Shayne Wissler
“… to understand is, above all, to unify.” – Albert Camus

The Axiom axiom

October 10 2014

(The following is an excerpt from REASON and LIBERTY.)


“Is there any knowledge in the world which is so certain that no reasonable man could doubt it? This question, which at first sight might not seem difficult, is really one of the most difficult that can be asked. When we have realized the obstacles in the way of a straightforward and confident answer, we shall be well launched on the study of philosophy – for philosophy is merely the attempt to answer such ultimate questions, not carelessly and dogmatically, as we do in ordinary life and even in the sciences, but critically, after exploring all that makes such questions puzzling, and after realizing all the vagueness and confusion that underlie our ordinary ideas.”

— Bertrand Russell The Problems of Philosophy (1912), Ch. I: Appearance and Reality

Your basic choice as a human being is whether or not to choose to “make sense” of your experience. What does it mean, to “make sense”? The clue is given out of the mouths of babes, in their question: “Why?” Once they learn that things have explanations, their desire to know is so strong that the constant questioning they produce can overwhelm adults. This natural yearning is at the foundation of philosophy, or as Aristotle wrote in Metaphysics (which in his understanding of the term meant “first philosophy”): “All men by nature desire to know.”

Plato held that knowledge is “justified true belief.” To believe is trivial; to know requires an often very difficult process: thinking. Thinking is not always productive, but always has the same aim: to know. What thinking produces is a link between a belief in question, and a chain of reasoning that supports it. This is the belief’s justification.

The choice to think or not is a gift that no other creature on earth but human beings have. Authentic philosophy is rooted in the choice to think – to produce reasons why. Pseudo-philosophy is rooted in the opposite choice: to believe without reasons.

To “justify” an idea is to present a reason why the idea is true, a means by which, if we follow a rational process, we can in some sense rightfully proceed from one idea to another. Since reasons are themselves ideas, we can apply this concept to the proffered reason why as well. This leads to the idea of “infinite regress” – an unending series of “whys”. But if there is an infinite regress, then because we are finite beings, there can never be a rational explanation for any idea, and the idea that there could be knowledge would fall. Even the idea that there is no justified knowledge would itself be unjustified. Therefore, if there is knowledge, there must be a justified end to the series – these terminals in the series are “axioms.” But by definition, axioms can’t be justified in the sense of providing reasons why. Can they be otherwise justified or are they merely arbitrary postulates?

A person who rejects axioms as justifiable, per se rejects knowledge. His rejection of axioms constitutes a belief that they are unjustifiable, and while he may offer “reasons” for this belief, ultimately, these are, by his own stipulations, necessarily without foundation. Usually, he admits as much. For him, philosophy is an idle entertainment or a game, but it has nothing to do with truth, and he will often cynically (and usually with an air of self-righteous superiority) view those who think otherwise as deluded. But why indeed is he justified in making all of these assessments? In the end, he must admit that everything he believes or assesses is merely accident or whimsical preference, for on his view, there really is no such thing as philosophy qua “love of wisdom.”

Just as one can choose to live or die, one can choose to accept the preconditions of knowledge or not. And one of those preconditions is: there must be justified axioms. How are they justified? In fact, we just justified one, the “Axiom axiom”: Knowledge is rooted in axioms. We determined that rejecting this axiom repudiates all knowledge, including the “knowledge” that knowledge has been repudiated. This is the hallmark of a justified axiom – that rejecting it is self-defeating. You may indeed decide that you don’t care if you have defeated yourself, but this decision evicts you from the realm of authentic philosophy. Just as truth is of no interest to you, you are of no interest to those who love truth.

Axioms are interrelated and interdependent; for example, the foregoing axiom presupposes that we can know and mean (these axioms will be elaborated on later). We depend on axioms at every step, and thus while we can analyze them separately, they are simultaneously and at least tacitly assumed at every point in the analysis.

People who claim to know anything whatsoever believe in axioms regardless of whether they admit them or not; the question is whether those axioms are justifiable (i.e. rejecting them constitutes a self-defeating position) or not: If you ask the reason why they believe anything, and then ask why they believe that, and so on, you will find that they either land at a proposition they have not yet explained, meaning they believe in at least this one axiom, or they will go in a circle, which means they believe in many. The choice then is not whether we shall have axioms or not, but in what our choice of axioms is.

In rational philosophy we seek axioms that are as simple and irreducible as possible, and that are implied in all discourse whatsoever. Axioms aren’t arbitrary, nor are they “self-evident” in the sense of being obvious, but they are self-evident in the sense that you must become aware of them through your own first-handed appraisal. They are not empirical in the sense of being externally measurable, but they are empirical in the sense that to notice them is to observe, and the unit of observing is an observation, a moment in time in which you are paying attention to something. What is the object of observation? Your own thought.

The alternative to explicitly recognizing axioms is not that they aren’t there, but that one takes an unanalyzed complexity of judgment calls about what is and isn’t true as axiomatically reliable and valid. Thus, a denial of axioms constitutes the implicit and extraordinarily arrogant subjectivism of asserting that one’s own judgment is the ultimate axiom (this move is not substantially altered when one alludes to external authority, since implicitly, the ultimate authority is the one who decrees who the authorities are).

“[A] Philosopher who affects to doubt of the Maxims of common Reason, and even of his Senses, declares sufficiently that he is not in earnest, and that he intends not to advance an Opinion which he would recommend as Standards of Judgment and Action.”

— David Hume

In the foregoing is a recurring theme in rational philosophy: there are beliefs that when analyzed, permit one to remain in the realm of rational philosophy, and beliefs which if decisively accepted, mean that one has evicted oneself. Most of the unnecessary tragedy in our past was caused by heeding the words of charlatans, and could have been avoided if society had accepted this principle. If we wish to avoid needless tragedy in the future, we must choose to accept it.