or Bradleyan moves: we are not forced to say, of motion, that it is not real just because we cannot make logical sense of it. (Wesley Salmon does not make logical sense of it -- but that's another post!) Nor are we forced to degrade mundane particulars to the status of appearances al la Bradley.

9. Second, here is a theory of the Trinity. The divine Persons compose God. The divine Persons are parts and God is the whole. As a chariot is both one whole and many parts, so God is both one God and three divine Persons. What's the problem? Michael Rea considers a relative identity theory of the Trinity like this. There is divine stuff, which we can individuate as one God or as three divine Persons. He says this is trouble: this is an anti-realist metaphysic, where something depends for its truth on theory or our individuating practices and so, in this case, the doctrine Trinity depends for its truth on theory or our individuating practices. Bad news.

BV: This is not what I meant. I already registered difficulties with thinking of God as divine stuff. I need to write a post on the ten or so senses of 'substance.'

10. Finally, don't believers in the Trinity want to say, not just that the divine Persons (taken together) are God, but that every divine Person (taken individually) is God? The theory does not deliver here.

BV: I agree!

Let me know if I have convinced you on points 1 and 8 in particular. Something tells me that I haven't. Your comments are excellent. Thanks very much.