Tag: Combination

Judgments

I usually think of judgment as a process of interpretation or a related kind of wisdom, but at least since early modern reformulations of Aristotelian logic, “a” judgment has also traditionally meant a logical proposition, or an assertion of a proposition.

An older, but still post-Aristotelian notion is that what the early moderns called a judgment “A is B” should be understood (on the model of its surface grammar) as the potentially arbitrary predication “A is B”. Such a potentially arbitrary predication by itself does not contain enough information for us to assess whether it is good or bad. The predication model was associated with a non-Aristotelian notion of truth as simple correspondence to supposed fact.

L. M. De Rijk, arguably the 20th century’s leading scholar on medieval Latin logic, developed a very detailed textual argument that the understanding of logical “judgments” in such grammatical terms is actually an unhistorical misreading of Aristotle. In the first volume of his Aristotle: Semantics and Ontology, De Rijk concluded that Aristotle’s own logical or semantic use of “is” or “is not” should be understood not in the traditionally accepted way as a “copula” or binary operator of predication, but rather as a unary operator of assertion on a compound expression — i.e., on the pair (A, B), as opposed to its two elements A and B.

I also want to emphasize that Aristotle himself did not admit simple, potentially arbitrary predications as “judgments”. The special form of Aristotelian propositions makes them express not arbitrary atomic claims as is the case with propositions in the standard modern sense, but two specific ways of compounding subclaims. Aristotle’s two truth-value-forming operations of combination and separation (expressed by “is” and “is not”) limit the scope of what qualifies as a proper Aristotelian “judgment” to cases that are effectively equivalent to what Brandom would call judgments of material consequence or material incompatibility (see Aristotelian Propositions). What the moderns would call Aristotelian “judgments” thus end up more specifically reflecting judgments of what Brandom would call goodness of material inference.

Proper Aristotelian “judgments” thus turn out to express not just arbitrary predications constructed without regard to meaning, but particular kinds of compound claims that can in principle be rationally evaluated for material well-formedness as compound thoughts, based on the actual content of the claims being compounded. (Non-compound claims are just claims, and do not have enough content to be subject to such intrinsic rational evaluation, but as soon as there is some compounding, internal criteria for well-formedness come into play.)

So, fortuitously, modern use of the term “judgment” for these ends up having more substance than it would for arbitrary predications. For Aristotle, truth and falsity only apply to what are actually compound thoughts, because truth and falsity express assessments of material well-formedness, and only compound thoughts can be assessed for such well-formedness. The case for the fundamental role of concerns of normativity rather than simple surface-level predication in Aristotelian truth-valued propositions is further supported by the ways Aristotle uses “said of” relations.

Independent of this sort of better reading of Aristotle, Brandom in the first of his 2007 Woodbridge lectures points out that Kant also strongly rejected the traditional analysis of judgment in terms of predication. Brandom goes on to argue that for Kant, “what makes an act or episode a judging in the first place is just its being subject to the normative demand that it be integrated” [emphasis in original] into a unity of apperception. This holistic, integrative view of Kantian judgment seems to me to be strongly supported by Kant’s discussion of unities of apperception in the second edition of the Critique of Pure Reason, as well as by the broad thrust of the Critique of Judgment.

Thus, a Kantian judgment also has more substance than the standard logical notion, but while an Aristotelian “judgment” gets its substantive, rational character from intra-propositional structure, a Kantian judgment gets it from inter-propositional structure.

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.