  However, once we have thrown out the old subject/predicate model, we can no longer identify the categorematic terms with the subject and predicate terms, as the medievals did. Nor can we think of the syncategorematic terms as the expressions that have no “independent” significance, or as the “glue” that binds together the categorematic terms to form a meaningful whole. Granted, there is a sense in which the “logical” function \(\refp{second-level}\) is the glue that binds together \(\refp{function-boat}\) and \(\refp{function-smaller}\) to yield \(\refp{moby-frege}\). But in the very same sense, the function \(\refp{smaller-than}\) is the glue that binds together “Shamu” and “Moby Dick” to yield \(\refp{shamu-smaller}\). If we count all functional expressions as syncategorematic on the grounds that they are “incomplete” or “unsaturated” and thus not “independently meaningful,” then the syncategorematic expressions will include not just connectives and quantifiers, but ordinary predicates. On the other hand, if we count all the functional expressions as categorematic, then the syncategoremata will be limited to variables, parentheses, and other signs that serve to indicate functional application and abstraction. In neither case would the distinction be useful for demarcating the logical constants. An intermediate proposal would be to count first-level functions as categoremata and second-level functions as syncategoremata. That would make \(\refp{second-level}\) syncategorematic and \(\refp{function-boat}\) and \(\refp{function-smaller}\) categorematic. However, not every second-level function is (intuitively) “logical.” Consider, for example, the second-level function