[gerard.casey]

Jerryb225: As I mention very early on in the lectures, there are always gaps between our natural reasoning and any formal system of logic. Sometimes, elements of our natural reasoning seem to be incapable of being ‘captured’ by our formal system; at other times, our formal system seems, as it were, to have a mind of its own and to come up with inferences that are, on the face of it, non-intuitive.

The traditional system of logic I teach in the course has two basic types: the first, where we can analyse the internal structure of the proposition (categorical proposition) and derive inferences from that; the second, where we are concerned with the external relationships between propositions taken as a whole (the hypothetical syllogism). [Have you got to the section on the hypothetical syllogism yet?]

If JohnD were to reformulate his argument, it might be susceptible to an analysis in the logic of the categorical proposition.

As things stand, however, I give an analysis of his argument in the logic of the hypothetical syllogism upon which it turns out the argument is valid. That being so, our attention now turns to the truth of the premises. I suggested that premises 1d and 3d were most likely true (their truth to be established by extra-logical means) and that the problematic premise was 2d. The truth of this has to be established either on the basis of non-logical evidence or as the conclusion of yet another argument.

As you can see from all this, logic is not a universal solvent for all our conceptual problems. In the end, the truth of our premises is, for the most part, derived from empirical evidence, history, and only occasionally by pure thought. Logic’s strength, however, is that, by allowing us to distinguish clearly between validity and soundness, it enables us to focus our attention where it needs to be rather than being distracted by the inessential.