The Unprovability of a God's Existence

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).

1. 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.

2. 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.

3. 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.

4. 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.

On Logic and Reason, the Bible, and A Priori Statements

The delving into metaphysics needs some clarification concerning objections to logic and reason.  The premise is the logic and reason are limited to understanding the true nature of existence because it's not possible to give the a priori statement in question because it requires that one uses logic and reason to conclude it.  I'm not going to argue against that objection because it is valid, though perhaps not conducive.  But I will argue against the Bible being the, or a, gap filler.

The first thing to look at is the premise that logic and reason are limited.  What this suggests is that while logic and reason are valid, they are limited to understanding the true nature of existence.  But what it does NOT say, and what I would suggest no one would claim, is that logic and reason is invalid.  Indeed, in order to have any sort of meaningful conversation, one requires the use of logic and reason to make communication coherent.  To accept logic and reason as tools of understanding is to accept that logic and reason are not contradictory, since by definition it necessitates non-contradiction.  Therefore, if there is a single exception arising from a separate a priori statement which removes the premise that logic and reason being valid, then logic and reason as a whole is invalid since it exists as a single a priori statement.  Since we accept logic and reason to be infallible (though human application of logic and reason is fallible) we must assume that should another premise invalidate the premise that logic and reason are valid, then we would throw out the other premise.  For a simple example, think about the premise that addition is valid so that one and one make two.  If we suggest a separate premise that gives rise to us concluding that one and one makes three, then we assume this separate premise is invalid, not the premise of addition being valid.

To summarize, I would suspect that we all believe logic and reason to exist and to be valid.  At the very least, logic and reason is therefore a subset of our understanding of existence.  To find an exception to logic and reason is to invalidate logic and reason.  We assume logic and reason to be valid.  Therefore, any premise that would invalidate logic and reason is invalid itself, and logic and reason remain.

Now the argument of the Bible comes into play.  The premise suggested is that the Bible gives truth to our existence (from here on out referred to as BB) beyond the limitation of logic and reason.  If we can find that this new premise leads to a contradiction with the premise of logic and reason, we will assume that the premise of the Bible is invalid.

As it goes, the Bible is in fact contradictory in its literal form and thus would necessitate an exception to the a priori of logic and reason (from here on out referred to as L&R).  Therefore we automatically can reject the idea that the Bible gives truth to our existence in its literal form.  Thus, in order for BB to hold weight, we must assume that the Bible must be interpreted.  As it is, the Bible has been interpreted many different ways that are mutually exclusive, as evidenced by the number of denominations of Christianity.  Since they are as whole mutually exclusive, they cannot all be correct and furthermore only one or few (if some small set of the denominations are not mutually exclusive) can be correct because otherwise they would constitute an exception to L&R.  Since this is the case, there is a very small minority of people (if any) who interpret the Bible who are correct in its interpretation.  But here's the kicker.  Roughly at least one person who follows any single interpretation will be just as convinced (or at least it cannot be proven otherwise) as someone else with another interpretation.  So how do we know which interpretation is the correct one?  In what capacity can we measure which interpretation is correct?  There is no answer to this and thus one can never assume to have the one true interpretation.  For any a priori statement to be made, it must be clear (i.e. not vague) and the very meaning of the a priori statement would have to be agreed upon or obvious, though not necessarily accepted.  Therefore, BB needs some extra clarification, specifically that it would be necessary to transform it to say that "a specific interpretation of the Bible, as written , gives truth to our existence" (from here on referred to as IB).

There's not much to say (that I know of) to someone who considers their interpretation to give rise to the IB in question.  All one can say is that there are perhaps an infinite other possibilities which could take the place of any particular IB (including other IBs) and it would suggest a delusion of grandeur for one to admit that only his/her interpretation is the true interpretation, though not invalid.  The only way to avoid this is to not accept L&R, which I again would suggest no one ought to or would do.  As it stands, the correct interpretation cannot be discovered by other a priori statements that don't have the same problem themselves, i.e. there is no objective means to discover the correct interpretation.  Since, then, very few people will agree to accept anyone's particular IB, it doesn't stand as a very strong a priori statement.  Moreover, interpretation requires another a priori of subjectivity, since interpretation is specifically subjective.  Specifically, one would require an a priori statement which decrees that subjective statements can be decided as true (from here on referred to as ST), for if it cannot be decided as true then no person can claim that their interpretation is correct, which implies that no person may claim any particular IB.  ST really opens up a whole floodgate of statements based on subjectivity including but not excluded to: faeces taste good as fact or theism is a good thing as fact (who's to say that these are not true?).  From merely an argument of absurdity, it would suggest that ST is not a valid a priori statement, and thus neither can an IB since it requires ST.

To summarize, BB is not sufficient in literal form since it would require an exception to L&R.  Thus, BB must be specialized to an IB.  IB is not self-evident, and requires ST.  ST leads to absurd statements (suggesting an exception to L&R) so we would/should not accept it.  Therefore, since IB relies on ST and ST is presumed not valid, IB is not valid.  Thus, BB in any form is not valid since it leads to an exception of L&R which no person ought to or would do.  Ergo, the Bible does not and cannot fill the gap (if it exists) where logic and reason leave off.