Are you sure?
In the last note, we dealt with one method – propounded by Rene Descartes – of dealing with the inadequacies of our human condition for grasping ontological certainty.
The second method of acquiring epistemic certainty is rooted in what philosophy considers self-evident principles, statements which might be considered axiomatic to logical thinking.
Let’s begin with the Law of Non-Contradiction. If the statement “A” is true, then the statement “not A” is false. If Socrates is a man, then we can’t say Socrates is not a man.
On closer inspection, this Law can be ultimately reduced to the definition of “word” as a referent: words identify themselves with substances existing in physical or metaphysical reality. This property is illustrated beautifully that that famous speech in Shakespeare’s “Romeo and Juliet”: “What is in a word? That which we call a rose, by any other name would smell as sweet.”
This referential property is what we mean when we speak of the meaning of words – they may be defined according to the substance by which they are identified. Moreover, the meaning of words is exclusive, for the nature of a thing excludes that which it is not. This is the universal common premise of any argument, a prerequisite to even speaking in coherent sentences.
However, as may be readily seen, the whole exercise of self-evident truth operates on a tautological loop, for here we see a cycle of definitions and meanings that relies entirely on itself to demonstrate its own veracity. The Law of Non-Contradiction can be neither proven nor disproven on its own grounds. Indeed, any proof of that Law must operate prior to our acceptance of it, and therefore needn’t exclude an equally valid disproof.
Confused? Me too.
In general, the problem with axioms is that they are not intrinsically demonstrable. We do not consider truths to be self-evident in themselves -- it is not in the axiom that we find confirmation, but in its antonym. The thesis is not self-proving. Rather, it is the perceived impossibility of the antithesis which provides the fuller confirmation.