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I have been informed here What is the difference between function and predicate? that in formal semantics, predicates are always functions that map from individuals (i.e. arguments) to truth values. There are other types of functions, though, namely those that map to individuals instead of to truth values. My understanding of this issue is therefore that in formal semantics, every predicate is a function, but there are functions that are not predicates. Function is therefore the broader concept, broader than predicate.

In syntax, content verbs, adjectives, and predicative expressions of various sorts are predicates, and many of these predicates cannot be construed as mapping to truth values, at least not in a straightforward way. This is often the case with embedded predicates, i.e. with predicates that are subordinate to the matrix predicate, e.g.

(1) Hank said Susan laughed.

(2) Hank considers Susan entertaining.

In sentence (1), there are two predicates, said and laughed. Only said can be construed as mapping to a truth value in a straightforward way. The sentence can be true or false regardless of whether or not Susan actually did or did not laugh. The situation is similar in sentence (2); there are two predicates there, considers and entertaining. The sentence can be true or false regardless of whether Susan is or is not entertaining.

I have been informed that intensionality is at play in sentences like (1) and (2), the implication being that intensionality allows one to maintain the position that all predicates map to truth values. I am confused about how this works, though. It would make sense to me if one assumes a third truth value, namely undecided. There would hence be three truth values (true 1, false 0, and undecided ?). Predicates like laughed in (1) and entertaining in (2) could then be construed as mapping to truth values, but in these cases, the truth value they map to would be undecided.

Thanks for your time!

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    I don't agree with what you say. In sentence 1. the two predicates are "said Susan laughed" and "laughed", being respectively the matrix and subordinate predicates. "Said" and "laughed" are just the heads of the predicates. In sentence 2. there is only one predicate, "considers Susan entertaining". "Entertaining" is an adjective serving as complement of "considers", and hence not a predicate.
    – BillJ
    Dec 5, 2022 at 18:14
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    Your understanding matches one of the definitions of predicate that one finds in standard dictionaries of linguistic terminology (e.g. Oxford Concise Dictionary of Linguistics or Oxford Dictionary of English Grammar). The other definition is the one assumed here, and is, I believe, the more prominent one among syntacticians and semanticists. See Carnie's (2013) textbook (Syntax: A Generative Introduction) in this regard (p. 57-58).
    – Buffoon
    Dec 8, 2022 at 15:21
  • I follow the work of Rodney Huddleston, the finest grammarian of the English language alive today, and the lead author of the award-winning Cambridge Grammar of the English Language. Incidentally, 'function' is the term used for the subject, object, complement, etc. in a clause. It contrasts with category (POS) such as noun, verb, adjective etc
    – BillJ
    Dec 8, 2022 at 17:45
  • Syntactically, in (1} "Susan laughed" is a declarative content clause functioning as complement (and thus a dependent) of "said". What evidence do you have that this subordinate clause is not part of the matrix predicate?
    – BillJ
    Dec 8, 2022 at 17:58
  • Incidentally, CGEL does not contain any reference to Carnie, either in the references or further reading.
    – BillJ
    Dec 8, 2022 at 18:11

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in formal semantics, predicates are always functions that map from individuals (i.e. arguments) to truth values

Not quite; it is specifically individual predicates which take individual arguments and always map from individuals. There are other kinds of predicates which also take other arguments, like such that take embedded propositions as in your example.

My understanding of this issue is therefore that in formal semantics, every predicate is a function, but there are functions that are not predicates. Function is therefore the broader concept, broader than predicate.

No, this is not correct. Every predicate denotes a function. Every so-called functional expression also denotes a function. A linguistic expression (predicational or functional) is not the same as a function or a supercategory or anything; they are two different things.

many of these predicates cannot be construed as mapping to truth values

No. "laughed" maps form an individual (Susan) to a truth value as usual. It is just that this truth value does not determine the truth value of the matrix sentence.

Instead of directly plugging in the actual truth value of the embedded sentence as the function argument for the matrix verb "said", we take the intension of the sentence. The details of this are something for a book chapter rather than an SE post, but the TLDR is that rather than looking just at the truth value of the sentence in the real world, we abstract over all possible hypothetical situations and collect in which of these situations the sentence would be true or false, and the resulting object is the intension of the sentence and what goes in as the second argument to "said", combined with the first argument "Hank" which is an individual. Using intensions, we don't need to resort to undefined truth values or the like to make sense of the embedded or the matrix sentence.

But the fact that "laughs" occurs embedded in this context does not change its syntax-semantics at all. It is a predicate whose denotation is a function that maps from an individual to a truth value, and makes it so that the sentence "Susan laughed" has a truth value. And the matrix sentence then proceeds to do something else.

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  • Thanks a lot！ I think what you mean is that the notion of intension is the key point here.
    – Buffoon
    Dec 8, 2022 at 8:35

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