PHIL 4150: Analytic Philosophy
Dr. Robert Lane
Lecture Notes: Tuesday August 28, 2012


[2.] Gottlob Frege.[1]


[2.1.] Introduction to Philosophy of Language.


One of the distinguishing characteristics of the tradition of analytic philosophy is its concern with language. Philosophers in this tradition believed that philosophy ought to concern itself with language in two ways:

(i)     as a means to an end, to help solve traditional philosophical problems;

(ii)   as a subject of philosophical investigation in its own right.


It was during the period of this tradition (from the late 19th century through the mid-to-late 20th century) that a new area of philosophy came into being:


philosophy of language (df.): the area of philosophy that attempts to answer questions about language, e.g.,

·         what is linguistic meaning (the sort of meaning possessed by a meaningful word, phrase or sentence)? is the meaning of a unit of language (i.e., the meaning of a word, phrase, or sentence) an entity? if so, what kind of entity is it? if meanings aren’t entities, then what exactly is meaning?

·         how do specific kinds of language (names, descriptions, subject and predicate terms) come to have meaning? in other words, how do those kinds of language work, exactly?

·         what is it for a language user to be competent in a given language?


A tremendous amount of work was done in this area in the 20th century, and it continues until this day. It is one of the central areas of analytic philosophy (in the sense of philosophy in the analytic style).


Many, perhaps even most, degree-granting programs in philosophy in the United States have at least one course devoted to philosophy of language (UWG’s program is an exception).


The turn away from a direct concern with epistemological, metaphysical, and ethical questions toward questions dealing directly with language has been dubbed “the Linguistic Turn.” This is the title of a well-known anthology of analytic writings edited by Richard Rorty and published in 1967 ( (UWG’s library owns a copy of this book.)


Many contemporary philosophers believe that “the linguistic turn” began with “On Sense and Reference” (“Über Sinn und Bedeutung”), an essay by Gottlob Frege published in 1892.[2]



[2.2.] Frege’s Life.[3]


·         1848-1925

·         Born in Wismar, Germany.

·         His father owned and was the headmaster of a private school for girls.

·         His father died in 1866, his mother took over the school, and Frege went off to college at the University of Jena (now called Friedrich Schiller University Jena[4]; Goethe and Hegel taught there).

·         As an undergraduate he studied a number of fields: math, chemistry, physics, and philosophy.

·         He then studied at the University of Göttingen[5] for two years and received his doctoral degree from there.

·         He returned to Jena, where he wrote a post-doctoral thesis that was required to become a university teacher.

·         He then took an unpaid teaching position in mathematics at Jena, and his mother moved to Jena to live with him and help support him.

·         He was eventually promoted to a paid position, and finally to a full professorship.

·         While on a hiking trip he met Margarete Lieseberg, and they married in 1897; she became ill and died in 1903.



[2.3.] Frege’s Project: Logicism.


Throughout much of his career, Frege’s central project was one that combined mathematics, logic and philosophy.


Its central question was: why is our knowledge of arithmetic so secure? And more specifically, why is it so much more secure than our empirical knowledge? [empirical (df.): derived from, or having to do with, sense experience]


Frege’s answer to that question, and the claim that much of his work was in support of, was logicism:


logicism (df.): the truths of arithmetic can be derived from (or “reduced to”) truths of logic.

·         Such a derivation would begin by defining arithmetical concepts, like the concept of number, in terms of logical concepts. For the purposes of logicism, such logical concepts included the concept of a set.[6]

·         If true, logicism would explain the apparent difference between our knowledge of arithmetic and our empirical knowledge. Arithmetical knowledge seems more secure and less dependent on sense experience than empirical knowledge; this seeming difference will be explained if arithmetic is, at bottom, nothing but logic.[7]


This was the central defining project of Frege’s professional life. His important philosophical work was all done in the service of this project.


In order to prove that logicism is true, Frege developed a new artificial language in which to express truths of arithmetic and logic: it was the first system of symbolic logic and was published in 1879 in Frege’s book, Begriffschrift (“Concept-writing”).[8]


His other important book-length works:

·         Foundations of Arithmetic (1884)

·         Basic Laws of Arithmetic v.1 (1893) & v.2 (1903)


It is now universally acknowledged that Frege did not achieve his goal of showing that the truths of arithmetic could be derived from the truths of logic, i.e., he failed to prove the truth of logicism.[9]


Despite this failure, much of the work that he did as part of his overall project was philosophically valuable. He revolutionized logic by creating a new artificial, symbolic language, and he initiated (or, at least, he renewed interest in) philosophy of language.


His 1892 paper “On Sense and Reference” (“Über Sinn und Bedeutung”) is where modern philosophy of language began.[10] Some issues covered in this article are:

·         the nature of identity;

·         the meaning of names;

·         whether sentences containing non-referring expressions (expressions that do not refer to anything, e.g., “The first dog on the moon was a pit bull”) are false, or neither true nor false.



[2.4.] Two Types of Identity.


