## Sunday, October 4, 2015

### The Modal Third Way

1. (x) (Cx □ → ◊ (t) ~xt).
2. (x) ◊ (□t) ~xt □ → ◊ (□t) (x) ~Pxt.
3. ~(x) (◊x □ → ◊(y) (x ^ Eyx)).
4. ~[(□x) ◊ (□y) Eyx □ → ~(□t) (x) ~Pxt].
5. ~Pxt → ~C(x).
6. :. ~C(x).
In English:
1. Every temporally contingent thing possibly fails to exist at some time.
2. If all things possibly fail to exist at some time, then it is possible that all things collectively fail to exist at some past time.
3. It is necessarily the case that possible truths are explicable.
4. It is necessarily the case that something is explicable if and only if there was not a time when nothing existed.
5. If there could never have been a time when nothing existed, then something temporally necessary exists.
6. Therefore, something temporally necessary exists.

1. I'm not convinced (1) as it stands is true. Suppose we've got a temporally contingent entity E whose chances of not existing at a given time t(n) are P(~E)=1/(10^10) (or any other sufficiently small number). Now, if I examine a probability space S of sufficient size, say w/ 10^20 seconds, then P(~E|S) =1, sure. But if I examine one with size, say, 5^10 seconds, then P(~E|S') = 1/2. So I think a phrasing which would make it more plausible would be:

1') Given infinite time every temporally contingent thing fails to exist at some time.

Now, if you run this with a probability space of countably- or asymptotically-countably-infinite size, then of course P(~E|S) → 1, (assuming something like the principle of plenitude as regards infinite time and infinitesimal possibilities). But then this argument can terminate equally well as a rejection of past-infinite time (which is, all cards on the table, how I like to run Thomas' argument).

Now, I agree that this is sort of a rephrasing, since I'm cashing it out in terms of probability instead of possibility. But I still think that the position holds when done in strictly modal terms. For instance, consider (2). If you restrict your consideration to past time, then it seems to me you've got to assume that it's possible, given a finite set of past instant, that there's an instant where all temporally contingent things fail to exist. But if we rephrase (2) as

2a. If all things possibly fail to exist at some time, and time is past-finite, then it is possible that all things collectively fail to exist at some past time.

then your opponent can simply say that, yes, given all infinite time, there is a time at which all temporally contingent things fail to obtain, but that the past is just a proper subset of that infinite set, and so your conclusion doesn't follow. If instead you go with

2b. If all things possible fail to exist at some time, and time is past-infinite, then it is possible that all things collectively fail to exist at some past time.

and then your premiss would be sound. But again, it's not clear whether the argument terminates as (6) or at the conclusion that time is not past-infinite.

2. Interesting thoughts, as always, Syllabus. The reservation I have is that premise (1) is true by definition. It's possible for a temporally contingent thing to fail to exist, even if it doesn't actually fail to exist.

The rest of your well thought-out post misconstrues the Third Way with the Modal Third Way. It's important to distinguish Thomas' Third Way with Robert Maydole's Modal Third Way.