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A picture of Friedrich Ludwig Gottlob Frege

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Gottlob Frege (1848–1925) introduced Frege's Puzzles at the beginning of his 1892 article "Über Sinn und Bedeutung" ("On Sense and Reference"), one of the most influential articles in analytic philosophy and philosophy of language.

Frege's puzzles concern meaning and reference. These puzzles dealt with the semantics of proper names, which are words that refer to specific individuals, as well as, in some cases, indexicals, which are words whose reference is contingent upon the context they are used in.

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.

The first puzzle[edit]

The first problem considers the following sentences:

1. Hesperus = Hesperus.
2. Hesperus = Phosphorus (Lucifer).

Both of these sentences are true because 'Hesperus' and 'Phosphorus' have the same reference. They both refer to the same object, which is the planet Venus. The planet Venus can be seen as the brightest star of the morning or the evening within a few months difference. 'Hesperus' and 'Phosphorus' mean the same thing, however, they do not say the same thing. If you forget about the object that they are both referring to and focus on the meanings, you realize that the two names have different senses. In this case, 'Hesperus' was the name used for the brightest celestial body seen around sunrise, and 'Phosphorus' was the name used for the brightest celestial body seen around sunset.

Saying that Hesperus is identical to itself (1) is not informative, but saying it is identical to Phosphorus (2) is informative. This is because (2) provides new information and does not repeat already-known information like (1) does. Frege describes (1) and (2) as having different "cognitive values." (1) is just a truth of logic that can be known a priori, whereas (2) records an empirical truth that was discovered by astronomers. However, 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 statements (1) and (2) 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 the observer. Thus 'Hesperus' and 'Phosphorus' have the same reference, but differ in sense because they present Venus in different ways. A name's reference is the object it names, and the sense is how that object is picked out. This solves the puzzle, by showing that there is a difference in statements (1) and (2), which come from the difference of sense rather than the difference of reference. Frege explained that sentences can portray different information based on their senses.

The second puzzle[edit]

The second puzzle concerns propositional attitude reports, such as belief reports. Ordinarily, within a sentence, two names with the same reference are substitutable salva veritate, that is, without changing the truth value of the whole sentence. For example, if 'Hesperus is bright' is true, then 'Phosphorus is bright' is also true, since that 'Hesperus' and 'Phosphorus' refer to the same planet. Frege then considers the following argument:

3. Alex believes Hesperus is visible in the evening.

4. Hesperus = Phosphorus.

5. Alex believes Phosphorus is visible in the evening.

This argument appears to be invalid: even if (3) and (4) are true, (5) could be false. If Alex is not aware that Hesperus and Phosphorus are the same planet, then it seems that he could believe that Hesperus is visible in the evening while rejecting the claim that Phosphorus is visible in the evening (perhaps he thinks Phosphorus, the morning star, is only visible in the morning). 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 appealing 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, refers to the planet Venus when it occurs in the sentence 'Phosphorus is visible in the evening' or in an identity sentence like (4), but when it occurs embedded in an attitude report like (5), it instead refers to its ordinary sense.

This maneuver allows Frege to avoid the second puzzle, because 'Hesperus' in (3) now does not have the same reference as 'Phosphorus' in (5), since the ordinary sense of 'Hesperus' (the reference of 'Hesperus' in (3)) is different from the ordinary sense of 'Phosphorus' (which is the reference of 'Phosphorus' in (5)).

New theories of reference and the return of Frege's puzzle[edit]

Frege's puzzle has received a great deal of attention since the attacks on the descriptivist theory of names mounted in the 1970s and 1980s by philosophers such as Keith Donnellan, Saul Kripke, Ruth Barcan Marcus, Hilary Putnam, and David Kaplan. In the wake of these attacks on descriptivism, many philosophers embraced the Millian or direct-reference view of proper names, according to which the meaning of a name is simply its referent. As noted above, this Millian view has the result that (1) and (2) express the same proposition. Similarly, the embedded sentences 'Hesperus is visible in the evening' and 'Phosphorus is visible in the evening' from (3) and (5) express the same proposition. Therefore, it looks like (3) and (5) cannot differ in truth value, since they attribute belief in one and the same proposition.

Given this problem, 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.

References

1. Zalta, Edward N., "Gottlob Frege", Stanford Encyclopedia of Philosophy (Fall 2014), Edward N. Zalta (ed.)
2. ^ Cicero wrote: Stella Veneris, quae Φωσφόρος Graece, Latine dicitur Lucifer, cum antegreditur solem, cum subsequitur autem Hesperos; The star of Venus, called Φωσφόρος in Greek and Lucifer in Latin when it precedes, Hesperos when it follows the sun – De Natura Deorum 2, 20, 53. Pliny the Elder: Sidus appellatum Veneris … ante matutinum exoriens Luciferi nomen accipit … contra ab occasu refulgens nuncupatur Vesper (The star called Venus … when it rises in the morning is given the name Lucifer … but when it shines at sunset it is called Vesper) Natural History 2, 36
3. ^ Salmani Nodoushan, M. A. (2017). Lexemes, practs, and those who have yet to decide. Linguistik Online, 81, 77-93.
4. ^ Salmani Nodoushan, M. A. (2018). Which view of indirect reports do Persian data corroborate? International Review of Pragmatics, 10(1), 76-100.
5. ^ Cumming, S. "Names", Stanford Encyclopedia of Philosophy Edward N. Zalta (ed.)