Theory of reference

The distinction between sense and reference was an innovation of the German philosopher and mathematician Gottlob Frege in 1892, reflecting the two ways he believed a singular term may have meaning. The reference (or "referent", German: Bedeutung)) of a proper name is the object it means or indicates (bedeuten), its sense is what the name expresses. The reference of a sentence is its truth value, its sense is the thought that it expresses. Frege justified the distinction in a number of ways.

Frege developed his original theory of meaning in early works like Begriffsschrift ('concept script') of 1879 and Grundlagen ('foundations of arithmetic') of 1884. On this theory, the meaning of a complete sentence consists in its being true or false, and the meaning of each significant expression in the sentence is an extralinguistic entity which Frege called its Bedeutung, literally 'meaning' or 'significance', but rendered by Frege's translators as 'reference', 'referent', 'Meaning', 'nominatum' etc. Frege supposed that some parts of speech are complete by themselves, and are analogous to the arguments of a mathematical function, but that other parts are incomplete, and contain an empty place, by analogy with the function itself. Thus 'Caesar conquered Gaul' divides into the complete term 'Caesar', whose reference is Caesar himself, and the incomplete term '—conquered Gaul', whose reference is a Concept. Only when the empty place is filled by a proper name does the reference of the completed sentence – its truth value – appear. This early theory of meaning explains how the significance or reference of a sentence (its truth value) depends on the significance or reference of its parts.

The Greek philosopher Antisthenes, a pupil of Socrates, apparently distinguished “a general object that can be aligned with the meaning of the utterance” from “a particular object of extensional reference.” This “suggests that he makes a distinction between sense and reference.” The principal basis of this claim is a quotation in Alexander of Aphrodisias’s “Comments on Aristotle’s ‘Topics’” with a three-way distinction:

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