The Importance Of Axioms

I once said that the intrinsic authority of logical axioms is not a particularly deep matter [1].  In stating this, I did not mean that the self-verifying, necessary nature of logical axioms is trivial, nor did I mean that the basic subject of logical axioms is shallow in any way.  Instead, I only meant that the basic nature of logical axioms (as opposed to the more esoteric ramifications I elaborated upon after that comment) is the simplest, most accessible part of reality.  This nature is the foundation upon which everything else stands.

All aspects of reality hinge on the preexisting, necessary nature of logic.  In this sense, nothing could be more fundamental or important.  A fact possesses depth to the extent that it is precise, important, or both of the aforementioned things.  Recognition of the self-verifying nature of logical axioms is therefore recognition of something deep--however, this is only the start of developing a full rationalistic worldview.  It is not that this first step in sound philosophy is unimportant or shallow, but that, in itself, it is only a first step.  It is merely a step that many people never wholly take.

In many cases, people mistake a simple truth for a deep one because it is uncommon for them to think or talk about it at all, or they do so because they discuss issues that might be genuinely deep, but in shallow ways.  These illusions of depth often keep people from confronting genuine depth, as they discourage them from either accidentally stumbling into it or intentionally discovering it.  When a person is intoxicated with simplicity, they might fail to recognize the need for thoroughness, precision, and consistency.

While it is true that many people are quick to treat anything more complex than the most basic truths as if it is deep, there are always relatively superficial and relatively deep aspects to any given part of reality.  Logical axioms and their self-evidence are vital, but they are not the whole of reality: there are more logical facts to discover, even though logical axioms govern all things.  Even the self-verifying nature of logic can lead someone to deeper aspects of itself, such as the fact that logic is the one thing that must exist without reference to anything else (other things can only exist if they are logically possible); these two facts are opposite sides of the same coin, even if the latter is esoteric and scarcely acknowledged or known.

This exemplifies how different aspects of the same philosophical facts can differ in their depth even though each of them are important in some way.  Without a sound foundation, a worldview could not be true.  Nevertheless, without the more precise ramifications that follow from that foundation, the base holds up nothing but itself.  Intellectual depth encompasses both the foundation and its ramifications, no matter how near to or far from the former the latter is.  In order to fasion a holistic and thorough worldview, one must examine the deeper components of many different philosophical matters in the light of reason, the self-evidence of which metaphysically and epistemologically holds up every truth that is not self-verifying.


[1].  https://thechristianrationalist.blogspot.com/2018/11/the-ramifications-of-axioms.html