1. There is a widely held opinion that, in contrast with, say, mathematics, there are no demonstrative arguments, or proofs, in philosophy. This opinion is held, not just by those not well acquainted with philosophy, but also by many or even most of those whom we all, including they themselves, would identify as accomplished philosophers. One member of the latter group is William (Bill) Vallicella, the famous or infamous, depending upon one’s political point of view, blogger publishing so prolifically at Maverick Philosopher. I offer as evidence that my inclusion of him in that group is justified the statement, made almost in passing, in his January 23, 2018, post, the “The Two Opposites of ‘Nothing’ and the Logical Irreducibility of Being (2018 Version).”
I won’t be able to prove my point because nothing in philosophy can be proven.
An obvious first reply, of course, is that our maverick philosopher offers no argument here for, much less any proof of, the thesis that “nothing in philosophy can be proven.” But, again of course, that observation invites the equally easy retort that neither is it itself an argument for or a proof of the thesis that “at least one thing in philosophy can be proven.” The aim of the present post is to prove that at least one thing in philosophy can be proven and to prove it by, well, proving at least one thing in philosophy.
2. The philosophical thesis which I will prove is that God does not exist, at least if he, she, or it is the cause of all and only those causes that do not cause themselves. Virtually all who have degrees in philosophy, and many others besides, will recognize in that thesis a precise analogue of the thesis, long ago proven by Bertrand Russell, that there is no class that is the class including all and only those classes that do not include themselves. That does not concern me, for my aim is, as I have said, to prove that something in philosophy can be proven and to prove it by proving something. It is not my aim to argue, much less to prove, that I am an original thinker.
3. The proof is very brief. It involves, first, an assumption that there is such a God, then an observation that such a assumption leads to a falsehood, and then the conclusion that that assumption is false; an argument of this sort goes by the name, reductio ad absurdum. First, then, the assumption: There is an existent, God, which is such that, for any existent y, God is the cause of y if and only if y is not self-caused, i.e., y is not the cause of y.
From that assumption, it follows, since God is, ex hypothesi, an existent, that God is the cause of God if and only if God is not the cause of God.
It cannot, however, be the case that God is the cause of God if and only if God is not the cause of God, just as it cannot be the case that it is 5:00 pm in Massachusetts if and only if it is not 5:00 pm in Massachusetts and as it cannot be the case that Donald Trump is a patriot if and only if Donald Trump is not a patriot.
Therefore, it cannot be the case that there is an existent, God, which is such that, for any existent y, God is the cause of y if and only if y is not self-caused, i.e., y is not the cause of y. Q.E.D.
4. It must be understood that, on the one hand, this proof is a proof that there is no such God in reality. It must also be understood, on the other, that it is not a proof that God as otherwise specified does not exist.
5. The foregoing proof is a philosophical proof. Therefore, at least one thing in philosophy can be proven. Q.E.D., once more.
Until next time.
Richard
After Aristotle 
Greetings,
The argument is a sophism. the major should be distinguished:
1. God exists (assumption).
2. For any existent, y, *other than God*, God is the cause of y if and only if y is not self-caused.
from 1-2, the absurd conclusion doesn’t follow.
pax.
Thank you for your challenge. Let me think a bit.
The first summer semester has been concluded and the annual Fourth of July family get together has come and gone, so I now have time to get back to my blog. Thank you for your patience.
Try as I might, I cannot find a way out of the proof that I offered. And of course I can’t, for the assumption that some existent is such that, for any existent, the former is the cause of the latter if and only if the latter is not a cause of itself directly implies the necessarily false proposition that the former is a cause of itself if and only if it is not a cause of itself.
And, once more, of course I can’t, for the proof I offer runs in exact parallel to the proof that Russell offered that the assumption that some class is such that, for any class, the former includes the latter if and only if the latter does not include itself directly implies the necessarily false proposition that the former includes itself if and only if it does not include itself
Let me state emphatically the proof that I offered does not prove that there is no God. Perhaps a change in the wording, though not of the logic, of the two arguments will help. Thus:
The assumption that some existent is such that it is the cause of all and only those existents that are not causes of themselves directly implies the necessarily false proposition that the former is a cause of itself if and only if it is not a cause of itself. Analogously, the assumption that some class is such that it includes all and only those classes that do not include themselves directly implies the necessarily false proposition that the former includes itself if and only if it does not include itself.
Taken by itself, my argument leaves it entirely possible that there exists a cause that is the cause of all, but not only, those causes that do not cause themselves. That is, it leaves it possible that there is a God that is the cause both of all those causes that do not cause themselves and of him, her, or itself; that God would be self-caused, of course. And, correspondingly, Russell’s argument, taken by itself, leaves it entirely possible that there exists a class that includes all, but not only, those classes that do not include themselves. That is, it leaves it possible that there is a class that includes both all those classes that do not include themselves and itself; that class would, of course, include itself.
A final note: I’m not sure what basis you have for saying that my premise (and therefore also, I presume, Russell’s) “should be distinguished.”