Every canonical Aristotelian *proposition* can be interpreted as expressing a judgment of material consequence or material incompatibility. This may seem surprising. First, a bit of background…

At the beginning of *On Interpretation*, Aristotle says that “falsity and truth have to do with combination and separation” (Ch. 1). On its face, the combination or separation at issue has to do not with propositions but with *terms*. But it is not quite so simple. The terms in question are canonically “universals” or types or *higher-order* terms, each of which is therefore convertible with a mentioned proposition that the higher-order term is or is not instantiated or does or does not apply. (We can read, e.g., “human” as the mentioned proposition “x human”.) Thus a canonical Aristotelian proposition is formed by “combining” or “separating” a *pair* of things that are *each interpretable as an implicit proposition* in the modern sense.

Propositions in the modern sense are treated as atomic. They are often associated with merely stipulated truth values, and in any case it makes no sense to ask for *internal* criteria that would help validate or invalidate a modern proposition. But we can *always* ask whether the *combination or separation* in a canonical Aristotelian proposition is *reasonable* for the arguments to which it is applied. Therefore, unlike a proposition in the modern sense, an Aristotelian proposition always implicitly carries with it a suggestion of criteria for its validation.

The only available criteria for critically assessing correctness of such elementary proposition-forming combination or separation are material in the sense that Sellars and Brandom have discussed. A judgment of “combination” in effect just is a judgment of material consequence; a judgment of “separation” in effect just is a judgment of material incompatibility. (This also helps clarify why it is essential to mention both combination and separation affirmatively, since, e.g., “human combine mortal” canonically means not just that human and mortal are not incompatible, but that if one is said to be human, one is thereby *also* said to be mortal.)

This means that Aristotle’s concept of the elementary truth and falsity of propositions can be understood as grounded in criteria for goodness of material inference, not some kind of correspondence with naively conceived facts. It also means that *every* Aristotelian proposition can be understood as expressing a judgment of material consequence or incompatibility, and that *truth* for Aristotle can therefore be understood as primarily said of *good* judgments of material consequence or incompatibility. Aristotle thus would seem to anticipate Brandom on truth.

This is the deeper meaning of Aristotle’s statement that a proposition in his sense does not just “say something” but “says something *about* something”. Such *aboutness* is not just grammatical, but material-inferential. This is in accordance with Aristotle’s logical uses of “said of”, which would be well explained by giving that a material-inferential interpretation as well.

The principle behind Aristotelian syllogism is a form of *composition*, formally interpretable as an instance of the composition of mathematical functions, where composition operates on the combination or separation of pairs of terms in each proposition. Aristotelian logic thus combines a kind of material inference in proposition formation and its validation with a kind of formal inference by composition. This is what Kant and Hegel meant by “logic”, apart from their own innovations.