St. Thomas's Third Way seems obviously fallacious. Here's the text, divided (by me) into two parts:
- The third way is taken from the possible and the necessary, and runs thus.
- We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be.
- But it is impossible for these always to exist, for that which is possible not to be at some time is not.
- Therefore, if everything is possible not to be, then at one time there could have been nothing in existence.
- Now if this were true, even now there would be nothing in existence, because that which does not exist only begins to exist by something already existing.
- Therefore, if at one time nothing was in existence, it would have been impossible for anything to have begun to exist; and thus even now nothing would be in existence—which is absurd.
- Therefore, not all beings are merely possible, but there must exist something the existence of which is necessary.
- But every necessary thing either has its necessity caused by another, or not.
- Now it is impossible to go on to infinity in necessary things which have their necessity caused by another, as has been already proved in regard to efficient causes.
- Therefore we cannot but postulate the existence of some being having of itself its own necessity, and not receiving it from another, but rather causing in others their necessity.
- This all men speak of as God.
Part B is relatively straightforward, but Part A causes lots of trouble. Our first problem is in line 3: "that which is possible not to be at some time is not". One common line of interpretation understands this to mean that everything which is possible happens at some point in time. This is patently absurd, however. Consider for example an infinite past which consists merely of one ice cube floating through space, toward another ice cube, then passing near it, and floating away from it. In such a universe there could be an infinite past without every possible state of being having occurred already.
The correct interpretation of line 3 returns to the thought in line 2, which is about generation and corruption. Thomas's understanding of "possible not to be" in this case is related to a thing's being generated and corruptible. If something is, and is possible not to be, then it must be generated and corrupted. And therefore it must at some point in the past not have existed, and will again in the future not exist.
Next he says that "if everything were possible not to be", i.e. if everything were the sort that is generated and corrupted, "then at one time there could have been nothing in existence", and therefore "even now there would be nothing in existence". One line of interpretation takes him to be making an immediate deduction here: "if everything were possible not to be, then at some point nothing that presently exists existed, and if this were the case nothing would exist presently".
This line of interpretation is, again, ridiculous, because it neglects the possibility that there were previous things which were generated and corrupted, which generated the presently existing universe. Thomas does not address this objection, presumably (if we are generous, as we should be) because he sees it as obvious and easily dealt with. The response to the objection is, that such prior generating causes would have had to generate the stuff of the presently existing universe ex nihilo, and this action, because it requires an unlimited power to give things existence, is incompatible with something whose existence itself is contingent. Therefore if we are to sustain the assumption of a purely contingent universe, we cannot admit a necessarily non-contingent creator in the past, and have to assume that the universe was utterly void of existence at some point, prior to the generation of all presently existing things, their parts, and their fundamental matter. This is absurd, however, because it would imply that nothing presently exists (since nihil ex nihilo fit). And so there must be at least something which is permanent and at least conditionally necessary.
Then follows the second half, which is as straightforward as the first and second ways.