Frege's Puzzle

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Frege's Puzzle is a puzzle about the semantics of proper names, although related puzzles also arise in the case of indexicals. Frege introduced the puzzle at the beginning of his article "Über Sinn und Bedeutung" ("On Sense and Reference"), one of the most influential articles in analytic philosophy and philosophy of language.

The Puzzles[edit]

The term "Frege's Puzzle" is commonly applied to two related problems. One is a problem about identity statements that Frege raised at the beginning of "On Sense and Reference", and another concerns propositional attitude reports.[1] For the first problem, consider the following two sentences:

(1) Hesperus is Hesperus.

(2) Hesperus is Phosphorus.

Each of these sentences is true, since 'Hesperus' refers to the same object as 'Phosphorus' (the planet Venus). Nonetheless, (1) and (2) seem to differ in their meaning or what Frege called "cognitive value". (1) is just a truth of logic that can be known a priori, whereas (2) records an empirical truth that was discovered by astronomers. The problem, however, is that proper names are often taken to have no meaning beyond their reference (a view often associated with John Stuart Mill). But this seems to imply that the two statements mean the same thing, or have the same cognitive value. Frege proposed to resolve this puzzle by postulating a second level of meaning besides reference in the form of what he called sense: a difference in the mode of presentation or the way an object can be "given" to us. Thus 'Hesperus' and 'Phosphorus' have the same reference, but differ in sense because they present Venus in different ways.

The second puzzle concerns propositional attitude reports, such as belief reports. Ordinarily, coreferring names are substitutable salva veritate, that is, without change in truth value. Thus if 'Hesperus is bright' is true then 'Phosphorus is bright' is also true. But now consider the following argument:

(1) Alex believes Hesperus is visible in the evening.

(2) Hesperus = Phosphorus.

(3) Alex believes Phosphorus is visible in the evening.

This argument appears to be invalid: even if (1) and (2) are true, (3) can be false. Alex might not be aware that Hesperus and Phosphorus are the same planet, and believe that although Phosphorus is visible in the morning, it isn't visible in the evening. The principle that coreferring names are substitutable salva veritate thus appears to fail in the context of belief reports (and similarly for other propositional attitude reports). Frege again proposed to solve this problem by appeal to his distinction between sense and reference. In particular, he held that when a proper name occurs in the context of an attitude report, its reference shifts to its ordinary sense: thus 'Phosphorus', for example, denotes the planet Venus when it occurs in a sentence like 'Phosphorus is bright', but when it occurs in an attitude reports like (3) it denotes its ordinary sense.

New Theories of Reference and the Return of Frege's Puzzle[edit]

Frege's solution was definitive for much of the Twentieth Century. Only recently, with the rise of anti-descriptivist (and thus anti-Fregean) theories of reference, has Frege's Puzzle become a dominant problem in the philosophy of language. (Though it should be noted that the descriptivist interpretation of Frege's notion of sense is now rejected by many scholars.)[citation needed] This trend began some time in the late 1960s and early 1970s, when such philosophers as Keith Donnellan, David Kaplan, Saul Kripke, Ruth Barcan Marcus, and Hilary Putnam began to entertain arguments against Frege's theory. Perhaps most influential in this regard is Kripke's book of lectures, Naming and Necessity. To some extent, the resulting new theories of reference mark a return to the Millian view of proper names, and thus invite the problem of Frege's puzzle anew.

In the last several decades, then, many philosophers of language have attempted to work out a solution to the puzzle within the confines of direct-reference theories of proper names. Some of these philosophers include Nathan Salmon (e.g. in Frege's Puzzle and Content, Cognition, and Communication), Howard Wettstein (e.g. in "Has Semantics Rested on a Mistake?"), Scott Soames, David Kaplan, John Perry (e.g. in Reference and Reflexivity), and Joseph Almog.

See also[edit]


  1. ^ Zalta, Edward N., "Gottlob Frege", The Stanford Encyclopedia of Philosophy (Fall 2014 Edition), Edward N. Zalta (ed.), URL = <>.