It is extremely common to see references to “predication” as if it were a central concept of Aristotelian logic. We are so used to a grammatical interpretation in terms of relations between subjects and predicates that it is hard to disengage from that. However, historically it was Aristotelian logic that influenced ancient Greek accounts of grammar, not vice versa.
Modern logicians distinguish between a neutral proposition — which might be merely mentioned, rather than asserted — and the assertion of the proposition. Grammatical predication in itself does not imply any logical assertion, only a normatively neutral syntactic relation between sentence components. But “said of” in Aristotle always refers to some kind of meaningful assertion that has a normative character, not to grammatical predication.
Aristotle talks about what we might call kinds of “sayables” (“categories”). He famously says that we can only have truth or falsity when one kind of sayable is “said of” another. Mere words or phrases by themselves don’t assert anything, and hence cannot be true or false; for that we need what modern writers have referred to as a “complete thought”.
The ordinary meaning of “to categorize” in ancient Greek was “to accuse in a court of law”. Aristotle used it to talk about assertions. It didn’t originally connote a classification. The modern connotation of classification seems to stem from the accident that independent of what “category” meant in his usage, Aristotle famously developed a classification of “categories”.
Aristotle also talks about logical “judgment” (apophansis, a different word from practical judgment or phronesis). Husserl for instance transliterated this to German, and followed the traditional association of logical judgment with “predication”. But the ordinary Greek verb apophainein just means to show or make known. Aristotle’s usage suggests a kind of definite assertion or expressive clarification related to demonstration, which makes sense, because demonstrations work by interrelating logical judgments.
All of Aristotle’s words and phrases that get translated with connotations of “predication” actually have to do with normative logical assertion, not any connecting of a grammatical subject with a grammatical predicate. Nietzsche and others have complained about the metaphysical status foisted on grammatical subjects, implicitly blaming Aristotle, but all these connotations are of later date.
The great 20th century scholar of ancient and medieval logic and semantics L. M. de Rijk in his Aristotle: Semantics and Ontology (2002) argued at length that Aristotle’s logical “is” and “is not” should be understood as not as binary operators connecting subjects and predicates, but as unary operators of assertion and negation on whole propositions formed from pairs of terms. (See also Aristotelian Propositions.)
As in similar cases, by no means do I wish to suggest that all the work done on the basis of the common translation of “predication” is valueless; far from it. But I think we can get additional clarity by carefully distinguishing the views and modes of expression of Aristotle himself from those of later commentators and logicians, and I think Aristotle’s own more unique perspectives are far fresher and more interesting than even good traditional readings would allow.