Monday, February 07, 2005

Another Ride on the Chariot

We have been discussing the doctrine of the Trinity, and our main concern has been one preliminary to the question of its truth, namely, the question of its conceivability. For if we cannot conceive it, or in plain English, think it, then we won’t know what we are affirming when we affirm it.

So we cast about for analogies and started in upon the physical analogies. (The mental or psychological analogies are arguably better, but for my didactic purposes, I decided to start with the cruder ones.) That brought us to the statue/lump analogy. The dialectic then drove us on to hylomorphic composition as such, and then to the apparently broader question of wholes and parts. At that point we took a ride on the chariot. The chariot is a classic Buddhist example invoked in support of the doctrine of anatta (Pali) or anatman (Sanskrit) according to which all samsaric entities are selfless, or devoid of substantiality. But this post is not about Buddhism.

Here are some theses on chariot-like partite entities. Let’s not worry about identity over time, but restrict ourselves to a consideration of partite entites at a time and the question of how they are related to their parts at a time. Ship of Theseus type puzzles may be placed on the back burner to simmer for the time being.

1. The chariot is not identical to any one of its proper parts. A proper part of a whole is a part that is not identical to the whole. Every whole is a part of itself, but not a proper part of itself. If I write ‘part’ without qualification, take it as elliptical for ‘proper part.’

2. The chariot is not identical to any collection of all or some of its (disconnected) proper parts, whether this collection be a set, a mereological sum, the extension of a list, the extension of a set if you care to distinguish the latter from a set, any logical construction (via the Wiener-Kuratowski procedure, e..g) from a set such as an ordered n-tuple. The reason for this non-identity is that the collection of parts can exist without the chariot existing. If that were not true, there would be no difference between an assembled chariot and the same chariot unassembled. The difference is real: Milinda can ride an assembled chariot into battle; he cannot ride a bunch of unassembled chariot-parts into battle.

3. The chariot is not identical to something above and beyond its proper parts. In other words, the chariot is not wholly diverse from its proper parts. After all, it is composed of them. If they don’t exist, it doesn’t exist. Chariots don’t have souls if by that is meant a self-identical immaterial something that can survive the destruction of its ‘body.’ The chariot is more than the sum of its parts, but it is not something wholly diverse from them.

Now here is the puzzle (and as I heard Roderick Chisholm once say, "You are not philosophizing until you have a puzzle"): Does the chariot exist or not? Each of (1)-(3) is indisputably true. Should we conclude that the chariot does not exist? Think about it: if the chariot is not one of its parts or all of its parts or something wholly diverse from its parts, then there is nothing to which it is identical, in which case, it is nothing at all.

To avoid this drastically counterintuitive conclusion, we might say that a fourth possibility has been overlooked:

4. The chariot is identical to its proper parts when these are properly connected.

Joseph Jedwab, however, objects: ". . .the chariot is neither identical to its parts nor identical to its parts in a particular arrangement. The chariot is one but the parts are many. No one thing is identical to many things. Composition is not numerical identity. In this sense, it is false to say the chariot is its parts in a particular arrangement."

I can’t agree with this. Although it is true that no one thing is identical to many things, when the chariot-parts are properly connected, they make one thing, namely, one chariot. A chariot and its parts properly connected are both one thing, one and the same thing. If Jedwab says that the parts properly connected are many, then I say that the same is true of the chariot: it is many in that it has many parts. A chariot is a whole of parts. As such, it is both one and many. The same goes for the chariot-parts properly connected.

Although composition, in general, is not numerical identity, we are at a point where the ‘is’ of composition collapses into the ‘is’ of identity. To say that the chariot is composed of its parts properly connected is to say that the chariot is identical to its parts properly connected.

But can we rest content with (4)? A chariot is not just its parts, but its parts PLUS their connectedness. The connectedness is not nothing, but it is also not a further part. If it were, a Bradley-type vicious infinite regress would arise. Nor is the connectedness identical to the chariot. As the connectedness of the parts, it is distinct from them both distributively and collectively, i.e., distinct from each of them and from all of them. And of course the connectedness is not something above and beyond the chariot.

The connectedness is not nothing, but it is also not something. It is not nothing because it is what makes the difference between disconnected chariot parts and a chariot. It is not something because it is neither a part of the chariot, nor the chariot, nor something wholly diverse from the chariot.

We are banging up against a tetralemma: each of (1)-(4) is reasonably rejected. I have already explained why each of (1)-(3) must be rejected. (4) is reasonably rejected on the ground that it entails a contradiction: the connectedness of parts in the chariot both is and is not something. Given this upshot, how can partite entities like chariots exist?

How can God be both one and many? That was our original conundrum. Well, how can a chariot, or any mundane partite item here below, be both one and many? After all, a chariot is both one and many. It is one chariot with many parts. What we have just seen is that it is very difficult to make sense of this. A partite entity is not a pure many. No entity without identity, to use a Quinean slogan in a non-Quinean way. The chariot is a unity of its parts. But this unity is not a further part, or the partite entity itself, or something wholly distinct from the partite entity. Will you tell me that a chariot is one and many in different respects? That it is one chariot with many parts? That is true, but it doesn’t explain how the oneness and the manyness fit together. Go back and study each of (1)-(4).

Now suppose we say this. The chariot exists, is actual, hence it is possible even though we cannot remove the threatening contradictions and show how it is possible. Similarly, the Trinity exists, is actual, hence is possible even though we cannot remove the threatening contradictions and show how it is possible.

What I am sketching, in other words, is a possible way of defending the rational acceptability of the Trinity and other apparently contradictory doctrines. If the apparent contradictoriness of chariots and material partite entities is compatible with their existence, then the apparent contradictoriness of the tri-une God is compatible with its existence.

Note that I am not saying that there are true or existent contradictions. What I am saying is that failure to remove an apparent contradiction (i.e., show that an apparent contradiction is merely apparent) does not show that it is irrational to accept the existence of the thing that exhibits the apparent contradiction.

Nor am I just announcing the the possibility of the Trinity is a mystery. That would be cheap and unphilosophical. What I am saying is that the possibility of obviously existent items like chariots is mysterious, and if this mysteriousness can be swallowed, then why strain at the mysteriousness of the Trinity?

And note that since solely the rational acceptability (not the truth) of the Trinity doctrine is at issue, it is not relevant to point out that the existence of chariots and such is given in sense-perception while the existence of the tri-une God is not.

In sum, the existence of the tri-une God is not ruled out by our inability to remove the apparent contradiction involved in a God who is both one and many, any more than the existence of Milinda’s chariot is ruled out by our inability to remove the apparent contradiction involved in material partite entities.

What say you, Jedwab, et al.? Have I proven the rational acceptability of the Trinity? Are we there yet?