1. It is possible that nothing exists. (Assumption)

2. If nothing exists, then possibility does not exist. (Premise)

3. If possibility does not exist, then it is not possible for any state of affairs to obtain. (Premise)

4. (1) is a state of affairs that obtains. (Premise)

5. Therefore, (1) is false. (From 1 - 4)

I went on to argue, much less transparently:

6. The concurrent nonexistence of all contingent things is possible. (Premise)

7. Therefore, something necessary exists. (From 5 and 6)

Of course, the argument was (and is) very underdeveloped. It assumes things like "possibilities exist," which are at least relatively contentious. Also, the necessary entity of (7)

*prima facie*could just be the set of possibilities. As a more informed Thomist than I was then, I now recognize that possibilities or potentialities cannot obtain unless there is something actual. I then fell back on the argument from change.

I'm not certain that 5 follows from 1-4. ISTM that for the deduction to be valid, you need 2 to say 'if it is possible that nothing exists, then possibility does not exist'. But then you've clearly assumed what you set out to prove.

ReplyDeleteIn fact, the argument can be simplified even further:

ReplyDelete1'. Necessarily, possibilities exist. (Premise)

2'. It is possible for nothing contingent to exist. (Premise)

3'. Hence, it is impossible for nothing to exist. (From 1' and 2')

4'. Therefore, something necessary exists. (From 2' and 3')

As you mention, though, arguments such as these often have a tendency to assume the conclusion in one of their premises. In both arguments, the existence of possibilities is merely asserted. One could argue for it, however, but I'm not too interested in seeking out arguments for the existence of possibilities. I guess I was just reminiscing.

ISTM that in this formulation, 3' follows directly from 1'---it's not possible for nothing to exist if something (possibilities) necessarily exist. But then the issue isn't so much that you've assumed that possibilities exist as assumed that possibilities exist

ReplyDeletenecessarily.It's an interesting train of thought, though. I've made a recent post about ontological arguments inspired by this post.

Come to think of it, I do defend the necessary existence of abstract objects, especially on the grounds of their indispensability. See my previous post, where I place a special emphasis on the laws of logic. Possibilities (presumably being abstract objects) may also be indispensable, and that's a line of thought that hadn't occurred to me until I read your reply above. I'll formulate the argument in terms of a

ReplyDeletereductio ad absurdum, this time with the laws of logic.Prove A: Something has necessary existence.

Assume ~A: Nothing has necessary existence.

~A --> B: If nothing has necessary existence, then the laws of logic are dispensable.

~B: The laws of logic are indispensable.

Hence, ~~A: by modus tollens.

Therefore, A: by negation.

Q.E.D.