I am looking here for any sources that respond to the question given:

Can Frege coherently admit expressions that have a sense but lack a reference?

I am familiar with a lot of the exegetical work on the Fregean sense/reference distinction, but I am interested particularly in this subtopic.

  • 2
    Do you think he has to? If yes, do you have an example of an expression that has a sense but lacks a bedeutung (denotation, reference)? As it stands, it's not very clear what the problem is. Mar 7, 2014 at 4:55
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    Frege's analysis of Sinn and Bedeutung clearly admits (in natural language) cases of expressions without B; he uses the example : "the least rapidly converging series". We understand it but it is provable that there is no such thing. But in his "ideal language" (begriffsschrift) this must not happen: "because the B of an entire proposition is determined by the B of its parts, it is important that every expression have a B so that all propositions have a determinate truth-value. Thus Frege insures that every sign expresses a Sinn that does pick out a Bedeutung." 1/2 Mar 7, 2014 at 9:22
  • ... from Kevin Klement, Frege and the Logic of Sense and Reference (2002), page 62. 2/2 Mar 7, 2014 at 9:22
  • The whole point of introducing sense was to accomodate expressions that have meaning but lack reference, like bearerless names such as Odysseus, and non-triviality of substitution into belief contexts like "John knows that Mark Twain is Samuel Clemens", see Miller, pp.23-39. Of course, ultimately Frege's theory couldn't explain how his "sense" is communicated, etc., which is why Russell reformed it, but his and all subsequent theories had their problems too. There is no satisfactory semantics of natural language even today, not even a blueprint of it.
    – Conifold
    Apr 25, 2016 at 22:27

2 Answers 2


In Frege's logical perfect language (Begriffsschrift) every well-formed expression must have a reference (Bedeutung).

The Bedeutung of an expression is the actual thing corresponding to it.

The Sinn of an expression, however, is the “mode of presentation” or cognitive content associated with the expression in virtue of which the Bedeutung is picked out.

As showed by Klement's example above, in "natural" language, we use expressions without reference, like : "the least rapidly converging series". Of course, we can "understand" them; so they must have sense.

But if the sense of an expression is what enables us to "pick out" its reference, what is the "role" of sense if there is not a reference ?

So, at least in a "logical perfect language" :

no reference, no sense.

  • He also liked to say at times (though I'd have to dig for a reference) that sense determines reference. Though I think that's within the context of a logically perfect language, where reference is assured.
    – Dennis
    Sep 28, 2014 at 3:04
  • @Dennis - Yes; Frege says that the sense is "the way" with which the reference is "presented" to us. This means that the same object - the reference - can be "known" by us in different ways [the Morning star vs the Evening star]. The object is the same but the sense of the two expression "presenting" it must be different : it may be that we do not know that the Morning star is the same star that the Evening one... Sep 28, 2014 at 9:26

According to Frege, the name (of the rational thought/empirical perception) is the sense. We can have multiple (infinitely many) senses of the same subject. Therefore the sense cannot be the truth value. The subject itself is the meaning in its ideality, i.e. truth value. That only is its real reference.

The answer to this question is " yes." Because meaning is in denotation. So we can continue in another question : is the denotation static or evolving?

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