Logical Necessity

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Wayne Olson — have I mentioned recently how refreshing it is to find a blog where the writer tackles real philosophy? — ponders the nature of necessity. In my pilgrimage to Orthodoxy, one of the things I refused to let go of was logic. Although my spiritual father repeatedly slandered logic in the catechism, it remains that the ancient Fathers of the Church had no hesitation to use logic at the service of true doctrine. My own patron, Saint Basil the Great, was well versed in Hellenic philosophy, rhetoric, and logic.

come confused about the role of logic when confronted with a robust and well-nuanced conception of mystery. (This is not an analysis of Wayne’s well-reasoned examination of logical necessity — simply an observation I have made seeing many people convert to Orthodoxy.) I find that when this confusion seeps in like a rotten odor, it is often helpful to examine the core proposition of logic.

I am speaking here of the original laws of logic discovered by Aristotle, not more esoteric systems. In my mind non-Aristotelean logic is like non-Euclidean geometry — fascinating, but not necessarily helpful, though I am told that non-Euclidean geometry has actually helped some influential modern discoveries. Science and math experts can rattle sabers with me in some other context.

The most basic law of logic is a is not equal to not-a. Every other law of logic — I’m simplifying here — is based on this. Which is essentially saying, “It is not possible that a proposition can be both true and false at the same time and in the same sense.” Which is simply reflecting what reasonable people know to be true about the real world, that it is not possible for an object to exist and not exist at the same time and in the same sense. (Quantum mechanics, for the hecklers in the audience, only demonstrates that the accuracy of our measurements of the position of a subatomic particle is inversely proportional to the accuracy of our measurements of its speed.)

Thus, logical necessity, when we are dealing with Aristotelean logic, is simply a reflection of the rules of existence when applied to propositional truth. Obviously, this depends in part upon a rather common-sense approach to language, viz., that a statement is true when it corresponds to objective reality. I acknowledge that this dependence on a sort of correspondence theory is a weakness only to the extent that I have not sufficiently thought about how to defend correspondence in the light of Kant and Wittgenstein. However, as a philosophy student, I have always been fond of common-sense realism, in which camp I include Aristotle, Thomas Aquinas, Thomas Reid, and modern Thomists like Jacques Maritain and Ralph McInerny.

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