Sense and Reference

The terms sense and reference in their technical meanings originate in the work of Gottlob FREGE, translating his "Sinn" and "Bedeutung" respectively (Frege 1967). According to Frege, every significant linguistic expression has both sense and reference, these being different kinds of semantic properties.

The reference of an expression is what it contributes to the truth or falsity of sentences in which it appears. Frege construed reference as a relation between the expression and some real object, the expression's referent. The referent of a singular term is what one would intuitively think the term stands for. The referent of both "Bill Clinton" and "The President of the United States in 1997" is the man, Bill Clinton. The referent of a sentence is its truth value, the True or the False, these being existent abstract objects. Predicative expressions refer to functions from objects to truth values. For example, the one-place predicate "runs" refers to a function that, given any object, x, as an argument, yields the value True if x runs and False if x does not run. In general, an n-place predicate refers to a function from ordered n-tuples to truth values. For example, the two-place predicate "likes" refers to a function from ordered pairs of objects, <x, y> to truth values; True if x likes y, False if x does not like y.

Reference is compositional in that the reference of a complex expression is determined by the reference of its parts and their syntactic mode of combination. Consider, for example, "Bill Clinton likes Al Gore." The two names provide the pair <Clinton, Gore>, and this pair is the argument to the function referred to by "likes." The referent of the sentence is then the value of that function, given <Clinton, Gore> as argument: True if Clinton likes Gore, False otherwise.

Frege applied a similar analysis to complex sentences built up from simpler ones. For example, a conjunction of the form "S1 and S2" has the value True, if S1 and S2 both have the value True, and False otherwise. So "and" refers to a function from pairs of truth values to truth values: it yields True given the pair <True, True> and False given any other pair.

Because an expression's referent is what it contributes to determining the truth values of sentences, reference is governed by principle (P):

(P) Co-referring expressions may be inter-substituted in any sentence without altering the truth value of that sentence.

For example, given that "Hesperus" and "Phosphorus" refer to the same thing (Venus), these terms ought to be intersubstitutable in any sentence without altering its truth value. (P) appears to be correct for many cases. However, as will be seen in a moment, there are also apparent counterexamples, and it is partly to deal with these that Frege introduced the notion of sense.

An expression's sense is an aspect of its SEMANTICS that is not accounted for in terms of reference. The referential properties of "Hesperus is Hesperus" and "Hesperus is Phosphorus" are identical. But whereas the former is a tautology, the latter carries empirical information and so has different cognitive value. Frege invoked sense to account for this cognitive value.

The sense of an expression is a "mode of presentation" of its referent, a way in which the referent is presented to the mind. The senses of the significant expressions in a sentence compose to form the sense of the sentence, which Frege called a "thought" ("Gedanke"). Thoughts are the contents of PROPOSITIONAL ATTITUDES. If, for example, someone believes that every even number is the sum of two primes, then they stand in a believing relation to the thought that every even number is the sum of two primes. If someone hopes that every even number is the sum of two primes, they stand in a hoping relation to the same thought.

In spite of their cognitive role, senses and thoughts are objective and mind-independent, in Frege's view: "When one apprehends . . . a thought one does not create it but only comes to stand in a certain relation . . . to what already existed beforehand" (1967: 30).

Because propositional attitudes are relations to thoughts, sentences ascribing propositional attitudes involve reference to thoughts. Notice that (P), above, appears to fail for (1) and (2), because one might be false while the other is true.

(1) Galileo believed that Hesperus is a planet.
(2) Galileo believed that Phosphorus is a planet.

Frege addressed this problem by proposing that in certain contexts (often called "referentially opaque contexts," after Whitehead and Russell 1925) words do not refer to their normal referents. Rather they refer to their normal senses. Thus (P) is preserved, because "Hesperus" and "Phosphorus" do not refer to the same thing in (1) and (2).

Sense also has a role in explaining reference. It is because an expression has its sense that it has its reference. Equally, a speaker's capacity to refer to or think about something is explained in terms of sense: a thinker thinks about a particular object by grasping a sense that presents that object (Evans 1982; Burge 1977; Dummett 1973).

It is sometimes thought that a further reason why Frege invoked senses was to account for the meaningfulness of expressions that lack a referent, such as "Vulcan" or "The largest prime." There is probably some truth in this, as Frege did allow that nonreferring expressions could have a sense. However, it is not clear that Frege should have allowed this, given the fundamental role of reference in his philosophy of language. (See Dummett 1973: 185; Evans 1982: chap. 1 for discussion.)

Frege's theories of sense and reference have been criticized in many ways. Most commentators have tended to propose modifications to the overall picture, rather than reject it outright. For example, it is a popular move to keep much of the account of reference in place, without insisting that truth values are objects or that predicates refer to functions. One replaces "refers to the True" by "is true," and replaces talk of predicates referring to functions by talk of predicates applying to objects under specified conditions, as in, for instance, "red" applies to any object x if and only if x is red (Davidson 1967; Evans 1982; McDowell 1977).

