Frege’s “sense” and “reference”

Frege was a mathematician, and his interest in questions about how language works derived, originally, from a concern to give a precise account of how the signs used in mathematics worked.

Frege's aim was to develop a theory of meaning, a philosophi­cal account that would tell us what we had to know about the words and sentences of a language in order to understand the way people use them. His fundamental idea was that the meaning of a word is just what you have to know about it in order to understand how it is used in a language. Since the word “semantic” means “having to do with meaning,” what Frege was doing is also called “philosophical semantics,” and his theory is called a “semantic theory.”

One of Frege's most important insights was that previous theories of meaning had started in the wrong place. Hobbes, as we saw, started by trying to explain the meaning of individual words, such as names. Frege pointed out that, in a sense, words on their own do not mean anything at all. For the meaning of a word is what you have to know in order to understand proper uses of that word in the lan­guage; and just saying “dog” is not a proper use of a word in English. Only if I use the word “dog” with other words to form a sentence will I be saying something that you can understand.

With this basic idea established, Frege sets out to discuss how we understand names like “Bucephalus.” He says that we must think of them as referring to some object. Given the primacy of the sen­tence, we must now ask what this means in terms of how words con­tribute to sentence meaning. A simple, preliminary answer is that a word “W” refers to an object, O, if and only if “W” is used in sen­tences to determine what those sentences are about. Thus, because the word “Bucephalus” refers to a certain horse, the sentence “Alexander rode Bucephalus” is about that horse. As we shall see, Frege had a better, more precise answer than this preliminary answer; but before I give it, we shall need some more of Frege's ter­minology.

Once Frege has introduced the idea of reference, he points out immediately that we cannot say that the thing that a name refers to—its reference—is all you need to know in order to understand how that name functions in our language. For if it were all that you had to know, then the meaning of two words with the same refer­ence would be identical; and he gives a famous example that shows that this is not so. Here is the example.

The planet Venus is often observable near the horizon both at sunset and at sunrise. In antiquity, people called Venus “the Evening Star” when they saw it at sunset and “the Morning Star” when they saw it at dawn, without realizing that they were talking about the very same heavenly body. (As you can see from the names, they didn't know it was not a star but a planet either.) In the course of the history of astronomy, it was discovered that the heavenly body people saw at sunset and the one they saw at sunrise were the same.

F: The Morning Star is the Evening Star.

Now suppose we held that the meaning of “the Morning Star” was just its reference, and likewise for “the Evening Star.” Then it would follow that, since these two names refer to the same thing, they must have the same meaning. If that were true, then the sentence, F, could not possibly be informative. For if the two words meant the same, then all you would have to know in order to know that F was true was what the two words meant. But the discovery that F was true is not something that people knew simply because they knew what the words meant; it was an astronomical discovery.

Frege made the same point in a slightly different way. He offered a reductio argument that showed that reference was not the same as meaning. The argument depends on the following assumption:

CT: If two words or phrases have the same meaning, then we should be able to replace one of them with the other in any sentence, S, without changing the meaning of S.

“Bachelor” and “unmarried adult male” mean the same. So “John is a bachelor” and “John is an unmarried adult male” mean the same also. I shall call CT the compositionality thesis for meanings. (I call it this because it is a consequence of the idea that the meaning of a sentence is composed out of the meanings of its component parts. That more general idea is often called “compositionality.”) The argument for it is quite simple. The meaning of a word or phrase is what you know if and only if you know how it is used in the language. Given the primacy of the sentence this means that the meaning of a word or phrase, “W,” is what you know if and only if you understand how “W” contributes to the meaning of any sen­tence containing it.

Frege asked us to compare F with

G: The Morning Star is the Morning Star.

He pointed out that G, unlike F, is a sentence that you know is true just because you know what the words mean. It follows from the compositionality thesis that if the meaning of “the Morning Star” is just what it refers to, then, since it refers to the same thing as “the Evening Star” does, F and G must mean the same. Since they plainly do not mean the same, this is a reductio of the claim that the meaning of a name is its reference.

Frege's explanation of why F and G differ in meaning is that “the Morning Star” and “the Evening Star,” though they have the same ref­erence, differ in the “mode of presentation” of what they refer to, and he calls the mode of presentation associated with a word its sense.

