The basic idea here is that we interpret "tall", in the likes of (6) and (12), as a two-place predicate, that is, as containing one more place than it appears to, and take "er-than" and "as" as two-place predicates, rather than sentential connectives.
Someone who takes the surface grammar of (6) as displaying its logical form would conclude that "er-than" forms a sentential connective of some sort and that "Alfred is tall" and "Brendan is tall" are not only grammatical constituents of (6) but are also logical ones.
Even if we assume that "Alfred is tall" and "Brendan is tall", as they occur in (6), are elliptical for sentences that combine "tall" with an appropriate noun or noun phrase, there is a further difficulty with the idea that "er-than" in (6) is a sentential connective, which is that it conflicts with a well-known piece of reasoning, derived from Frege.
Since substituting another sentence having the same truth-value for "Brendan is tall" may alter the truth-value of (6), "er-than" must be a non-truth-functional sentential connective (if it is a sentential connective at all).
Anyone who accepts this principle as well as our earlier claims about "taller than" must discard the idea that "er-than" creates a sentential context, and together with it the idea that it constitutes a sentential connective.
The argument sketched earlier, however, shows that "after" in (15) cannot be regarded as a sentential connective and that "Alfred arrived" and "Brendan departed" cannot be regarded as sentential components of (15).
Contrary to grammatical appearance, "arrived" and "departed" are two-place predicates rather than one-place predicates, and "after" is a two-place predicate, true of pairs of times, rather than a sentential connective.
appears to contain a sentential connective linking the constituent clauses "Jack fell down" and "Jack broke his crown".