Material Inference

Most “real world” reasoning is actually material in the sense developed by Sellars and Brandom. The “materiality” of material inference recalls several things.

Material inference addresses meant realities through the medium of their expression in ordinary language.

The “materiality” of material inference also refers to the fact that it always involves meaning-based judgments about proprieties of inference, not simple mechanical application of formal transformations. These may subsequently be given formal representation, but the starting point is what I want to call a form of ethical judgment, that it is right to make this inference about these things in this situation. This could equally be applied to questions of what really is the case, or of the appropriateness of actions. The “meaning” at issue should itself be understood in terms of other normative material inferences, provisionally held constant while the inference at hand is assessed.

Finally, the “materiality” of material inference also recalls its recursive dependence on previous concrete judgments.

Material inference works with two kinds of relational judgments: material consequence and material incompatibility.

Things Said

Saying is a specialized form of doing. When saying and doing are contrasted, what is asserted is a contrast between kinds of doing that have different implications. Proprieties of both saying and doing are matter for material inference.

Implicit consideration of a material-inferential ethical dimension is what distinguishes canonical Aristotelian saying from the mere emission of words. This dimension of ethics of material inference gives more specific content to epistemic conscientiousness.

Saying is also a social act that occurs in a larger social context. This gives it a second ethical dimension, starting from consideration of others and situational appropriateness. (See also Interpretive Charity; Honesty, Kindness; Intellectual Virtue, Love; Mutual Recognition.)

Aristotelian Propositions

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 combines with 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.