# sentential connectives

## sentential connectives

[sen¦ten·chəl kə′nek·tivz]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Apparently binary quantifiers can be defined in terms of unary quantifiers plus sentential connectives. One can quantify over some entities without being able to think or talk about them individually.
By focusing on certain complex examples in which sentences with a specific type of semantics are embedded inside the scope of sentential connectives, TSA alms to demonstrate that Grice cannot retain his semantic commitments and account for the interplay of meanings in communication.
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. Accordingly, the logical form of (6), and hence of (4), would be that of an existentially quantified conjunction; likewise with (12) and (11).
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. This explains why (15) permits substitution of co-referential expressions (the positions occupied by "Alfred" and "Brendan" in (15[prime]) are purely referentially) and also why we may not, in general, substitute other sentences having the same truth-value for "Alfred arrived" and "Brendan departed": "Alfred arrived" and "Brendan departed" occur in (15) not as sentential components but as parts of the predicate expressions "Alfred arrived at t" and "Brendan departed at t[prime]", respectively.
appears to contain a sentential connective linking the constituent clauses "Jack fell down" and "Jack broke his crown".
Thus, the standard sentential connectives are interpreted in exactly the same way in all domains.

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