The account of sense is often criticized on the grounds that no one kind of thing can play all the roles that Frege assigned to sense. For example, it is often held that cognitive value does not determine reference, because two expressions might refer to different things, yet share the same cognitive value. For example "That man" might be used once to refer to Castor and then, on a separate occasion, to refer to Castor's identical twin, Pollux. The way in which the speaker thinks of Castor might be just the same as the way he thinks of Pollux, so the cognitive values of the expressions might be the same, although their referents differ (Burge 1977; Kaplan 1990; Perry 1990; for a defense of Frege, see Evans 1990).

Frege himself was primarily concerned with the development of symbolic LOGIC and semantics for formal languages of mathematics and science, rather than with a theory of natural language. Nevertheless, he provides a theory of content that can be applied to propositional attitudes and the other psychological states that are the subject matter of the cognitive sciences. Frege's work raises fundamental questions that lie at the heart of cognitive science and the philosophy thereof. Perhaps the most basic is whether the notion of content in cognitive science can be assimilated with either sense or reference or both (cf. PRAGMATICS; Segal 1995; Fodor 1994; Millikan 1997; Chomsky 1995).

See also

Additional links

-- Gabriel Segal


Burge, T. (1977). Belief de re.The Journal of Philosophy 74:338-362.

Chomsky, N. (1995). Language and nature. Mind 104:1-61.

Davidson, D. (1967). Truth and meaning. Synthese 17:304-323.

Dummett, M. (1973). Frege: Philosophy of Language. London: Duckworth.

Evans, G. (1982). The Varieties of Reference. Oxford: Oxford University Press.

Evans, G. (1990). Understanding demonstratives. In P. Yourgrau, Ed., Demonstratives. Oxford: Oxford University Press.

Fodor, J. (1994). The Elm and the Expert. Cambridge, MA: MIT Press.

Frege, G. (1952/1892). On sense and reference. In P. Geach and M. Black, Eds., Translations of the Philosophical Writings of Gottlob Frege. Oxford: Blackwell.

Frege, G. (1967/1918). The thought: A logical enquiry. Translated by A. and M. Quinton; reprinted in P. F. Strawson, Ed., Philosophical Logic. Oxford: Oxford University Press.

Kaplan, D. (1990). Thoughts on demonstratives. In P. Yourgrau, Ed., Demonstratives. Oxford: Oxford University Press.

McDowell, J. (1977). The sense and reference of a proper name. Mind 86:159-185.

Millikan, R. (1997). Images of identity: In search of modes of presentation. Mind 106:499-519.

Perry, J. (1990). Frege on demonstratives. In P. Yourgrau, Ed., Demonstratives. Oxford: Oxford University Press.

Segal, G. (1995). Truth and Sense. In J. Biro and P. Kotatko, Eds., Frege: Sense and Reference 100 Years On. Dordrecht: Kluwer.

Whitehead, A. N., and B. Russell. (1925). Principia Mathematica. 2nd. ed. Cambridge: Cambridge University Press.

Further Readings

Burge, T. (1979). Sinning against Frege. Philosophical Review 58:398-432.

Burge, T. (1986). Frege on Truth. In L. Haaparanta and J. Hintikka, Eds., Frege Synthesised. Dordrecht: Reidel.

Burge, T. (1992). Frege on knowing and the third realm. Mind 101:633-650.

Dummett, M. (1981). The Interpretation of Frege's Philosophy. London: Duckworth.

Frege, G. (1980). Philosophical and Mathematical Correspondence. G. Gabriel, H. Hermes, et al., Eds. Oxford: Blackwell.

Frege, G. (1979). Posthumous Writings. H. Hermes, F. Kembertal, et al., Eds. Oxford: Blackwell.

Kripke, S. (1979). A puzzle about belief. In A. Margalit, Ed., Meaning and Use. Dordrecht: Reidel.

Kripke, S. (1980). Naming and Necessity. Cambridge, MA: Harvard University Press.

Larson, R., and G. Segal. (1995). Knowledge of Meaning: An Introduction to Semantic Theory. Cambridge, MA: MIT Press.

McDowell, J. (1984). De re senses. In C. Wright, Ed., Frege: Tradition and Influence. Oxford: Blackwell, pp. 98-109.

Millikan, R. (1984). Language, Thought and Other Biological Categories. Cambridge, MA: MIT Press.

Millikan, R. (1991). Perceptual content and the Fregean myth. Mind 100:439-459.

Noonan, H. (1984). Fregean thoughts. In C. Wright, Ed., Frege: Tradition and Influence. Oxford: Blackwell, pp. 20-39.

Putnam, H. (1975). The meaning of "meaning." Reprinted in Putnam's Philosophical Papers 2, Mind, Language and Reality. Cambridge: Cambridge University Press.

Russell, B. (1905). On denoting. Mind 14:479-493.

Salmon, N. (1986). Frege's Puzzle. Cambridge, MA: MIT Press.

Weiner, J. (1990). Frege in Perspective. Ithaca, NY: Cornell University Press.

Wright, C., Ed. (1984). Frege: Tradition and Influence. Oxford: Blackwell.