Sense and Reference

In brief

In 1892 Gottlob Frege (1848 to 1925) published a short paper, "Über Sinn und Bedeutung," usually translated "On Sense and Reference." It opens with a puzzle about identity. The statement "the morning star is the evening star" told astronomers something they did not already know: the bright body seen at dawn and the one seen at dusk are a single planet, Venus. Yet "the morning star is the morning star" tells no one anything. If the meaning of a name were simply the object it names, the two statements would say the same thing, since both flank the identity sign with expressions for Venus. Frege's answer was that a name contributes more than its object. It contributes a sense, a particular way the object is presented to the mind. Same object, two senses, and the difference in sense is what makes one statement informative and the other empty.

The full treatment

The puzzle it answers

Frege calls it a puzzle about the cognitive value of identity statements. Take the schematic forms "a = a" and "a = b." The first is knowable in advance, true by logic alone, carrying no information. The second, when true, can be a real extension of knowledge, sometimes a great one. But if the only semantic job a name does is to stand for its bearer, and "a" and "b" stand for the same bearer, then "a = b" and "a = a" express the very same proposition, and there is no room for one to be informative and the other trivial. Something in the meaning of "a" and "b" must differ even when their bearer does not. That something is what Frege names Sinn, sense.

How the distinction works

Frege splits the meaning of an expression into two components. The Bedeutung, translated as reference (also "meaning" or "denotation" in various renderings), is the object the expression stands for. The Sinn, sense, is the mode of presentation of that object, the manner in which it is given. "The morning star" and "the evening star" have the same reference, Venus, but present it differently, one as the last star fading at dawn, the other as the first appearing at dusk. His own geometric image is precise: consider the point where the three medians of a triangle meet. "The intersection of medians a and b" and "the intersection of medians b and c" pick out the same point by different routes. The point is the reference; each route is a sense.

Frege extends the two layers upward. A whole declarative sentence also has both. Its sense is the thought it expresses, a proposition that is not a private mental image but an objective content graspable by anyone. Its reference, on his striking and controversial claim, is its truth value: every true sentence refers to the True, every false sentence to the False. He is driven to this by a compositional principle he holds throughout: the reference of a complex expression depends only on the references of its parts. Swap "the morning star" for "the evening star" inside a sentence and the truth value cannot change, because reference is preserved. What can change is the thought expressed, the sense.

Why sense is not merely psychological

Frege guards the distinction against a natural misreading. Sense is not a private idea in someone's head. The idea I associate with "Venus," my mental picture, is subjective and varies from person to person. Sense is public and shared: two competent speakers grasp the same sense when they understand the same expression, which is why they can communicate, disagree, and reason together at all. He locates senses, and the thoughts built from them, in what he calls a "third realm," neither physical objects nor private mental contents but abstract entities that are objective yet non-spatial. This anti-psychologism, the refusal to reduce logic and meaning to facts about the mind, is one of the deepest commitments of his whole program and a founding move of analytic philosophy.

The case of empty names

The distinction does work that a one-layer theory cannot. "Odysseus" and "the greatest prime number" have a sense: we understand them, they figure in intelligible sentences. But they have no reference; there is no such man, no such number. On the bare view that meaning is reference, these expressions would be meaningless, and sentences containing them would say nothing. Frege's split lets him say the natural thing: they are meaningful, they express thoughts, they simply fail to pick anything out. This also explains why, in fiction or in mistaken belief, we grasp sentences perfectly well while the question of their truth value lapses.

Lineage

Frege was building the foundations of arithmetic, arguing in The Foundations of Arithmetic (1884) that mathematics reduces to logic, a project called logicism. To carry it out he had already invented modern quantificational logic in his Begriffsschrift (1879), the notation of variables, quantifiers, and functions that superseded the term logic descended from Aristotle (384 to 322 BCE). The sense and reference distinction grew from that technical work: he needed to explain how mathematical identities could be both provable and informative. Against the empiricist tradition running through David Hume and John Stuart Mill, for whom numbers and names were tied to experience and to what they denote, Frege set an objective realm of abstract meaning, closer in spirit to the a priori structures of Immanuel Kant (1724 to 1804), though Frege rejected Kant's claim that arithmetic rests on intuition. The distinction is the semantic heart of a program meant to secure the objectivity of logic and number.

