The MTW Reformulated
1. Necessarily, two possible propositions that do not yield a contradiction when in conjunction with one another are compossible. (Premise)
2. Possibly, something presently exists. (Premise)
3. Possibly, there was a past time at which nothing contingent existed. (Premise)
4. Necessarily, if there was a past time at which nothing existed, then nothing would presently exist. (Premise)
5. The conjunction of (2) and (3) does not yield a contradiction. (Premise)
6. Possibly, something necessary exists. (Implied by 1 - 5)
7. Therefore, something necessary exists. (From 6 and S5)
The Argument's Validity
Assume (8): something necessary does not exist. (8) and S5 imply (9): it is not possible for something necessary to exist.
However, we know from (1) and (5) that (10): "something presently exists" and "there was a past time at which nothing contingent existed" are compossible. Let's call this possible world w1. In conjunction with (4), it follows from (10) that (11): there was never a past time in w1 at which nothing existed. Since the only remaining entity that could exist at the time that all contingent things failed to exist is something necessary, it follows that (12): something necessary exists in w1. Because (12) contradicts (9), we may conclude that (9), as well as (8) by extension, are false. Therefore, something necessary exists.
Q.E.D.
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I'd dispute the ability of standard modal logic to express premise 6 (self-promotion: I've extended the language to cope here: http://bit.ly/xU0uXy /self-promotion)
ReplyDeleteStandard modal logic can express modalities (modal qualifications of entities) it has nothing to express meta-modalities (the modal qualification of a modal qualification of an entity)
I think 5 should read:
ReplyDelete5. The conjunction of 'something presently exists' and 'there was a past time at which nothing contingent existed' does not yield a contradiction. (Premise)
I am worried about 1. By "contradiction", do you mean a contradiction in the narrow logical sense?
I'm not sure what the difference between (5) and your revision of it are, but I see no problem with the revision.
ReplyDeleteIn (1), I had in mind a broadly logical contradiction. I take it that few would deny that the two propositions are narrowly logically compossible. It's just that once the latter is established, it seems to me that their broadly logical compossibility ought to be granted barring any defeater. What do you think?
a. The difference is that your (5) says that 'It is possible that something presently exists' and 'It is posisble that there was a past time...' do not yield a contradiction.
ReplyDeleteb. I am worried about step (5) then. Two things can be narrowly compatible while being broadly incompatible. Consider these two propositions:
A. The only egg ever to exist is caused by the only dragon ever to exist.
B. The only dragon ever to exist is caused by the only egg ever to exist.
Then, A and B are metaphysically possible, and they are not logically narrowly contradictory, but they are broadly contradictory, since nothing can be a cause of itself.
c. If you're talking about broad contradiction in 5, you don't actually need premises 2 and 3. For if p and q are not broadly contradictory, then they are each possible, and compossible, too.
I think the egg/dragon example would be an example of a broadly logical contradiction, as you say, because a defeater can be presented (e.g. nothing can be the cause of itself). The question is then whether (5) can be defeated in a similar fashion. I don't know of any forthcoming arguments, but I could be overlooking one.
ReplyDelete(2) and (3) may be superfluous, but I included it in order to keep focus on the individual propositions.
I guess a revised version of the argument would look like this:
1. Necessarily, two possible propositions that do not yield a broadly logical contradiction when in conjunction with one another are compossible. (Premise)
2. Necessarily, if there were a past time at which nothing existed, then nothing would presently exist. (Premise)
3. "Something presently exists" and "there was a past time at which nothing contingent existed" are compossible. (Premise)
4. Possibly, something necessary exists. (Implied by 1 - 3)
5. Therefore, something necessary exists. (From 4 and S5)