We can see what Frege means by a “mode of presentation,” and thus by a “sense,” in the case we have been considering. To know the sense of “the Morning Star” you have to know that it refers to the heavenly body that often appears at a certain point on the horizon in the morning. To know the sense of “the Evening Star” you have to know that it refers to the heavenly body that often appears at a certain point on the horizon in the evening. In other words, for a name, a sense is a way of identifying the referent. If you know the sense of a name, you know what determines whether any object is the reference of that name. It is very important, as we shall see later, that a sense is defined as something you have to know in order to understand its use in sentences. This follows, of course, from Frege's basic idea that meaning is what you have to know in order to understand how words are used in sentences.

Proper names are, of course, only one class among many classes of expressions that a theory of meaning has to explain.

We now ask after the sense and reference of a whole assertoric sentence. Such a sentence contains a thought. Is this thought now to be regarded as its sense or its reference? Let us suppose for the moment that the sentence has a refer­ence! Now replace a word in that sentence with another word with the same reference, but a different sense; then this can have no influence on the refer­ence of the sentence. But now we see that the thought is in fact altered in such a case; because, for example, the thought in the sentence “The Morning Star is a body illuminated by the sun” is different from that in the sentence “The Evening Star is a body illuminated by the Sun.” Someone who didn't know that the Evening Star is the Morning Star could take one of these thoughts to be true and the other to be false. The thought then cannot be the reference of the sentence; we will do better to interpret it as its sense.

Frege says in a footnote that by a “thought” he means “not the sub­jective activity of thinking, but its objective content, which is capa­ble of being the common property of many people.” So his claim is that the sense of the sentence “The Morning Star is a body illumi­nated by the Sun” is the content of the belief shared by two people who both believe that the Morning Star is a body illuminated by the Sun. This shared content is what philosophers have usually meant by the word “proposition.” We often say that a sentence expresses a proposition, which means that it has a certain content.

Notice that in this passage Frege applies something like the com­positionality thesis to references when he says that if we “substitute in it a word with another word with the same reference, but a dif­ferent sense... this can have no influence on the reference of the sentence.” In other words, he is assuming that the reference of a sentence is determined exclusively by the references of the compo­nent words or phrases.

So far we only know what the sense and reference of proper names are. We call two names with the same reference “co- referential.” So the question we must ask is: What property of sentences is always preserved if we replace the names in them by other co-referential names? Frege's answer is that the property that is preserved is what he calls the “truth value.” “I understand by the truth value of a sen­tence the circumstance that it is true or that it is false. There are no other truth values.” Frege's point is that if we substitute one name for another co-referential name in any sentence, then we shall not affect whether that sentence is true or false.

Thus, since “the Morning Star” and “the Evening Star” are co- referential, we should be able to replace one by the other in any true sentence and get a sentence that is true; and we should likewise be able to replace one by the other in any false sentence and get a sen­tence that is false. Let us accept, for the moment, that this is correct.

If the reference of a sentence is a truth value, then just as the sense of a name is a mode of presentation of the reference, so the sense of a sentence should be a mode of presentation of a truth value. And just as the sense of a name is a way of identifying the object it refers to, so the sense of a sentence will be a way of identifying whether or not the sentence is true. If you know the sense of a sentence, you know what determines whether that sentence is true or false. And the referent of a sentence in the actual world is its truth value.

If you know what determines whether a sentence is true or false, we say that you know its truth conditions. Thus, Frege's theory of meaning says that the meaning of a sentence is its truth conditions. Since, on Frege's view, every sentence that is not true is false, if you know when a sentence would be true, you know its truth conditions. For in any circumstance where it was not true, it would be false.

We have now reached a point where another major reason for philosophical interest in language becomes clear. Language is the medium in which we express truths. From the very beginning of Western philosophy, the nature of truth has been regarded as a cru­cial philosophical question. The theory of meaning provides one route to an answer. For looking at how sentences express truth and falsehood helps us to understand the nature of truth. In Frege's the­ory, where there is this close connection between meaning and truth, this traditional problem is central to philosophical semantics.

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