When I have discussed a priori synthetic judgment in Kant, I have frequently cited the Critique of Pure Reason (B 201*) to distinguish between synthesis as the a posteriori determination of something “in common” (e.g., a concept) to a set of phenomena from synthesis as the a priori “adding to” the phenomena of something not given directly in the phenomena. I took the term nexus to refer to a posteriori synthesis and compositio to refer to a priori synthesis. I should have read B 201* more carefully.
Whereas Kant most certainly made the distinction between a posteriori synthesis and a priori synthesis (see B 748, 750, 751-752), his distinction between nexus and compositio at B 201* is concerned with two kinds of a priori synthesis.
B 201* is concerned with distinguishing between a priori “mathematical” and a priori “dynamical” synthesis. He is talking here about a priori “combinations” (syntheses) that are either “not necessary” (mathematical) or that are “necessary” (dynamical). Unnecessary combinations he calls “compositio,” whereas necessary combinations he calls “nexus.”
The issue here, then, is not a priori (adding to phenomena) judgments versus a posteriori (deriving from) judgments but “unnecessary” and “necessary” a priori judgments. Mathematical judgments (formal, logical conditions) are not necessary because they are “merely” logical. Dynamical judgments (concerned with “forces” and “change”) are necessary because they are concerned with empirical phenomena.
Compositio are a priori syntheses that are not (!) arrived at out of “necessity” (in the sense of the necessary conditions of possibility for experiencing a set of phenomena) but logically, and they can be an “aggregation” (concerned with “extensive” size) or a “coalition” (concerned with “intensive” size). Extensive size involves amounts and multiplicity and is concerned with the representation of the parts of a perception that make possible the representation of the whole – hence, the parts precede the whole. It is a logical procedure. Intensive size is concerned with contents and their diversity, logical significance, and fruitfulness for understanding insofar as the contents lead to multiple and significant consequences (not quantity but quality).
Nexus are a priori syntheses that are (!) necessary as the conditions of possibility for experiencing a set of phenomena (i.e., they are not simply logical). Kant uses the examples of “substance and its accidents” and “cause and effect.” These elements are not equivalent but are “connected” a priori. Because they are not arbitrary or capricious, Kant calls them “dynamic” (concerned with “forces” and “change”).
My “metaphorical interference” was to take compositio to mean a priori “construction/adding to” the phenomena and to take nexus to mean a posteriori “discovery of a unity in the phenomena.” However, for Kant both forms of synthesis are a priori and refer to two kinds of a priori synthesis: “unnecessary” (i.e., logical), mathematical judgments (compositio) and “necessary” (i.e., required to understand phenomena), dynamical judgments (nexus).
In addition to the Critique of Pure Reason, we find Kant’s distinction between a priori and a posteriori synthetic judgment in the Prolegomena to Any Future Metaphysics § 22:
“[…] uniting in a consciousness is either analytic by identity [e.g., arrived at a posteriori], or synthetic by the combination and addition of various representations one to another [e.g., added a priori]. Experience consists in the synthetic connection of appearances (perceptions) in consciousness, so far as this connection is necessary. Hence the pure concepts of the understanding [which are the necessary condition for a priori synthetic judgments] are those under which all perceptions must first be subsumed before they can serve for judgments of experience in which the synthetic unity of the perceptions is represented as necessary and universally valid.”
Here Kant adds a footnote:
“But how does the proposition that judgments of experience contain necessity [emphasis added] in the synthesis of perceptions agree with my statement [… made so often before] that experience, as cognition a posteriori, can [… give us] only contingent [not necessary] judgments? When I say that experience teaches me something, I mean only the perception that lies in experience—for example, that heat always follows the shining of the sun on a stone; consequently, the proposition of experience is always so far contingent [emphasis added]. That this heat necessarily [emphasis added] follows the shining of the sun is contained indeed in the judgment of experience (by means of the concept of cause [emphasis added]), yet is a fact not learned by experience [emphasis added]; for, conversely, experience is first of all generated by this addition of the concept of the understanding (of cause) to perception [emphasis added].”