Frege proposed that the meaning of a sentence is its truth value in "Über Sinn und Bedeutung" (close to "On Sense and Meaning"). This is not correct because some (many) English sentences do not have any truth value.

For example, an interrogative sentence cannot have a truth value because it seems to be both true and false at the same time. A declarative sentence which contains an if (whether) clause cannot be assigned a truth value too because it can be true and false as well. Lastly, sentences contain logic contradictions such as the Liar paradox or Richard's paradox do not have truth values.

Is this view of Frege accepted only for propositions that are only part of sentences?

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    Name is more close to Sinn in this case, and sense is quite misleading. Russell realized this as well and used denotation instead which is synonymous to name. – hermes Dec 12 '19 at 22:46
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    Freg's theory applies to declarative sentences : "The Moon is bright", etc. – Mauro ALLEGRANZA Dec 13 '19 at 6:32
  • Frege proposed that the sense (Sinn) of a sentence is its truth value. In addition to that its "meaning" involves reference (Bedeutung), force (distinguishing assertions, questions and commands), and tone (emotional, etc., coloring). Determinate if-then sentences do have a truth value, if they contain indeterminates their sense is the truth valued function over them. Modern theories also distinguish "literal sense" given by semantics and context dependent variations given by pragmatics. Bearerless names/sentences were a problem that Russell tried to address with definite descriptions. – Conifold Dec 13 '19 at 7:32
  • @Conifold I believe your first sentence is the other way around. "The reference of a sentence is its truth value, its sense is the thought that it expresses." – Adam Sharpe Dec 13 '19 at 13:41
  • @AdamSharpe Yes, my mistake. – Conifold Dec 14 '19 at 1:31

See Sense and Reference, Eng.transl. (1948), page 214 :

"So far we have considered the sense and referents only of such expressions, words, or signs as we have called proper names. We now inquire concerning the sense and referent of an entire declarative sentence. Such a sentence contains a thought."

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  • So Freg's theory is not entirely correct as many declarative sentences do not have any truth value. – hermes Dec 13 '19 at 18:05
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    @MathWizard - No; Frege's theory is debatable, but his point of view is that of modern mathematical logic : every declarative sentence has a definite truth value. – Mauro ALLEGRANZA Dec 14 '19 at 14:22
  • @ALLEGRANZA, I am afraid that this claim is not correct. For example, "The only sentence on the board is not true" is a declarative sentence, but it does not have a truth value because either assuming its truth or falseness will lead to the converse. – hermes Dec 14 '19 at 17:35

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