Frege's Puzzle
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Frege's puzzles are puzzles about the
semantics Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...
of
proper name A proper noun is a noun that identifies a single entity and is used to refer to that entity (''Africa''; ''Jupiter''; ''Sarah''; ''Walmart'') as distinguished from a common noun, which is a noun that refers to a class of entities (''continent, pl ...
s, although related puzzles also arise in the case of
indexical In semiotics, linguistics, anthropology, and philosophy of language, indexicality is the phenomenon of a '' sign'' pointing to (or ''indexing'') some element in the context in which it occurs. A sign that signifies indexically is called an index o ...
s.
Gottlob Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philos ...
(1848–1925) introduced the puzzle at the beginning of his article "Über Sinn und Bedeutung" ("
On Sense and Reference In the philosophy of language, the distinction between sense and reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the ...
") in 1892 in one of the most influential articles in
analytic philosophy Analytic philosophy is a broad movement within Western philosophy, especially English-speaking world, anglophone philosophy, focused on analysis as a philosophical method; clarity of prose; rigor in arguments; and making use of formal logic, mat ...
and
philosophy of language Philosophy of language refers to the philosophical study of the nature of language. It investigates the relationship between language, language users, and the world. Investigations may include inquiry into the nature of Meaning (philosophy), me ...
.


The puzzles

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

The first problem considers the following sentences: #
Hesperus In Greek mythology, Hesperus (; ) is the Evening Star, the planet Venus in the evening. A son of the dawn goddess Eos ( Roman Aurora), he is the half-brother of her other son, Phosphorus (also called Eosphorus; the "Morning Star"). Hesperus' Rom ...
is Hesperus. # Hesperus is
Phosphorus Phosphorus is a chemical element; it has Chemical symbol, symbol P and atomic number 15. All elemental forms of phosphorus are highly Reactivity (chemistry), reactive and are therefore never found in nature. They can nevertheless be prepared ar ...
(
Lucifer The most common meaning for Lucifer in English is as a name for the Devil in Christian theology. He appeared in the King James Version of the Bible in Isaiah and before that in the Vulgate (the late-4th-century Latin translation of the Bib ...
). Each of these sentences is true, since 'Hesperus' refers to the same object as 'Phosphorus' (the planet Venus which few months apart can be seen as the brightest star of morning or of evening). 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 ('from the earlier') and ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, Justification (epistemology), justification, or argument by their reliance on experience. knowledge is independent from any ...
, 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 John Stuart Mill (20 May 1806 – 7 May 1873) was an English philosopher, political economist, politician and civil servant. One of the most influential thinkers in the history of liberalism and social liberalism, he contributed widely to s ...
). 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 sense is a biological system used by an organism for sensation, the process of gathering information about the surroundings through the detection of Stimulus (physiology), stimuli. Although, in some cultures, five human senses were traditio ...
: 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.


The second puzzle

The second puzzle concerns
propositional attitude A propositional attitude is a mental state held by an agent or organism toward a proposition. In philosophy, propositional attitudes can be considered to be neurally realized, causally efficacious, content-bearing internal states (personal princip ...
reports, such as belief reports. Ordinarily, coreferring names are substitutable ''
salva veritate In philosophy, salva veritate (or intersubstitutivity) is the logical condition by which two expressions may be interchanged without altering the truth-value of statements in which the expressions occur. Substitution ''salva veritate'' of co-extens ...
'', that is, without change in truth value. For example, if 'Hesperus is bright' is true then 'Phosphorus is bright' is also true given that 'Hesperus' and 'Phosphorus' refer to the same planet. Frege then considers 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 Invalid may refer to: * Patient, a sick person * one who is confined to home or bed because of illness, disability or injury (sometimes considered a politically incorrect term) * Invalid (film), a 2023 Slovak black comedy movie * .invalid, a top-l ...
: 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 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 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 denotes its ordinary ''sense.''


New theories of reference and the return of Frege's puzzle

Frege's puzzle has received a great deal of attention since the attacks on the
descriptivist theory of names In the philosophy of language, the descriptivist theory of proper names (also descriptivist theory of reference) is the view that the meaning or semantic content of a proper name is identical to the descriptions associated with it by speakers, whi ...
mounted in the 1970s and 1980s by philosophers such as
Keith Donnellan Keith Sedgwick Donnellan (; June 25, 1931 – February 20, 2015) was an American philosopher and professor of philosophy (later professor emeritus) at the University of California, Los Angeles. Donnellan contributed to the philosophy of languag ...
,
Saul Kripke Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American analytic philosophy, analytic philosopher and logician. He was Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emer ...
,
Ruth Barcan Marcus Ruth Barcan Marcus (; born Ruth Charlotte Barcan; 2 August 1921 – 19 February 2012) was an American academic philosopher and logician best known for her work in modal and philosophical logic. She developed the first formal systems of quant ...
,
Hilary Putnam Hilary Whitehall Putnam (; July 31, 1926 – March 13, 2016) was an American philosopher, mathematician, computer scientist, and figure in analytic philosophy in the second half of the 20th century. He contributed to the studies of philosophy of ...
, and David Kaplan.Cumming, S.
Names
, ''
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') is a freely available online philosophy resource published and maintained by Stanford University, encompassing both an online encyclopedia of philosophy and peer-reviewed original publication ...
'' Edward N. Zalta (ed.)
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. It therefore looks like (3) and (5) cannot differ in truth value since they attribute belief in one and the same proposition. In view of 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 Nathan U. Salmon (; né Nathan Salmon Ucuzoglu; born January 2, 1951) is an American philosopher in the analytic tradition, specializing in metaphysics, philosophy of language, and philosophy of logic. Life and career Salmon was born Janua ...
(e.g. in ''Frege's puzzle'' and ''Content, Cognition, and Communication''),
Howard Wettstein Howard is a masculine given name derived from the English surname Howard. ''The Oxford Dictionary of English Christian Names'' notes that "the use of this surname as a christian name is quite recent and there seems to be no particular reason for i ...
(e.g. in "Has Semantics Rested on a Mistake?"),
Scott Soames Scott Soames (; born 1945) is an American philosopher. He is a professor of philosophy at the University of Southern California (since 2004), and before that at Princeton University. He specializes in the philosophy of language and the history of ...
, David Kaplan, John Perry (e.g. in ''Reference and Reflexivity''), and
Joseph Almog Joseph is a common male name, derived from the Hebrew (). "Joseph" is used, along with " Josef", mostly in English, French and partially German languages. This spelling is also found as a variant in the languages of the modern-day Nordic count ...
.


References

Philosophical problems Philosophy of language Meaning (philosophy of language) Names {{Formal semantics