Connection and Continuity in Inference

Inference connects conceptual entities to each other; in fact, it is definitionaily true to say inference is connective. Inference does not create conceptual connections, either formal or semantic (meaning); it makes implicit connections explicit. If I know that all A is B and that all B is C, then by inference I can know that all A is C. The conclusion is deductively connected to the premises whether or not anyone ever actually infers it. The deductive connection becomes known to me by virtue of inference. Confusion has been rife in philosophic discussions on the subject of "connection,"1 and some clarity is needed on a fundamental level. Much, though not all, of the confusion is due largely to crudely mixing aspects of connection with aspects of juxtaposition (called "conjunction" by Hume).2 The lack of properly understanding connection goes hand-in-hand with a lack of sophistication about the contrast between genuine continuity and discreteness.3 The connectivity of inference is analyzable in terms of continuity and not discreteness, while, in contrast, juxtaposition is understood in terms of discreteness.