The Ramifications Of Axioms

The only reason why many people regard talk about the basic nature of axioms as particularly deep is because it is generally rare to find people who engage in serious discussion about even the elementary aspects of reality.  The self-evident, self-verifying existence of axioms is the simplest, most foundational component of reality, and yet it is often overlooked.  Nevertheless, there is nothing incredibly deep about merely realizing or describing simple axioms, like how truth must exist because it would otherwise be true that truth does not exist.  This is because axioms are at the foundation of everything else: it is impossible for there to be anything more basic or fundamental.

Now, there are certainly truths about axioms that do possess a different kind of depth--and are quite esoteric, due to the near-universal ignorance of them.  There is not a single historical philosopher or theologian I know of who admitted the truths in question (which I will elaborate on below)--it is very common for there to be at least a handful of truths about a matter that are rarely discovered or discussed by even public intellectuals, however important those truths are.  It is often a simple thing to get someone to admit that truth exists, that a thing is what it is, or that contradictions are impossible, though there are people so incompetent at reasoning that they will deny even these necessary truths, and contradict themselves as a result.  But several precise things which follow from the necessary nature of these logical truths are almost never discovered or verbalized in any way.

Almost no philosophers or theologians (in the professional sense) seem to realize that logical axioms and laws are not only self-verifying and true by necessity, but also must remain in existence in the absence of all matter, consciousnesses, and other existents, like time.  Furthermore, the facts about metaphysics that follow from this are vital.  There are least four major ramifications that few will ever even mention.

• First, there is no such thing as absolutely nothing: even if matter, time, and consciousness cease to exist, logic still exists because it is impossible for it not to.

It is common for theists to say that God is the reason there is "something rather than nothing."  While it is true that there is an uncaused cause [1], which I call God, this entity cannot create what must exist by necessity.  If there was no God, it would be true that there is no God--meaning truth would still exist.  Truth, a function of logic, exists independent of any deity.  One could provide other examples of logical truths that exist independent of anything else.  The law of non-contradiction, for instance, exists by necessity if God does not.  After all, if God does not exist, then it cannot be true that God does exist.

In a godless reality there is no creation, but there is still such a thing as reality (that truth exists, that God does not exist, that the law of non-contradiction exists, and so on, are all logical facts about reality) and reality is what it is.  This means that the law of identity still exists.  It is true that there something that has both always existed and cannot not exist, but that thing is not God; it is logic and all of the laws therein.  Since logic has to exist and reality could not be any other way, the very notion of "absolutely nothing" is impossible.  However, it is not impossible because of the existence of God, as the next point emphasizes.

• Second, there is nothing impossible about God ceasing to exist, yet the same is not true of logic.

The uncaused cause of the physical universe (God) exists necessarily as long as creation does, since creation, being a caused, contingent thing, relies on its cause for its existence.  This does not alter the brute fact that there is nothing impossible about either creation or God suddenly vanishing into nonexistence.  Creation could disappear without God ceasing to exist, but the nonexistence of God would necessarily mean the nonexistence of creation.  I have already proven that logic cannot not exist.  God could remove himself completely from existence, but neither his existence nor his nonexistence can affect the necessary, independent existence of logic.  God is only necessary in that the existence of the universe and time, things with a finite and demonstrable beginning, logically requires an uncaused cause. 

• Third, the necessary existence of logic in the absence of all other things means that it is impossible for my mind to be the only thing that exists.

The fact that logic exists independent of all consciousness, including my own, means that I do not even need to establish than an external world of matter exists in order to know with absolute certainty that there is something that exists outside of my mind.  There is an external world of matter, and this is knowable with absolute certainty [2].  But even if there was no external world or if the external world could not be proven to exist, solipsism still cannot be true.  Since logic cannot cease to exist and exists independent of me, it cannot be a construct of my mind; I cannot legitimately say the same about matter itself, since it is possible but very unlikely that I am the uncaused cause without knowing it.  The very notion of solipsism is an asinine fantasy; the existence of matter is not even necessary for it to be proven false.

• Fourth, it is the necessary, independent existence of logic that makes it universally true.

If it was even possible for logic to not exist (which would be the case only if it was dependent on something external to itself), then logic would not have to be true, since it would be possible for it to not even exist to begin with.  However, logic must be in existence.  This provides the metaphysical basis for its universality.  Of course, people have to approach logic from the opposite direction.  They first realize that necessary truths must be true, because their absence or negation results in self-refuting and impossible contradictions, and then they realize this means that logic cannot not exist--even if the material world, human consciousness, and the uncaused cause vanish.  Any willing person knows the infallibility of logic by recognizing the self-refuting nature of denying it, even if they don't understand that logic is the one thing that must exist by its own intrinsic necessity.  It remains true that logic cannot have intrinsic veracity in any particular case if it relies on anything other than itself.

The core of all metaphysics is not God, but the laws of logic.

The ramifications of necessary truths that go undiscovered and unspoken during the majority of human existence are of immense significance, and because of this esoteric and important nature, they are my favorite aspects of axioms to contemplate and discuss.  Although the particular truths about logic that I have addressed here cannot be any other way, the reaction of many Christians to a recitation of such facts is vehement.  It is important for Christians to realize that nothing in the Bible contradicts anything I have said.  What these facts do contradict is the irrationalism of a great deal of the evangelical world.  However, if the Bible did deny even a single logical truth, including any of the logical truths explained in this article, then the Bible is false, not reason.  Christians can rejoice in the fact that nothing in Scripture denies even a single necessary truth of logic.

[1].  https://thechristianrationalist.blogspot.com/2017/04/the-uncaused-cause.html

[2].  https://thechristianrationalist.blogspot.com/2017/07/dreams-and-consciousness.html