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April Chlumsky



Frege on Sense and Reference

Gottlob Frege developed the theory of sense and reference into a thorough philosophy of language. He assigned logic the task of discovering the laws of truth, not of assertion or thought. The work ?On Sense and Reference? has received a great deal of attention throughout the years. Indeed, the work ?On Sense and Reference? by Frege, is one of his most read and most refuted works.

In Frege?s best-known work ?On Sense and Reference? ?two-thirds of the text is concerned with explaining how the distinction between ?sinn? and ?bedeutung? (sense and reference) applies to sentences. After it has been argued that the reference of a sentence is a truth-value, the remainder of the essay tries to show how apparent counter-examples to the claim can be accounted for.?1 Frege makes progress in this doctrine by assigning thoughts to a different semantic level than that of truth-values. He also shows that ?the paradigm of reference seems to be the relation between a name and what it names.?1 After this he becomes occupied with his discussion of proper names ( the reference of the sentence) and definite descriptions (the sense of the sentence) then moves on to the second part of his essay. Here he raises questions about declarative sentences. These questions seem to be unrelated to his explanation of ?sense and reference? up to this point. The rest of the essay is his examination of what sense and reference for sentences is.


In his ontology, Frege asserted the existence of two special objects, namely, the truth-values ?true? and ?false? and defined concepts as a special kind of function, namely any function that connected objects to truth values. ?To Frege ?a sentence stands for or designates a truth-value, it expresses a thought. The truth-value is the reference of the sentence; the thought expressed is its sense. The truth-value fulfills one role of judgeable-content: it is the value of concepts (functions).?2 Rules of asserting, thinking, judging, and inferring follow from the laws of truth. The truth-value is tied to assertions.

To Frege, thoughts are what are judged, asserted, or entertained. They are either true or false and stand in contrast to ideas. ?Thoughts are existence- and identity-independent of a bearer (thinker).?2 Thoughts are also public and can be shared with others, and are also held in reality. The only sentences that can express a complete thought are declarative sentences. Yet Frege points out that non-declarative sentences can have meaning. For example ?Help! I am trapped? expresses an idea that has meaning.

This moves us to what ideas are. Ideas cannot be seen or touched as they are private. They are that which helps us in our denotation of sentences. Frege believes that ideas (sense) are had. One has sensations, feelings, moods, inclinations, and wishes. An idea, which someone has, belongs to the content of his consciousness. Ideas need a


bearer and every idea has only one bearer.?3 Qualities are examples of ideas. For example red or bitter are ideas.

The difference between thoughts and ideas is that thoughts are of objects, which can be touched and seen. They are not only inside of the mind. He suggests that every word in a sentence has a name, but he recognizes that ?names without content (that do not ?stand for anything?) may nevertheless contribute to the judgeable-content expressed. They have sense, but lack reference.?4 The thoughts are what truth claims are made out of not ideas. Also, a thought cannot be an idea according to Frege. For, you have to have a thought in-order to have language. You cannot have language with thoughts alone.

Sense is that which ?distinguishes from tone or coloring?4 in a sentence. Substituting ?I? in-place-of ?Mr. Jones? may affect the coloring of the sentence, but the thought will remain the same. The listener will only conceive a different mental image of what is being expressed. An example of this may be the following:

Mr. Jones may utter the statement, ?I went to the party?.

Mr. Smith says of Jones, ?Mr. Jones went to the party?.

A different sense is expressed when Mr. Jones tells people that he went to a party than if Mr. Smith tells others about Mr. Jones going to a party. When someone hears ?I went to the party? they automatically have an idea of what ?I? is. However, if they hear ?Mr.


Jones went to the party? they might have an image of a man that lives in a blue house on Bliss Street. The sense is therefore different even-though the reference, Mr. Jones, remains the same.

?The sense of a proper name determines what the reference is, if there is one. The sense of, for example, ?the teacher of Alexander the Great? belongs to Aristotle, who is thus the name?s reference, determined by the sense.?5

Michael Dummett, in his book Frege and Other Philosophers, proposes that ?Frege should be understood as holding that the reference of an expression can be stated, but its sense cannot. Rather, he suggests that we show what its sense is or is to be by the particular way (out of a number of possible non-equivalent ways) in which we say what its reference is or is not to be.?6 Yet Frege still gives importance to the reference. The ?dictum? of sense only being able to be shown, but not stated is of crucial importance. Frege?s explanation on his notion of sense is one that is open to mystery. He introduces sense as that being attached to words or expressions. It is something that is communicated through utterances.

The distinction between sense and reference is that a reference picks out an object of some kind, while the sense is what allows us to understand the thought. Sense is the


syntax of the thought. We cannot have language without the sense, but we can have language without reference. Sense gives you a statement, while reference allows you to check if it is true or false.

