Frege Sense And Reference Analysis Essay

Our discussion will focus primarily on pp. 56-65 (209-214 of the JStor version).

Note that the JStor PDF is an older translation, but it is usable. Other relevant papers of Frege's are "On Concept and Object" (JStor) and "Function and Concept", as well as Part I of his Basic Laws of Arithmetic.

There is a major issue about how one of Frege's key terms is to be translated. The German word is "Bedeutung", and it is the term being translated as "reference" in the title of the paper. It is translated "nominatum" in the older translation available through the JStor link, and it has also been translated "denotation". In ordinary German, however, it just means "meaning", and so it is also sometimes translated that way (for example, in Frege's Collected Papers and Posthumous Writings). So "On Sense and Meaning" is the same paper, as is "On Sense and Denotation".

There are places in Frege's writings that he uses "Bedeutung" with its ordinary meaning of "meaning", but it is mostly a technical term for him, and the closest technical term in current philosophical usage is probably "reference". On the other hand, however, Frege uses "Bedeutung" in a somewhat wider sense from how "reference" is typically used, as one will see from Frege's discussion of the question whether sentences have Bedeutungen, i.e., references. And in this usage, it means something more like "semantic value". But our main focus will be on proper names, where "Bedeutung" pretty much does mean "reference", and our real focus will be more on sense than on reference, anyway.

The central purpose of this paper is to establish a distinction between the reference of an expression—primarily, a proper name—and what Frege calls its sense. The reference of a name is the name's bearer: the thing it is a name of. So the reference of the name "Gottlob Frege" is Gottlob Frege, that very person. It is not so easy to say what the sense of the name is, and Frege does not seem to tell us very much about what it is. Rather, as I said, his purpose here is to argue that names do have sense, and that their sense is different from their reference. In particular, the claim is, it is possible for two names to have the same reference but to have different senses.

The argument for this claim is contained in the first pargraph of the paper. It is not an easy argument to understand. Trust me on this.

Frege begins by mentioning a puzzle about identity statements, such as "Hesperus (the evening star) is the same thing as Phosphorous (the morning star)". As it happens, this is true: Hesperus and Phosphorous are both Venus. The puzzle is generated by the fact that such a statement can be informative and, in particular, that such statements need not be analytic or a priori but, as Frege puts it, may "often contain very valuable extensions of our knowledge". The problem, however, is that if identity is a relation between objects, then it looks as if "Hesperus is Phosophorous" and "Hesperus is Hesperus" assert that exactly the same relation obtains, namely, a relation between Venus and itself. But then how can the former be informative and the latter a mere instance of the law of self-identity? How, as it is put, can the one have a different "cognitive value" from the other?

Frege mentions that, for such reasons, he once held himself (in his first book Begriffsschrift, or Conceptual Notation) that identity was not a relation between objects, but was actually a relation between names. Thus, "Hesperus is Phosphorous" was supposed to mean something like: The names "Hesperus" and "Phosphorous" have the same denotation. In the middle of the paragraph, beginning with the words, "But this relation would hold...", Frege argues against this view. To be kind, it is not obvious what argument Frege is giving here. The key seems to be Frege's observation that the relation between a name and its bearer is arbitrary or, perhaps, conventional. But his underlying thought seems to be that the claim that "Hesperus" and "Phosphorous" have the same denotation is a claim about linguistic practice, whereas "Hesperus is Phosphorous" was meant to be a claim about celestial bodies. So the `name view' of identity gets the subject-matter of such statements wrong.

Frege then transitions, without explicit mention, into the development of his own view. He notes that the mere difference of shape (spelling, pronunciation, whatever) between "Hesperus" and "Phosphorous" cannot be what accounts for the difference in cognitive value that we are trying to explain. Rather, there will be a difference in cognitive value only if there is a difference in the "mode of presentation", which Frege illustrates using a geometrical example.

Can you give an example to show that the mere difference of shape (spelling, pronunciation, whatever) between "Hesperus" and "Phosphorous" cannot be what accounts for the difference in cognitive value that we are trying to explain?

Frege then says that each name has a "sense" that "contains" a "mode of presentation" that is associated with that name, but most commentators have simply supposed that the sense is the mode of presentation. In any event, the implication (which Frege makes explicit elsewhere) is that the fact that "Hesperus is Hesperus" and "Hesperus is Phosphorous" have differ in cognitive value is explained by the fact that "Hesperus" and "Phosphorous" have different senses.

It is important to note that the puzzle here, though particularly stark in connection with identity-statements, is not essentially about identity. The sentences "Hesperus is a planet" and "Phosphorous is a planet" also have different "cognitive values" (in German "Erkenntniswert", literally: value for knowledge), and Frege also holds that this difference is explained by the fact that "Hesperus" and "Phosphorous" have different senses. (Frege does not mention this extension of the point here but does so, again, in other places.)

