An Axiom Qualified is Not an Axiom; and the Pure Abstraction Which is Mathematics: Conversations with Tom (Part One)

Recently I engaged commenter “Tom” over at  What developed was an interesting discussion concerning the idea of “axioms in a specific context”…a concept which Tom introduced.  I’d never heard of a “contextual axiom” before, and upon musing for a bit, I realized just why that was.

It’s a contradiction in terms.  By definition, I submit, if something is an axiom, it cannot depend on context.  Axioms, I further submit, ARE the context by which everything man observes has a relative relationship with him and other objects in the universe.  They, themselves, are non-contextual, and thus, they are axiomatic.  They are fundamentally, irreducibly true as a matter of the whole of material reality.

When one begins to take the terms by which we organize a fundamental belief system and employ them inconsistently (which is usually a matter of convenience, in order to deceive), one inevitably travels the path of mysticism and despotism.  This is precisely the suicide/homicide mission Tom was on as he attempted to introduce a rank contradiction as the sound basis for a discussion of philosophy.  I was compelled thus to challenge Tom’s premise frankly, which I did…an action to which he did not take kindly, putting it mildly.

Whatever…his impugning of my motives as a means to short circuit the argument, or because he felt intellectually disadvantaged (that’s merely a self-esteem issue, not an issue of aptitude, by the way) is not the point here.  The point is that we must always be bold when we are confronted with those–well-intentioned or evil-intentioned–who would serve us the poison of logical contradiction while explaining its sublime health benefits.  This, I submit, is how the devil operates.  He gives you a rat and calls it a hat; and then lauds your smoldering epistemological wreckage as a holy virtue when you proclaim “humbly” your failure to rationally apprehend this “truth”.

This kind of thing must never go unchallenged, regardless of the amount of verbal (or physical or psychological) violence heaped upon us.  And Tom…er, heaped a LOT.

By the way, if you want further proof that despotic movements employ this tactic often and with great enthusiasm (that is, the redefining of words to fit their destructive doctrines), just look at how America’s neo-Calvinists discuss the term “antinomianism”.  It is a word that perfectly applies, with bulls-eye precision, to their own reformed theology and yet they use it as a pejorative descriptor of their theological enemies.  Their hypocrisy is a deep, deep well.


In this article I pull a few short excerpts from Tom’s comments–the relevant bits–and then proceed to explain my contrary position in some detail.  Much of the material which comprises these explanations was taken from my responses to Tom as seen on Spiritual Tyranny; however, I have elaborated and expanded, in some cases significantly, upon them in order to more precisely and fully flesh out my perspective.  Something which is difficult to do in a comments thread.


Tom said:

“In mathematics, one can produce Axioms that are relevant, well understood, and atomic within a context. Why can this not be done in Philosophy?

So, again, what do philosophers call a “Set of Axioms Defined and Relevant in a Specified Context?”

Tom said:

Wikipedia defines Axiom this way: “As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy.”

Within Christendom, “Jesus is Lord” is a premise so evident as to be accepted as true without controversy. So within Christendom, “Jesus is Lord” can reasonably be called an axiom.

There isn’t any such thing as a contextual axiom. “Contextual axioms” is a contradiction in terms. What this means is that outside of its context, the axiom is not in fact axiomatic. This makes the contextual axiom merely–and contradictorily–a relative posit. It’s the same reason the Bible cannot be infallible. “Infallibility” cannot have a context. As soon as you explain that the Bible cannot be used to fly a hundred people on the red-eye from Philly to LA the apologists start claiming context. And once they do that, they’ve already lost the debate, they just don’t know it because contradictions are endemic to their belief system, and so they spout rank nonsense, nod confidently as if to say “You see?! Simple!“, and then become confused, which quickly morphs into anger when you refuse to accept “mystery” and “paradox” as legitimate interpretive premises.