In “On Sense and Reference,” Frege identified a philosophical puzzle which is now well-known and widely written about.


It is a puzzle about statements of identity (in German, “Gleichheit”; the translation in your textbook translates this word as equality).[11]


To understand the puzzle, we need to distinguish between two different meanings of the word “identity”—the puzzle involves only one of them...


qualitative identity (df.): x and y are qualitatively identical if and only if they have all of the same qualities or properties (except location in time and space).

·         You and I might wear identical shirts (both are long-sleeved, red, manufactured in Singapore, sold by Urban Outfitters in 2012). The shirts are alike in all their physical characteristics (except location in space—mine is in my closet, and yours is in your closet). A statement expressing this qualitative identity of our shirts might be: “My shirt is identical to your shirt.”


This is not the sort of identity statement that is relevant to Frege’s puzzle about identity.


The sort of identity that is relevant is the sort of identity expressed by a sentence like “Superman is identical to Clark Kent.” This means that Superman and Clark Kent are one and the same being. It means, not that they share all the same qualities (being male, being Kryptonian, having super powers, etc.), but that they are one and the same entity. This sort of identity is known as numerical or quantitative identity.


numerical identity a.k.a. quantitative identity (df.): x and y are numerically identical if and only if x is one and the same thing as y (e.g., as Clark Kent is identical to Superman, as Mark Twain is identical to Samuel Clemens, as Barack Obama is identical to the 44th President of the United States, etc.).


Frege’s puzzle about identity is a puzzle regarding statements about numerical identity.



[2.5.] Frege’s Puzzle About Identity.


“Morning Star” and “Evening Star” are two names for the same heavenly body: Venus.


Important interlude: the use/mention distinction.


Notice that in the above sentence, the names “Morning Star” and “Evening Star” are surrounded by quotation marks, while the name “Venus” is not. This illustrates the use/mention distinction:

·         In that sentence, the name “Venus” is being used to refer to the planet Venus.

·         But the names “Morning Star” and “Evening Star” are being mentioned—the sentence is saying something about those names, i.e., about those pieces of the English language.

·         When you are mentioning words (or other linguistic expressions, like phrases or sentences) themselves, you should indicate this by surrounding those expressions in quotation marks. For example:

·         Cats have four legs, and so do dogs.

·          “Cats” has four letters, and so does “dogs.”[12]


But it was not always known that “Morning Star” and “Evening Star” name the same object. Sailors would refer to the first star to appear at night at certain times of the year as the Evening Star, and the last star to disappear in the morning at other times of the year as the Morning Star, without realizing that the Morning Star and the Evening Star are actually one and the same object.


The sentence “The Morning Star = the Evening Star” (or “The Morning State is the Evening Star”) seems to express a discovery. That is, it seems that the sentence cannot be known to be true simply by understanding the meaning of its words. We have to discover whether it is true by some sort of sensory observation. This sentence is a posteriori:


a posteriori: (df.) describes a sentence (statement, proposition, etc.) which one can know to be true or false only by way of (after, posterior to) sense experience.


This is unlike the sentence “The Morning Star = the Morning Star” (or “The Morning Star is the Morning Star.”) This sentence does not express a discovery; you do not need to have any sort of sensory experience to know whether it is true. Anyone who understands the meaning of “The Morning Star = the Morning Star” will know that it is true. It is a priori:


a priori: (df.) describes a statement which one can know to be true or false independently of (prior to) sense experience.


Frege describes the difference between the sentences by saying that “The Morning Star = the Evening Star” has cognitive value, but “The Morning Star = the Morning Star” does not.


Frege’s puzzle about identity is this:


Given that the Morning Star is in fact identical to the Evening Star, how can there be any difference in cognitive value between the two sentences:

“The Morning Star = the Evening Star”


“The Morning Star = the Morning Star”


Since the name “the Morning Star” and the name “the Evening Star” mean the same thing (they both mean Venus), those two sentences should mean exactly the same thing. So how is it that one has cognitive value and the other does not?


More generally, the question is this:


How can “a = a” and “a = b” differ in cognitive value when “a = b” is true?



[2.5.1.] Frege’s Earlier Solution.


“On Sense and Reference” begins with Frege explaining how he had solved this puzzle in his 1879 book Begriffschrift; he then rejects that earlier solution and provides a new one.


The explanation he gives of his earlier solution involves the concept of a relation:


relation: (df.) a property that holds between two or more objects or between an object and itself; e.g., being the brother of, being shorter than, being between, admiring, etc.

·         It might be that identity (being identical to) is a relation; Frege raises the question whether identity (equality, Gleichheit) is a relation at the beginning of “On Sense and Reference.”


(Remember, the translation of “On Sense and Reference in your textbook translates “Gleichheit” not as “identity” but as “equality.”)