How exactly is the fact that "Herperus" and "Phosphorous" have different senses supposed to explain the difference in cognitive value between "Hesperus is a planet" and "Phosphorous is a planet"? What assumptions about sense and cognitive value must such an explanation make?

In the next few paragraphs (pp. 57-9), Frege states several theses about sense and its relation to reference:

  • The sense of a name is a linguistic feature of it, one anyone who understands the name must know.
  • Names with the same sense must have the same reference (sense determines reference), but names with the same reference may have different senses.
  • It is possible for a name to have sense without having a reference.
  • Ordinarily, when one uses a name, one uses it to talk about its reference.
  • But when one uses words in 'indirect speech', one uses them to talk about their sense. Thus, if one says, "Lois said that Superman can fly", then one is talking about the sense of Lois's remarks, as is clear from the fact that it is one thing to say that Superman can fly and another to say that Clark can fly. The same is true of such constructs as "Lois believes that Superman can fly". Here it looks as if what one is saying Lois believes is determined by the sense of the name "Superman", since Lois does believe that Superman can fly, but not that Clark can.

Over the next several pargaraphs (pp. 59-62), Frege argues that the sense one associates with a name must "be distinguished from the associated idea", by which he means something like a mental image. The larger point at issue here, though, is whether sense is subjective.

What is Frege's argument that senses are not "ideas"? How much of the argument turns on special features of ideas as oppposed to something else subjective that sense might be? That is: To what extent does the argument show that senses are not only not ideas but are not subjective at all? Perhaps more importantly: What does the way Frege argues here tell us about how he is thinking about 'sense'?

Frege then turns to the question what we should regard as the sense and reference, not of a name, but of a whole (declarative) sentence. Frege says first that "Such a sentence contains a thought", by which he means a certain "objective content, which is capable of being the common property of several thinkers". Frege then argues that the thought "contained" in a sentence cannot be its reference. He then concludes that the thought must instead be the sentence's sense and goes on to argue that the reference of a sentence is just its truth-value. For our purposes, we need not consider the details of this argument, but my own view, for what it is worth, is that Frege's reasons are ultimately logical in character: What lies behind this discussion is the role of truth-functional connectives in formal logic.

What is Frege's argument that the thought "contained" in a sentence cannot be its reference? To what assumptions about thoughts and references does it appeal?

Oddly, Frege does not seem actually to give any argument for the claim that the thought "contained" in a sentence is its sense. Some people therefore have suggested that by a "thought" Frege just means: sense of a sentence, so that "thought" for him is just defined as "sense of a sentence". Does that seem right? What alternative might there be? One might find inspiration for such an alternative in what Frege said earlier about indirect speech.

"Sinn" redirects here. For the watchmaker, see Sinn (watchmaker). For the river in Germany, see Sinn (river).

In the philosophy of language, the distinction between sense and reference was an innovation of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"),[1] reflecting the two ways he believed a singular term may have meaning.

The reference (or "referent"; Bedeutung) of a proper name is the object it means or indicates (bedeuten), its sense (Sinn) is what the name expresses. The reference of a sentence is its truth value, its sense is the thought that it expresses.[1] Frege justified the distinction in a number of ways.

  1. Sense is something possessed by a name, whether or not it has a reference. For example, the name "Odysseus" is intelligible, and therefore has a sense, even though there is no individual object (its reference) to which the name corresponds.
  2. The sense of different names is different, even when their reference is the same. Frege argued that if an identity statement such as "Hesperus is the same planet as Phosphorus" is to be informative, the proper names flanking the identity sign must have a different meaning or sense. But clearly, if the statement is true, they must have the same reference.[2] The sense is a 'mode of presentation', which serves to illuminate only a single aspect of the referent.[3]

Much of analytic philosophy is traceable to Frege's philosophy of language.[4] Frege's views on logic (i.e., his idea that some parts of speech are complete by themselves, and are analogous to the arguments of a mathematical function) led to his views about what we now call theory of reference.[4]


Frege developed his original theory of meaning in early works like Begriffsschrift ('concept script') of 1879 and Grundlagen ('foundations of arithmetic') of 1884. On this theory, the meaning of a complete sentence consists in its being true or false,[5] and the meaning of each significant expression in the sentence is an extralinguistic entity which Frege called its Bedeutung, literally 'meaning' or 'significance', but rendered by Frege's translators as 'reference', 'referent', 'Meaning', 'nominatum', etc. Frege supposed that some parts of speech are complete by themselves, and are analogous to the arguments of a mathematical function, but that other parts are incomplete, and contain an empty place, by analogy with the function itself.[6] Thus 'Caesar conquered Gaul' divides into the complete term 'Caesar', whose reference is Caesar himself, and the incomplete term '—conquered Gaul', whose reference is a Concept. Only when the empty place is filled by a proper name does the reference of the completed sentence – its truth value – appear. This early theory of meaning explains how the significance or reference of a sentence (its truth value) depends on the significance or reference of its parts.