Frege suggested that names and descriptions express a sense in addition to having a denotation. The sense of an expression accounts for its cognitive significance. This cognitive significance is the way by which one can conceive of the denotation of a term. The expressions ?4? and ?2+2? have the same denotation, ie the quantity four, but express different senses. The former involves the property ?addition?. One of the more famous examples used to explain this is Frege?s example of the ?morning star? and ?evening star?. They both denote the same planet, namely Venus, but they express different modes of presenting the planet Venus and so they differ in sense. Frege can account for the difference in cognitive significance between identity statements of the form ?a = a? and ?a = b?. The sense of the whole statement, in Frege?s view, is a function of the senses of its component parts. Since ?a? differs from ?b? in sense the components of ?a = a? and ?a = b? are different and so the sense of the whole expression will be different in both cases. In this the sense of an expression accounts for its cognitive significance.

Frege asserts that when a name or a description follows a prepositional verb, it will no longer denote what it originally denoted. Instead in this context the term denotes its ordinary sense. Take for instance the names ?Mark Twain? and ?Samuel Clemens?. They both denote different senses when they occur in the following sentences:

John believes that Mark Twain wrote Huckleberry Finn.

John believes that Samuel Clemens wrote Huckleberry Finn.


Both sentences are talking about the same person so they have the same referent or denotation, but they differ in sense. If they did not denote the same object, then there would be not reason to think that substituting one name for another would preserve the truth.

In Frege?s view, each word in the sentence ?John loves Mary? is a name and the sentence as a whole is a complex name. Each name has both sense and denotation. Frege breaks down this sentence in the following way:

d[j] refers to the denotation of the name ?John?.

d[m] refers to the denotation of the name ?Mary?.

d[L] refers to the denotation of the name ?loves?.

s[j] refers to the sense of the name ?John?.

s[m] refers to the sense of the name ?Mary?.

s[L] refers to the sense of the name ?loves?.

With this breakdown of the sentence Frege then moves on to working toward a theoretical description of the denotation of the sentence as a whole. On Frege?s view, d[j] and d[m] are the real individuals John and Mary, respectively. The function d[L] maps d[m] (Mary) to a function that serves as the denotation of the predicate ?loves Mary?. Let us refer to this function as d[Lm]. Now the function d[Lm] maps d[j] to the denotation of the sentence ?John loves Mary?. Let us refer to the denotation of the sentence as d[jLm]. Frege identifies this denotation as one of two truth-values. This makes a concept because d[Lm] maps the objects to truth-values. Thus d[jLm] is true if


the concept d[Lm] contains John; otherwise the truth-value is false. So the sentence ?John loves Mary? names a truth-value according to Frege.

Frege even goes farther with the example of ?John loves Mary? by saying it also expresses a sense. Its sense is described as follows. First, the sense of the name ?loves? is identified as a function. This function maps the sense of the name ?Mary? to the sense

of the predicate ?loves Mary?. Now the function of the sense of ?loves Mary? maps the sense of the name ?John? to the sense of the whole sentence. Frege calls this sense of the whole sentence thought. Even though there are only two truth-values, there are an infinite number of thoughts.

Different languages also play a part in changing the sense of a sentence. ?The notions of sense has to do with the speakers? understanding of their language, that is, with their grasp of the meaning.?7 Take for instance the following Italian and English:

Esta frio. = It is cold.

Both mean the same thing, but for someone who does not know Italian they will just look at ?Esta frio? and wonder what it means. It has the same reference, but different sense.

Take again the sentence ?4 = 2+2? and ?4 = 4? both stand for the same thing, ?but they are not logically equivalent. They make different assertions, require different proofs, and their inter-substitution in a proof need not preserve cogency of argument. Hence they are now said to express different thoughts.?8 Now the previously labeled ?judgeable content?, is called ?a thought?, which is the sense of the sentence. Similarly,


?Mark Twain = Mark Twain? and ?Mark Twain = Samuel Clemens? denote the same truth-value, but express different thoughts even though the sense of the names differ. The entire declarative sentence ?Mark Twain wrote Huckleberry Finn? denotes it ordinary sense, which is its thought. The thought is an entity, which is distinct from the truth-value. This truth-value of the sentence is its reference.

Frege writing ?On Sense and Reference? paved the road for Russell and Wittenstein to take another step. One of the big holes in Frege?s system is that he wanted us to denote every name in order to get to if the statement is true or not. ??(more)


Dummett, Michael. Frege and Other Philosophers. Clarendon Press, Oxford. 1991.

Frege, Gottlob. The thought: A Logical Inquiry. Mind a Quarterly Review of

Psychology and Philosophy. 1956.

Klemke, E. D. Essays on Frege. University of Illinois Press. 1968.

Sluga, Hans. Gottlob Frege. Routledge & Kegan Paul. 1980.

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