The Bible being infallible in context only means that it must be fallible outside of context. Thus, strictly speaking, the biblical infallibility apologists are attempting to argue that the Bible is both fallible and infallible at the same time. Which is of course impossible. These concepts are mutually exclusive. If the Bible is both of them, then it is really neither, by definition.  Absolute fallibility and absolute infallibility quite obviously cancel each other out.  And you are left with…zero.  Void.  Irrelevance. Biblical inerrant-ists are nothing more than Bible deniers.  They have no definition for the Bible, and thus, the can argue no purpose for it. Whether they know this or not is irrelevant.  It IS the case when you attempt to reconcile mutually exclusive ideas and present them as the “truth” of the Bible.  Denying the Bible as having anything practical to offer man’s life, or any efficacious philosophical value  may allow the voracious “Christian” ecclesiastical leadership to creatively contort its ideas in the interest of their horribly flawed and preconceived hermeneutic, but it is hardly honoring of the scriptures to do so.  The Bible, like humanity, is exploited in service to doctrine.  It is nothing more than a convenient means by which neo-Calvinist governing bodies satisfy their insatiable will to power.


The same is true for axioms. If the axiom is axiomatic in context (that is…the axiom is qualified), then the clear implication is that it is NOT axiomatic outside of context, and thus, is not in fact an axiom.  An axiom cannot be both irreducibly true and wholly untrue at the same time.  Once an axiom is no longer axiomatic–like a “contextual axiom” outside of its context–then it is no longer an axiom by definition. Further, If an axiom is considered both true and untrue simultaneously at any given moment, then it must be neither. Which means it has a practical and applicable value of zero.

A practical value of zero where exactly? Where ANY axioms actually matter…in the real world.  And reality is never contextual…reality…existence, IS context.  And since reality and existence is the sphere in which philosophy is wholly focused, philosophical axioms are the only ones which can be truly defined as such, because they are immutable, and irreducibly true, precisely because they cannot be considered contextual and thus cannot be considered qualified in any sense.  In other words, philosophical axioms are the only ones that are actually axiomatic, because they are irreducible truths as a function of existence itself. The existence of what IS is what philosophy and its truisms/axioms concerns itself with.

Now, this is not to argue that all philosophies are equally rational.  A cursory glance at some of the more common schools of thought (like Calvinism) prove this to be otherwise.  But the point is that philosophy, of whatever flavor, seeks a comprehensive explanation of the roots of human and universal existence, from the metaphysical (the IS of what is) to the aesthetic (how what IS is ultimately represented in a culture’s art).  Thus, the axioms in which philosophy dabbles are sprung from the roots of existence itself, and thus they are intended to provide the foundation upon which reality operates, BEING the very context of everything that is.

Though I recognize the controversial nature of the following statement, it must be made regardless:  Mathematics has absolutely nothing to do with reality or the universe as it exists materially and actually soIt is neither a product/extension of the objects and agents in existence nor is it a governing force of them.  On the contrary, it is purely a product of human cognition.  It is the apogee of human conceptual abstraction…it is abstraction in its purest form. It bears little resemblance as a field of study to philosophy even though some of the earliest philosophers where also some of the earliest physicists and mathematicians.  And I submit that this tradition of merging what I consider to be mutually exclusive studies is the seed of all manner of human destruction, war, bloodshed, paranoia, and political madness.  Ever since the earliest philosophers attempted to make mathematical law a causal force of universal and human existence, human beings have been relegated to the status of “by-product”.  An unfortunate blight upon an otherwise perfectly ordered reality.  Humanity’s free will, instead of being considered an act of natural perfection in and of itself, has been seen as an offense to truth and morality.  And ever since the causal force of mathematical law was thrust upon us in an act of pure insanity, man has been paying for it in blood ever since.  His free will is either punished relentlessly by becoming the very source of immorality itself, or it is tortured without mercy in an attempt to exorcise it from the human body so that the “laws of nature” may regain control of man…to stifle his wicked rebellion of SELF and to help him once again take his rightful place amongst the perfect order of the universe’s immaculate proofs.