The strongest case for it

The distinction earns its keep by solving several problems at one stroke with a single, economical idea. It resolves the identity puzzle: informativeness tracks difference in sense, not difference in reference. It explains meaningful but empty names without declaring them nonsense. And it handles what are now called opaque contexts, the failures of substitution inside reports of belief and other attitudes. "Lois Lane believes Superman can fly" can be true while "Lois Lane believes Clark Kent can fly" is false, though Superman is Clark Kent. Frege's account is elegant: inside a belief report, expressions refer not to their ordinary references but to their ordinary senses, so swapping co-referring names can change truth value because it changes which sense is in play. That three distinct and stubborn phenomena fall out of one distinction is a strong argument that the distinction is carving meaning at a real joint. The framework also gives compositionality a clean statement, and much of twentieth-century formal semantics, through Rudolf Carnap's intension and extension and beyond, is a development of Frege's two levels.

The strongest case against it

The framework has been pressed hard from two directions.

Bertrand Russell (1872 to 1970), in "On Denoting" (1905), rejected Frege's treatment of definite descriptions. Phrases like "the present king of France," Russell argued, are not names with a sense that presents an object; they are disguised quantifiers. "The king of France is bald" unpacks as: there is exactly one king of France, and he is bald. This is simply false, not truth-valueless, when there is no king, and it dissolves the puzzles about empty descriptions without any appeal to sense. Russell's analysis became the model of logical analysis for a generation and is still the standard treatment of descriptions.

The deeper challenge came from Saul Kripke (1940 to 2022) in Naming and Necessity (1980). Frege is read as holding a description theory of proper names: the sense of "Aristotle" is something like "the pupil of Plato who taught Alexander." Kripke attacked this. Names, he argued, are rigid designators: "Aristotle" picks out the same man in every possible situation, even those in which he taught no one and Plato never met him. If the name were equivalent to a description, "Aristotle taught Alexander" would be necessary, which it plainly is not; Aristotle might have done otherwise. Kripke also pressed the semantic argument: ordinary speakers refer to Kurt Gödel with the name "Gödel" even while associating with it only the false description "the man who proved the incompleteness of arithmetic," a theorem someone else might really have proved. Reference, on this causal-historical picture, is fixed by a chain of use traced back to an initial baptism, not by any sense the speaker grasps. Direct-reference theorists such as Kripke, Keith Donnellan, and later David Kaplan concluded that proper names contribute only their bearer, with no Fregean sense, reopening the very identity puzzle Frege set out to solve.

Ludwig Wittgenstein (1889 to 1951), who absorbed Frege early and visited him, later turned against the whole picture of meaning as a fixed relation between word and object. In the Philosophical Investigations (published 1953) he argued that meaning is not an abstract entity attached to a word but a matter of use in the practices of a language, and that Frege's tidy correspondence of name to object misdescribes how words actually function. On this view the search for a determinate sense that mechanically fixes reference is a philosopher's mirage.

Where it stands now

No single verdict has settled it, which is itself a measure of the idea's depth. Frege's distinction is the origin point of philosophy of language as a discipline and of formal semantics as a field, revived and made central by Michael Dummett's reconstruction in the 1970s. For definite descriptions, Russell's quantifier analysis largely prevails. For proper names, Kripke's rigid designation is the dominant orthodoxy, and the mainstream view is that Frege's simple description theory of names fails. Yet sense refuses to die. The puzzles Frege raised, informativeness of identities and the opacity of belief reports, remain live problems for direct-reference theories, which must reconstruct in some other vocabulary the work that sense once did. Neo-Fregeans and two-dimensional semanticists such as David Chalmers keep a descendant of sense alive precisely because reference alone still cannot explain why "Hesperus is Phosphorus" was a discovery. The distinction may be wrong in detail and indispensable in outline.

Test yourself

You know that "water" and "H2O" pick out the same stuff. Was learning that they are the same an empty tautology, like "water is water," or did it add to what you knew? If it added something, then the two expressions are doing more than pointing at one substance. Try to say, in your own words, what the extra thing is. Whatever you land on is your version of what Frege called sense.