Frege introduced the notion of Sense (German: Sinn) to accommodate difficulties in his early theory of meaning.

First, if the entire significance of a sentence consists in its truth value, it follows that the sentence will have the same significance if we replace a word of the sentence with one having an identical reference, for this will not change the truth value of the sentence.[7] The reference of the whole is determined by the reference of the parts. If 'the evening star' has the same reference as 'the morning star', it follows that 'the evening star is a body illuminated by the Sun' has the same truth value as 'the morning star is a body illuminated by the Sun'. But someone may think that the first sentence is true, but the second is false, and so the thought corresponding to the sentence cannot be its reference, but something else, which Frege called its sense.

Second, sentences which contain proper names that have no reference cannot have a truth value at all. Yet the sentence 'Odysseus was set ashore at Ithaca while sound asleep' obviously has a sense, even though 'Odysseus' has no reference. The thought remains the same whether or not 'Odysseus' has a reference.[8] Furthermore, a thought cannot contain the objects which it is about. For example, Mont Blanc, 'with its snowfields', cannot be a component of the thought that Mont Blanc is more than 4,000 metres high. Nor can a thought about Etna contain lumps of solidified lava.[9]

Frege's notion of sense is somewhat obscure, and neo-Fregeans have come up with different candidates for its role.[10] Accounts based on the work of Carnap[11] and Church[12] treat sense as an intension, or a function from possible worlds to extensions. For example, the intension of ‘number of planets’ is a function that maps any possible world to the number of planets in that world. John McDowell supplies cognitive and reference-determining roles.[13] Devitt[14] treats senses as causal-historical chains connecting names to referents.

Sense and description[edit]

In his theory of descriptions, Bertrand Russell held the view that most proper names in ordinary language are in fact disguised definite descriptions. For example, 'Aristotle' can be understood as "The pupil of Plato and teacher of Alexander," or by some other uniquely applying description. This is known as the descriptivist theory of names. Because Frege used definite descriptions in many of his examples, he is often taken to have endorsed the descriptivist theory. Thus Russell's theory of descriptions was conflated with Frege's theory of sense, and for most of the twentieth century this 'Frege-Russell' view was the orthodox view of proper name semantics. However, Saul Kripke argued compellingly against the descriptivist theory. According to Kripke,[15] proper names are rigid designators which designate the same object in every possible world. Descriptions such as 'the President of the U.S. in 1970' do not designate the same in every possible world. For example, someone other than Richard Nixon, e.g. Hubert Humphrey, might have been the President in 1970. Hence a description (or cluster of descriptions) cannot be a rigid designator, and thus a proper name cannot mean the same as a description.[16]

However, the Russellian descriptivist reading of Frege has been rejected by many scholars, in particular by Gareth Evans in The Varieties of Reference[17] and by John McDowell in "The Sense and Reference of a Proper Name,"[18] following Michael Dummett, who argued that Frege's notion of sense should not be equated with a description. Evans further developed this line, arguing that a sense without a referent was not possible. He and McDowell both take the line that Frege's discussion of empty names, and of the idea of sense without reference, are inconsistent, and that his apparent endorsement of descriptivism rests only on a small number of imprecise and perhaps offhand remarks. And both point to the power that the sense-reference distinction does have (i.e., to solve at least the first two problems), even if it is not given a descriptivist reading.

Translation of Bedeutung[edit]

As noted above, translators of Frege have rendered the German Bedeutung in various ways. The term 'reference' has been the most widely adopted, but this fails to capture the meaning of the original German ('meaning' or 'significance'), and does not reflect the decision to standardise key terms across different editions of Frege's works published by Blackwell.[19] The decision was based on the principle of exegetical neutrality, namely that 'if at any point in a text there is a passage that raises for the native speaker legitimate questions of exegesis, then, if at all possible, a translator should strive to confront the reader of his version with the same questions of exegesis and not produce a version which in his mind resolves those questions'.[20] The term 'meaning' best captures the standard German meaning of Bedeutung, and Frege's own use of the term sounds as odd when translated into English as it does in German. Moreover, 'meaning' captures Frege's early use of Bedeutung well,[21] and it would be problematic to translate Frege's early use as 'meaning' and his later use as 'reference', suggesting a change in terminology not evident in the original German.