Or, man’s free will has been declared an illusion.  A farce.  A cosmic sleight of hand for which man has fallen in his unique-to-creation gullibility (research  Spinoza).  Man, of all the animals, is the most vile and pitiful, because only man is stupid enough to believe that he is actually capable of thought and therefore volition.  And so many philosophies have concerned themselves with convincing man that he is not special.  On the contrary, he is the cosmos’s greatest blunder.  An imbecile.  A moron.  Worthy of death like no other animal on earth, because no other animal pretends that they are somehow above the natural and all-determining mathematical order.

Now, the hypocrisy and contradictions which rage perpetually across this kind of thinking like the wildfires of hell are stark and obvious once one grasps just a few key truths.  But dismantling this kind of bullshit is the topic of another article.  Suffice to say that the sacrificing of man to his own concepts, like mathematics, is a categorically evil thing.  And yet, as we can see in Tom’s comment, equating mathematical examples with the examples of reality is considered quite reasonable.  The reciprocity between pure abstraction and the material universe is simply self-evident.

This never ceases to amaze me.

In truth, mathematics is merely a way man organizes the relative movement of the things he observes in his environment.  Mathematics itself cannot be observed, obviously, because mathematics does not actually exist . Further, mathematics, being purely conceptual/abstract, is not causal…is not determinative. It is an effect of human existence and cognition, not a cause of them. Philosophy is the study of the nature of what IS, not an abstract method of organizing its relative movement.  Mathematics and philosophy are simply not the same thing, regardless of the amount of historical precedence.  Mathematics attempts to organize the relative movement of objects.  Philosophy attempts to explain how objects can relatively move in the first place.

Hence, Tom’s mathematical axioms are not actually axioms at all. They are a direct function of man and his material reality. As such, they are not irreducible…they, in a vacuum of themselves, are nothing at all. Axioms are observable truths as a function of what is real which are irreducible in any context because they precede context. They provide the reality by which everything else has context.

Tom said:


You misstate my position (straw man) and then prove that I am a moron by flogging the straw man…

However, let me try on my amateur philosopher hat for a moment.

Argo: If the axiom is wholly true in context, then the implication is that it is wholly untrue outside of that context.
Me: Really? In what universe does that naturally follow? Not this one.

Axiom: within the context of healthy, unmaimed, genetically normal cats, it is axiomatic that such cats have four legs.
Argo Bizarro Universe implication: no animal has four legs unless it is a healthy, unmaimed, genetically normal cat.
Argo Bizarro 2: Outside of the context of healthy, unmaimed, genetically normal, no cat has four legs.

As John Immel has said, we group concepts and abstract them. I DO NOT CARE what we call these things that are self-evident and not controversial. Wikipedia calls them “Axioms,” but please tell me what you would like to call them.

Tom quotes me thus:

If the axiom is wholly true in context, then the implication is that it is wholly untrue outside of that context.”

He then begins to take issue with my statement by providing examples of what he thinks I mean.  Frankly, his examples are obtuse at best and nonsense at worst and reflect literally nothing of the point I was making, but I’ll get to that in a minute.

My statement is entirely reasonable: If something is wholly true as a function of a specific context, then it can only be wholly untrue beyond of that context. By Tom’s own admission the salient point is not the axiom itself but the CONTEXT…that is, it is not that the axiom is in fact axiomatic, being the sum and substance of its own definition, but context is what makes the axiom axiomatic.  Which is a contradiction in terms because an axiom is axiomatic precisely because it cannot be qualified by context but simply IS (like, man IS SELF, for example)…that is, it is true because it is reflective of the absolute nature of existence of which it represents, and existence by definition is a-contextual.

