Sinn - Sense Without Reference

Sense Without Reference

One application Frege saw for the distinction concerns what are called nonreferring, nondenoting, or empty, expressions. These expressions do not have a reference, for example "the greatest integer". Since there is not a greatest integer, the expression doesn't refer to anything. But it seems perfectly meaningful, since we seem to understand claims like "The greatest integer is larger than one million". Employing the sense-reference distinction, we can say that the expression has a sense but lacks a reference.

Although the term "the greatest integer" has no reference in the conventional arithmetic, in the ultra-intuitionistic arithmetic suggested by Alexander Esenin-Volpin (1960), it has a reference because one of the axioms of this arithmetic is that there is "the greatest integer." So, in one universe, an expression can have sense without reference, while in another universe, the same expression can have both sense and reference.

Another example is Odysseus. Since he is a fictional character, the name Odysseus does not appear to mean anyone at all; yet sentences like "Odysseus was set down on the beach at Ithaca" are meaningful, in that they can be true or false. If a sentence's meaning is a function of the meanings of its parts, then parts of the sentence, such as Odysseus, seemingly do have meaning.

Whether this solution works, and whether it was even seriously intended by Frege, is disputed. In order for it to work, it must be possible for a term to have a sense without a reference, and this requires that sense cannot be defined simply as the mode of presentation of the reference, since sometimes there is no reference being presented. Thus the view that the sense-reference distinction solves the problem of empty names encourages the view that a sense is an individuating description (which could be understood with or without a reference satisfying it). This makes a sense equivalent to a Russellian description (see below), and makes Frege's position "descriptivist", leaving it prey to a number of difficulties raised against that view. Other philosophers have argued that Frege is not a descriptivist, and hence that the sense-reference distinction does not solve the problem of fictional names. Proponents of this view often claim that sentences using empty names do not in fact express propositions, hence are not literally meaningful, despite appearances. They face the difficulty of explaining the apparent meaningfulness of sentences using the word Odysseus. On one view, fictional names merely pretend to express propositions. Our understanding of sentences about Odysseus consists then in our "playing along" (see Gareth Evans, Saul Kripke).