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I'm relatively new to philosophy and I'm starting out with the 'staple' philosophers - namely Frege and Russell. I've read Frege's "Sense and Reference" and Russell's "On Denoting."

One thing I have an issue with distinguishing and properly putting into words is how Frege and Russell deal with definite descriptions differently. If the sentence was something like "John believes that the present Queen of America is bald," where "the present Queen of America" does not denote any real object or person - how do their respective theories still argue that such a sentence can be true?

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  • See Pelletier & Linski, What is Frege’s Theory of Descriptions ?. In a nutshell. Frege's view is formulated in the context of his semantical theory (Sinn-Bedeutung) where Russell's fundamental analysis is about the proper logical form of sentences involving definite descriptions and the difference with "surface" grammatical form of the sentences. – Mauro ALLEGRANZA Mar 15 at 7:47
  • But in "mature" Frege (Grundgesetze (1893)) there is a full formalization of the article "the": it is different from subsequent Russell's analysis. Do you refer to that one ? – Mauro ALLEGRANZA Mar 15 at 9:43
  • Hi! I'm referring to his semantical theory on Sinn-Bedeutung alone. Is the correct way to understand Frege for definite descriptions wherein there is no referent: Frege mentions that in cases embedded sentences no longer has its usual bedeutung, and that in such cases, words are not interpreted with the usual bedeutung, but with the usual sense that the individual words themselves have. Combining this with his compositionality theory, it can be said that there is truth value since the 'usual sense' is now taken as the bedeutung? Would you think Russell's analysis better than Frege's? – Ryan Mar 15 at 10:11
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    Frege's position was that definite descriptions are names, and sentences with them can have a Sinn without being either true or false. Trouble is, sentence truth/falsity is the linchpin of Frege's assignment of meaning to everything else. So in effect, he introduces a property which is supposed to impart meaning, and then says that something can still be meaningful without having it. Russell's solution was that definite descriptions aren't names, and sentences with bearerless names have a depth grammar distinct from their surface grammar. Once converted to reveal it, they are true or false – Conifold Mar 15 at 18:48
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For Russell, sentences with definite descriptions of the form "The F is G" have the logical form:

There is a unique x that is F, and x is G.

So to believe that the present queen of American is bald, according to Russell, is to believe that there is a unique individual who is a queen of America and that individual is bald. There's no failure of reference there, and one can certainly believe such a thing.

According to Frege, while "the queen is America is bald" is neither true nor false since it has a failure of reference, it does have a sense. In belief reports, such as "John believes that the queen of America is bald", the phrase "that the queen of America is bald" refers to the sense and not the (missing) truth value of the sentence "the queen of America is bald". Since the sense does exist, it can be believed. So according to Frege too such belief reports can be true.

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