But further examining Tom’s definition:  absent context, there is no way to validate the absolute nature of the axiom…and an axiom must be absolute and irreducible to be considered an axiom.   If it is absolute within context, then it is NOT absolute outside of context.  And the opposite of absolute is void…is nothing.  Is NON-truth.  Is irrelevance. Absent context an axiom is at best irrelevant, and thus NOT axiomatic…which is the same as saying it is false.  For there is no such thing as an irrelevant truth. That, like so many of Tom’s ideas, is a contradiction.

Therefore, what I was attempting to get across to Tom, using his own Wikipedia-cited definition, was that that axioms–non-controversial, self-evident truths–simply cannot be contextual. Because outside of context, they are NOT self-evident and NOT non-controversial. Which means they are not axiomatic…again, by Tom’s own definition.

For example, to say “Jesus is Lord” is an axiom, which Tom declared, according to the definition he provides (as an axiom within the context of the Christian church) is false, because “Jesus is Lord” is both controversial and non-self evident to those who do not identify themselves as Christians and do not identify with the Christian church.

Further, Tom’s ridiculous example wherein he attempts to mock me was a perfect illustration of the sporadic and disconnected nature of his thought:

“Axiom: within the context of healthy, un-maimed, genetically normal cats, it is axiomatic that such cats have four legs.”

This is not an axiom because, again, an axiom cannot be contextual. Being a cat is not a context, it is a SELF. It is an essence of being. It is an IS. It IS, absolutely, non-contextually, a cat. It is a materially existent THING. Tom believing that states of being, such as being a cat, imply a contextual existence is the utter root of his rank cognitive dissonance.  As though being what one IS is contextual to..well, to what, exactly?  I mean, seriously….what exactly is the outside context where a cat is not really a cat and thus the axiom of “being a cat who is healthy and therefore has four legs” could also exist in a contrary form…that is, where is the context of “outside the SELF of cat” where a “cat” could non-axiomatically exist?

I mean, this literally makes no sense unless one is a rank mystic attempting to proclaim a external-to-SELF-existence which is the source of all truth.   If the cat or any other agent or object (like man…who is really the only relevant object in the matter) is not absolutely a cat, it is nothing.  This is observably true…it is axiomatically true.  Except Tom does not concede this.  I submit that he is fully convinced that there is some “reality” outside the context of the SELF of objects and agents where they somehow are themselves, but also are not.  That is, their BEING what we observe them to be is purely an illusion, or part of the truth at best.  Reality itself or at least the relevant and salient “component” of reality  exists outside of the root metaphysical SELF of all objects and agents, and only there is “truth” found.  Thus, truth is never a function of reason or observation, but of divine, mystic revelation.  And that’s exactly the argument Tom is making, and either he doesn’t want to state it openly, or he is not really seeing it, blinded by his own assumptions.

Also, Tom accuses me of hindering the conversation.  This is merely subterfuge…an attempt to impugn my character and motives in order to distract from the issue at hand and his own serious logical flaws. This is either because Tom is pushing an agenda or he senses that he is intellectually out of his depth.  Personally, I don’t care which.  My point is that any reasonable person can engage disagreement with civility…it doesn’t take a genius to do this.  Hell, it doesn’t even take an adult to do this. A child can understand the basics of propriety and reasonable social interaction.

At any rate, I was clearly not stifling the conversation. I was attempting to take it to the next level by illustrating the contradictions which hinder the progression of logical thought. If we assume a contradiction can be true and then stumble on to the next step in our rank ignorance, then it is a truism to proclaim that we will never arrive at truth. And I understand Tom’s  desire to merely establish a new word if “I or John don’t like ‘axiom’” and move on, but the more important thing is to understand the foundational contradictions which undergird our thought process so that we can move forward from a place of reason. Otherwise, we are just circling the drain of mysticism yet again. And if I know anything at all it is this: Contradictions have a tendency to snowball in philosophy.  If contradictions are allowed to pass as legitimate benchmarks of truth then there is really no need for further discussion at all. We can all believe what we want and be lost in a sea of epistemological equivalence where everything is true and therefore nothing is ever true.

Stay tuned for part two.  Thanks for reading!

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