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For Frege, all kinds of expressions have a sense as well as a reference.^[1] About proper names he writes that the sense is the mode of presentation of the thing named. More generally, he characterizes the sense and expression as what determines the reference of that expression. Further, the sense of an expression is identified as that expression’s contribution to the cognitive content of the sentences of which the expression is a part. Thus, Frege writes that the sense of a sentence is a thought, and that such sense determines the reference of the sense, which is its truth-value. Frege sees the distinction between sense and reference as the key to solve the puzzle about identity statements. The original question remains: if an identity statement expresses a relation between an object and itself, then how can a statement such as (3),

(3) The morning star is identical to the evening star

say, if true, anything different from what a statement such as (4),

(4) The morning star is identical to the morning star

says? Does each not assert one and the same relation; that is, identity, between one and the same object and itself; that is, the morning star?

Typically, with each ‘proper name� there is associated a sense and a reference. Frege’s notion of a proper name corresponds roughly to the notion of a (definite singular) noun phrase. Thus phrases like ‘the present king of France� or ‘John’s favorite dog� count as proper names for Frege. A name, according to Frege, designates or denotes its reference and expresses its sense. A sense is said, in turn, to determine a reference as displayed in figure 1. The reference of a name is typically an individual object -though the term ‘object� must be understood broadly. For example, the reference of the name ‘John� is the man John, the reference of the noun phrase, ‘Tony’s favorite color� is whatever color happens to be most favored by Tony, the reference of ‘The Second World War� is a certain complex, scattered event which occurred between 1939 and 1945.

Figure 1. A name expresses its sense, denotes its reference
(Source: Kenneth Taylor, 2000: 6)

Sense is a more difficult notion. Frege himself often talks in metaphors when it comes to explaining exactly what a sense is. He says a sense is a “way of being given a reference� or a “mode of presentation of a reference.� The crucial further claim is that the same reference can be given or presented in different ways, via different modes of presentation. In his Frege: Philosophy of Language, Dummett (1981) uses the apt metaphor of a sense containing a ‘one-side illumination� of a referent which shows the reference forth in a particular manner, under a particular guise, as it were. The ‘onesidedness� of such illumination is revealed by the fact that names which share a reference, need not share a sense. Senses have also been analogized to routes. A sense is to its reference as a route is to its destination. To follow the analogy further, two senses which ‘present� the same reference are like two distinct routes to the same destination. Just as one can travel two routes without knowing that they are routes to the same destination, so one can grasp two senses without knowing that they are senses which determine the same reference.

But if sense is a route to reference it is a one-way route. For although each sense ‘determines� a unique reference, a variety of distinct senses will co-determine, as we might say, the same reference. So when we have merely specified a given reference, we have not yet specified the route we have traveled to reach that reference. Hence there will be no single path ‘back up�, that leads from a given reference to a determinate sense. Suppose, for example, that ‘John�, ‘the brother of Mary�, and ‘Joe’s dearest friend� all designate John.

Figure 2. Sense is a one-way route to reference

These expressions will share a reference, but will have different senses. And given just that John is the reference in question, there is no determining via which of these three senses he has been presented.

Indeed, according to Taylor (2000), Frege himself never fully cashed out the metaphors by which he introduced the notion of sense. In due course, we shall examine at least one attempt to replace the metaphors with rigorous set-theoretic constructs. But even given the metaphors, we can begin to appreciate the role that the distinction is meant to play in resolving Frege’s puzzle. The crucial point is that informative statements of identity occur when and only when names which denote the same reference, but express different senses flank the identity sign. When two such names occur we have the same object presented again, but via different senses. And this fact is supposed to explain the possibility of informative, but true identity statements.

Footnotes and references:

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[1]:

See Frege’s ‘On Concept and Object�, and ‘On Sense and meaning� in (Frege 1984a) Collected Papers on Mathematics, Logic, and Philosophy, ed. B. McGuinness. Oxford: Basil Blackwell, pp. 157-77; and 182-94.