Stopping point for Tuesday August 28. For next time, read pp.9-12 (to the end of the first paragraph on p.12). MAKE SURE THAT YOU READ THE CORRESPONDING ENDNOTES AS YOU GO. Be prepared to answer these questions in class:

1.      What solution do his puzzle about identity did Frege give earlier?

2.      What reason does he now give for rejecting the earlier solution to the puzzle about identity?

3.      What solution to the puzzle does he now give?



[1] For further information on Frege, see Edward N. Zalta, “Gottlob Frege”, The Stanford Encyclopedia of Philosophy (Summer 2005 Edition), Edward N. Zalta (ed.), URL = <>.


[2] According to Hans Sluga, Frege “can be considered the first analytic philosopher.” (Frege, Routledge, 1980, p.2.) However, unlike many analytic philosophers who are interested in Frege’s work and who tend to treat Frege as if his views were a true revolution in the history of philosophy, Sluga emphasizes the continuity between Frege’s thought and other nineteenth-century German philosophers.


[3] From Joan Weiner, Frege (Oxford University Press, 1999), ch.1. Wiener recounts a decision that Frege made shortly after his wife’s death:


Although Frege and his wife had had no children, after her death Frege took responsibility for bringing up a child. In 1908, 5-year-old Alfred Fuchs’s mother was seriously ill and his father had been committed to an asylum. No suitable guardian could be found among the relatives of his parents, and the people who knew Alfred in Gniebsdorf regarded him as incorrigible. At the suggestion of Frege’s nephew, who was a pastor in Gniebsdorf, Frege became Alfred’s guardian. Later, when Alfred came of age, Frege adopted him. Frege was, by all accounts, a kind and loving father. Alfred’s school records indicate that he was well behaved and diligent. Alfred ultimately became a mechanical engineer.

                It is difficult to fail to be moved by the generosity of spirit suggested by this information about Frege’s later life.[3]


But Weiner also relays another, more troubling aspect of Frege’s personality. Late in his life he kept a diary in which he recorded thoughts on politics. After Germany’s defeat during WWI, and perhaps in response to what he took to be overly harsh terms in the Treaty of Versailles, Frege developed anti-democratic views, as well as an apparent streak of anti-semitism. One passage, from April 1924, reads:


One can acknowledge that there are Jews of the highest respectability, and yet regard it as a misfortune that there are so many Jews in Germany, and that they have complete equality of political rights with citizens of Aryan descent; but how little is achieved by the wish that the Jews in Germany should lose their political rights or better yet vanish from Germany. If one wanted laws passed to remedy these evils, the first question to be answered would be: how can one distinguish Jews from non-Jews for certain? That may have been relatively easy 60 years ago. Now, it appears to me to be quite difficult. Perhaps one must be satisfied with fighting the ways of thinking which show up in the activities of the Jews and are so harmful, and to punish exactly these activities with the loss of civil rights and to make the achievement of civil rights more difficult.[3]


Weiner concludes: “the available evidence leaves us with a complex picture of Frege’s character—a picture that combines admirable and abhorrent features.” (3)






[6]The objects of study of Set Theory are sets. As sets are fundamental objects that can be used to define all other concepts in mathematics, they are not defined in terms of more fundamental concepts. Rather, sets are introduced either informally, and are understood as something self-evident, or, as is now standard in modern mathematics, axiomatically, and their properties are postulated by the appropriate formal axioms.” Thomas Jech, “Set Theory”, The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), URL = < >.


[7] Some logicists believed that all of mathematics, not just arithmetic, can be reduced to logic. One example of a proponent of this broader form of logicism was Bertrand Russell.


[8] Frege’s Begreiffschrift, or “concept writing,” was a system of formal logic that united the propositional logic and class-logic in a single language. It was the same sort of language we study in PHIL 4160 (Symbolic Logic) under the name “predicate logic.”


[9] The contemporary British philosopher Crispin Wright ( has argued that Frege’s project can be made to succeed by making changes in Frege’s original system. Wright argued for this neo-logicism in Frege’s Conception of Numbers as Objects (1983).


[10] A searchable online version is here: .


[11] This is sometimes referred to as “Frege’s Puzzle,” but there is another puzzle identified by Frege, about the meaning of terms that occur within reports of propositional attitudes (“John believes that....”, “Jill desires that...”, James knows that...”), that is also called “Frege’s puzzle.” We will deal with this second puzzle soon.

[12] W. V. O. Quine, who we will study later, illustrates the use/mention distinction as follows:


“Boston is populous” is about Boson and contains “Boston”; “‘Boston’ is disyllabic’ is about “Boston”, which in turn designates Boston. To mention Boston we use “Boston” or a synonym, and to mention “Boston” we use ‘“Boston”’ or a synonym. “‘Boston’” contains six letters and just one pair of quotation marks; “Boston” contains six letters and no quotation marks; and Boston contains some 800,000 people. (Mathematical Logic, New York: Norton, 1940, §4; quoted at Claire Ortiz Hill, Rethinking Identity and Metaphysics: On the Foundations of Analytic Philosophy, New Haven: Yale University Press, 1997, p.12)

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