I submit to you a proposed proof, expanded on a basis from David Hume, that nothing can be proven to exist, other than the mind, including God, thus eradicating the possibility of any proof based on knowledge (not based on arguments a posteriori, or based on empiricism) of a god's existence, including the traditional cosmological, ontological, and teleological arguments, et al.
As a preliminary, I only ask that we accept the laws of logic as knowledge a priori since otherwise nothing is communicable or tenable without. Of the laws of logic, I will only invoke the usage of axioms derived from intuitionistic logic, but claim knowledge of the excluded middle principle only as an indicator that a narrow acceptance of that which is logical still applies to the broader realm of sets of axioms of logic. I make mention of this exclusion of the excluded middle, and others, because it is debated whether it is tenable (see Quine's Paradox).
- The only way to prove something a priori is if its opposite implies a contradiction.
Let's first take a look at whether if the opposite of a statement a priori implies a contradiction, then the statement is true. Given logic, we have the law of (non-)contradiction. It says that two contradictory statements cannot be both true. Now, the only way to test an a priori statement is to subject it to other proven or accepted a priori statements. The only statement we've allotted a priori is logic, which means that we assume logic to be absolutely true. Therefore, if an a priori statement were to be true, then the opposite (being a priori itself) would have to be false, by the law of non-contradiction. If the opposite implies a contradiction with another statement a priori (for us we only so far have logic), then it must be false (because the other statement a priori is proven or accepted as true) and the original a priori statement in question is thus true. Thus if the opposite of an a priori statement implies a contradiction, the statement is true. Next we have to ask whether it is the only way.
Of the six axioms of logic, three of them (commutativity, associativity, and distributivity) say nothing about why a proposition would be true, rather it describes equivalent statements. Identity only says that which is, is. The excluded middle only says that which is not, given that which is, and whose use in a proof invokes the law of (non-)contradiction. Therefore, the only option left of logic is the law of (non-)contradiction or something derived from it. Thus, by elimination and the previous proof that contradiction of the opposite proves a statement a priori, we have that the only way to prove something a priori is if its opposite implies a contradiction.
- If something implies a contradiction, then it is inconceivable.
We, as human beings, are capable of logic, and that which is illogical is indeed inconceivable. You might say that surely you can conceive of say a square circle by simply the fact that you can say it. But it is not the phrase 'square circle' that is in question; it's the object the language is targeted at. An object cannot both have 4 sides and no sides. It's a contradiction and it's inconceivable. You might be able to come close in having 4 circles with radii approaching infinity thus giving the appearance of 4 straight sides of a square, but in actuality it is impossible (or inconceivable) to have a circle with 'infinite' size radii. We can think about it by abstracting from a finite case, but it can never be realized. Similarly, the Penrose stairs might give the appearance of stairs in a loop that always increase, but closer inspection shows that this is an optical illusion of perspective and could never be realized in three-dimensions, i.e. the 3-dimensional objected that our brains try to project when we view the 2-dimensional drawing is inconceivable (try it). More succinctly, you cannot conceive of something that both is and is not.
- Everything can be conceived not to exist, except the mind.
I did make one change to the traditional way this argument is made, and that is the part 'except the mind'. The only a priori that need exist is that thought exists and that there is a perspective that I call (or is called) me, or I. To paraphrase Descartes: "There are thoughts as viewed from a perspective that is called I." Why this might be the case is given by the statement in question. We require the ability for things to be conceived, which requires that there exists a mind (defined as nothing more than a thought or collection of thoughts) to do the conceiving (not as a descriptor of action). Thus, we require the small caveat of 'except the mind'.
What follows, then, is that the only thing we can ascertain is that there are thoughts which by all means does not necessitate for there to be a cause of these thoughts. I can conceive thoughts to just exist in a non-temporal 'existence' of which nothing exists but thoughts. Pain, laughter, anger, joy, etc. are all products of the mind which may always have existed in a determinate manner only as thoughts and not dependent on anything else existing. Thus all things that I might conceive to exist externally from my mind can also be conceived to not exist - them being merely thoughts. My body may be all an illusion, as might be the whole external world. Time may not be existent as I can never be sure that what I thought before wasn't merely what I always thought when I reflect upon it now. I might very well be a single state thought with an illusion of having previous thoughts (that being one of the thoughts I have now). Therefore, everything that might exist, apart from the mind, can be conceived to be only a thought, and thus can be conceived to not exist outside the mind (or to exist as merely a thought).
Now, I know a lot of this is deeply metaphysical and in all practical sense is easily disregarded. I won't pretend that I don't assume many things without knowing that they are true, but I will always acknowledge the valid objections to such assumptions. Since proofs of a god's existence definitively relates to metaphysics, it is proper when considering whether a god(s) exist to ask ourselves all the appropriate metaphysical dilemmas, of which this is one.
- Nothing can be proven to exist, apart from the mind, a priori, including God.
This is a direct result of our previous theorems. The proof is as follows using the law of (non-)contradiction: Assume, without loss of generality, that something X other than the mind can be proven to exist a priori. Then by #1, the opposite of X, namely that X doesn't exist, implies a contradiction. By #2, X not existing is inconceivable. But #3 says that everything can be conceived not to exist. So by #3, X not existing is conceivable. Therefore we have a contradiction. Therefore it is false to say that something X other than the mind can be proven to exist a priori. Ergo, nothing can be proven to exist, apart from the mind, a priori, including God.
This is the case for why a god's existence, or rather anything supernatural, is not provable, which should be indicative (or, rather, necessary) that all attempted and to be attempted proofs of god's existence based off necessity derived from a priori statements are both fallacious and futile.
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