St. Thomas did divide formal and material logic, but he did not understand the division as we do. For us, formal logic is a homogenous group of blank templates which, if filled in with terms, necessarily yield valid conclusions. Logical forms are not that different from tax forms- we pick out the one we want, fill in the blanks, and are then certain that our conclusion is valid. If our conclusion is rejected, it will not be because we failed to complete the proper steps.
For St. Thomas, the syllogism is a series of relations of containment and exclusion of universality which must be acknowleged as such. If we try to prescind from universality (as we do in our account of formal validity), we lose the reason why certain terms are called “major” (more universal) ”minor” (less universal) and “middle”, which are the essential parts of the syllogism as St. Thomas understands it. The meanings of these terms are analogous in such a way that they are only fully verified in the first figure, and so any notion that syllogistic forms are homogeneous by generating true conclusions must go by the board. Only the first figure is valid in itself, and all other forms of the syllogism are valid by some participation in the first figure, and their parts are understood as certain ways of falling short of the first figure.
The difference between St. Thomas’s account of the form of the syllogism and our own is that for him the syllogism is a certain proper order of things in the mind so far as they are in the mind, and what is in intellect is universal. Contemporary philosophers, to my knowledge, simply do not see the nature of mental existence as relevant to logic, and so they simply cannot see what St. Thomas meant by logic.
