Many places I have come across the opinion that to read Aquinas without a grounding in traditional logic, the logic of the scholastics, you will not quite understand St. Thomas (Peter Kreeft, Joseph Owens, Ralph McInerny, and others have maintained this position). others- even some thomists- have said the traditional logic is to be abandoned and replaced completely by mathematical logic (Peter Geach, a fan of Thomas, but no thomist, argued this again and again). Having studied only mathematical logic I am wondering whether the former position is true?
I tend to agree with the first group, though I have only limited background in mathematical logic and was first taught the Aristotelian sort. Symbolic logic, at least as justified in truth tables (and “possible worlds”) always struck me as quasi-empiricist, and so missing the force that Aristotle’s logic at least claims to give. That is, by having a formula’s truth value determined by examining in a truth table all possible values, symbolic logic seems somewhat arbitrary and the connections between premises and conclusions divorced from the things, fact if you prefer, which make them true. For instance, “if p, then q” seems to mean more in natural language than that it is false only when p is true and q is false. Likewise when it is true that “x is necessarily F,” I’m not sure that the fact that it is (or might be) true, in every possible world in which there are x and F, that x is F even has anything to do with the necessity, in this world, of x being F.
Symbolic logic is still an abstraction insofar as it ignores particular values, and alot of its utility and power arises precisely because it is an abstraction, but it seems to miss what Thomas would call “intellectus” or understanding, the grasping of things in their essential natures which is what logical reasoning is supposed to produce. For Aristotle and Aquinas, when one understands that “Socrates is mortal” on the basis of “Socrates is a man” and “Man is mortal,” one knows more than the truth of Socrates’ mortality, one also knows the reason; as Aristotle says, the premises are contained virtually in the conclusion. One understands Socrates’ mortality by understanding his humanity.
If one were to reduce Thomas’ arguments to merely their formal structure, one would, I think, miss the understanding that he is trying to reproduce in his syllogisms. Formal structure is important also for Aristotle and Aquinas, but since logical principles are abstracted from the world, the formal structure of logic reflects the structure of reality, and so is useful for producing understanding of the nature of things.