The Greek philosopher Antisthenes, a pupil of Socrates, apparently distinguished "a general object that can be aligned with the meaning of the utterance” from “a particular object of extensional reference." This "suggests that he makes a distinction between sense and reference."[22] The principal basis of this claim is a quotation in Alexander of Aphrodisias's “Comments on Aristotle's 'Topics'” with a three-way distinction:

  1. the semantic medium, δι' ὧν λέγουσι
  2. an object external to the semantic medium, περὶ οὗ λέγουσιν
  3. the direct indication of a thing, σημαίνειν … τὸ …[23]

John Stuart Mill[edit]

The sense-reference distinction is commonly confused with that between connotation and denotation, which originates with John Stuart Mill.[24] According to Mill, a common term like 'white' denotes all white things, as snow, paper. But according to Frege, a common term does not refer to any individual white thing, but rather to an abstract Concept (Begriff). We must distinguish between the relation of reference, which holds between a proper name and the object it refers to, such as between the name 'Earth', and the planet Earth, and the relation of 'falling under', such as when the Earth falls under the concept planet. The relation of a proper name to the object it designates is direct, whereas a word like 'planet' has no such direct relation at all to the Earth at all, but only to a concept that the Earth falls under. Moreover, judging of anything that it falls under this concept is not in any way part of our knowledge of what the word 'planet' means.[25] The distinction between connotation and denotation is closer to that between Concept and Object, than to that between 'sense' and 'reference'.

See also[edit]


  1. ^ ab"On Sense and Reference" ["Über Sinn und Bedeutung"], Zeitschrift für Philosophie und philosophische Kritik, vol. 100 (1892), pp. 25–50, esp. p. 31.[non-primary source needed]
  2. ^"On Sense and Reference", p. 25
  3. ^"On Sense and Reference", p. 27
  4. ^ abJeff Speaks, "Frege's theory of reference" (2011)
  5. ^Gareth Evans, The Varieties of Reference, Oxford: Clarendon 1982, p. 8
  6. ^"Function and Concept", p. 16.
  7. ^"On Sense and Reference", p. 32
  8. ^"On Sense and Reference", p. 32
  9. ^See Frege's undated letter to Philip Jourdain, published in Frege's Philosophical and Mathematical Correspondence, ed. Gottfried Gabriel, Hans Hermes, Friedrich Kanbartel, Christian Thiel and Albet Veraart, transl. Hans Kaal, Oxford: Blackwell 1980. (See also Frege's letter to Russell dated 1904, in the same collection.)
  10. ^Sam Cumming, Names, Stanford Encyclopedia of Philosophy 2013
  11. ^Meaning and Necessity, Chicago: University of Chicago Press, 1947.
  12. ^“A Formulation of the Logic of Sense and Denotation”, in P. Henle, M. Kallen, and S. K. Langer, eds., Structure, Method, and Meaning, New York: Liberal Arts Press, 1951
  13. ^“On the Sense and Reference of a Proper Name”, Mind, 86: 159–85, 1977.
  14. ^Designation, New York: Columbia University Press, 1981.
  15. ^Naming and Necessity, Cambridge, MA: Harvard University Press, 1980, 48-9
  16. ^Naming and Necessity p.57
  17. ^Evans, Gareth (1982). John McDowell, ed. The Varieties of Reference. Oxford: Oxford University Press. 
  18. ^McDowell, John (April 1977). "On the Sense and Reference of a Proper Name". Mind. New Series. 86 (342). 
  19. ^According to Beaney (The Frege Reader, Oxford: Blackwell 1997, p. 36) 'the decision was taken at a meeting in the early 1970s attended by Michael Dummett, Peter Geach, William Kneale, Roger White and a representative from Blackwell. The translation of Bedeutung by 'meaning' was unanimously agreed after lengthy discussion'.
  20. ^Long, P. and White, A., 'On the Translation of Frege's Bedeutung: A Reply to Dr. Bell', Analysis 40 pp. 196-202, 1980, p. 196. See also Bell, D., "On the Translation of Frege's Bedeutung", Analysis Vol. 40, No. 4 (Oct., 1980), pp. 191-195.
  21. ^Beaney, p. 37
  22. ^Prince, Susan (2015). Antisthenes of Athens: Texts, Translations, and Commentary. University of Michigan Press.  p. 20
  23. ^Prince 2015, pp. 518–522 (Antisthenes' literary remains: t. 153B.1).
  24. ^See section §5 of book I, chapter i of Mill's A System of Logic
  25. ^Frege, "A critical elucidation of some points in E. Schroeder's Vorlesungen Ueber Die Algebra der Logik, Archiv fur systematische Philosophie 1895, pp. 433-456, transl. Geach, in Geach & Black 86-106.[non-primary source needed]
Die Gleichheit fordert das Nachdenken heraus durch Fragen, die sich daran knüpfen und nicht ganz leicht zu beantworten sind. Equality gives rise to challenging questions which are not altogether easy to answer


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