Sense and reference

From Academic Kids

The distinction between sense and reference was an innovation of the German philosopher and mathematician Gottlob Frege in his 1892 paper "▄ber Sinn und Bedeutung". According to Frege, sense and reference are two aspects of the meaning of a linguistic expression. The reference of an expression is simply the object that the expression refers to. The sense of an expression, more controversially, is what provides the cognitive significance of the expression. Though the distinction has its home in philosophy of language, it carries over into other areas of philosophy, including philosophy of mind, metaphysics, and metaethics.


About the distinction

The distinction can be illustrated with an example from Frege. Take the two expressions "the Morning Star" and "the Evening Star". It looks like these expressions have quite different meanings: "the Morning Star" means the bright object in the eastern sky at sunrise and "the Evening Star" means the bright object in the western sky at sunset. But, as it turns out, both expressions refer to the same object—the planet Venus. That is, the Morning Star is exactly the same thing as the Evening Star. This interesting fact was discovered by an ancient astronomer (perhaps Pythagoras); before that, people thought they were observing two different celestial bodies.

Now we can apply the sense-reference distinction. Both expressions have the same reference—that is, "the Morning Star" and "the Evening Star" refer to the same object. But they have different senses—after all, "the Morning Star" means something quite different from "the Evening Star". The two aspects of meaning should now be clear. On the one hand, there is the object referred to (reference). On the other hand, there is a more cognitive aspect of meaning (sense). And, as the case of Venus shows, sometimes we cognize a single object in several ways—with different senses corresponding to the same reference.

Another application of the sense-reference distinction concerns what are called nonreferring, nondenoting, or empty, expressions. These expressions do not have a reference, e.g., "the greatest integer" (Frege's example is "the least rapidly convergent series", and there is always "the present King of France"). After all, there isn't a greatest integer, and so there is nothing for the expression to refer to. But, despite the lack of a reference, the expression still seems perfectly meaningful—we understand what the expression is saying. Employing the sense-reference distinction, we can say that the expression has a sense but lacks a reference. And, indeed, when Quine appeals to "a gulf between meaning and naming" in his article "On What There Is", he uses the above Fregean example of Venus to make the point: an expression can be meaningful without there being anything referred to by the expression. Sense is one thing, and reference another.


There is an overabundance of inconsistent terminology in the literature. Frege's terms in the original German were Sinn and Bedeutung, and they are usually translated as sense and reference. But sometimes the pair of terms is translated as sense and meaning or as sense and nominatum. For the cognitive aspect of meaning, writers have used the terms sense, meaning, intension, connotation, and content. For the objectual aspect of meaning, writers have used the terms reference, referent, extension, denotation, nominatum, and designatum. Of course, the precise meaning of these terms can vary quite significantly from writer to writer, so some caution is due.

Terminology has also sprung up to capture the relation between an expression and its sense and that between an expression and its reference. Frege is typically translated as saying that an expression "expresses its sense" and "stands for or designates its reference". But earlier in the essay, he offers up another verb, writing of "that to which the sign refers, which may be called the reference of the sign". Since then, writers have variously said that an expression stands for, designates, refers to, or denotes its reference. We can also say that an expression picks out its reference, or (alternatively) that the sense of an expression is what picks out its reference.

Frege on sense and reference

Frege's famous article is the origin of the sense-reference distinction, and it is still widely read today. Frege begins with a simple puzzle about identity claims: Supposing that 'a' and 'b' both refer to the same object, why is it that a=b has greater cognitive significance than a=a? That is, why is it that claims like a=b are informative (sometimes conveying truly important knowledge), whereas claims like a=a are so trivial?

In considering this puzzle, Frege examines two simple (and problematic) views concerning the subject matter of identity claims. The first view is that an identity claim is about a relation between objects. On this view, the claim a=b is about the object designated by 'a' and the object designated by 'b'. The problem with this view, Frege says, is that it fails to make sense of the greater cognitive significance of a=b relative to a=a. After all, if 'a' and 'b' both refer to the same object, then this view has a=b and a=a saying exactly the same thing—both are saying that a certain object is identical to itself.

The second (metalinguistic) view is that an identity claim is about a relation between expressions ("names or signs of objects"). On this view, the claim a=b is about the expressions 'a' and 'b'. This view, Frege says, also has problems. First, the view misrepresents the subject matter of the claim a=b: after all, a=b looks like a claim about a and b, not a claim about 'a' and 'b'. Moreover, we miss out on the fact that claims like a=b can convey truly important knowledge if we construe such claims as expressing uninteresting knowledge about arbitrary linguistic matters.

Frege then offers his resolution of the puzzle by introducing the sense of an expression. The important difference between 'a' and 'b', Frege says, is a "difference in the mode of presentation of that which is designated". And the sense of an expression is just that "wherein the mode of presentation is contained"—Frege seems to use the phrase "mode of presentation" to capture the way an object is presented to us in cognition. Taking Frege's example, with a, b, and c as the three medians of a triangle, "[t]he point of intersection of a and b is then the same as the point of intersection of b and c. So we have different designations for the same point, and these names ('point of intersection of a and b', 'point of intersection of b and c') likewise indicate the mode of presentation; and hence the statement contains actual knowledge". Now we can explain the differing cognitive value of a=b and a=a. As Frege says at the end of the essay, "the explanation is that for the purpose of knowledge, the sense of the no less relevant than its reference".

Outline of the problem

Frege introduced the distinction in über Sinn und Bedeutung in order to account for several problems he had already noticed.

  1. Identity statements can be informative. That is, "Cicero is Tully" can be used to give a new piece of information, in a way that "Cicero is Cicero" cannot. This suggests that "Cicero" and "Tully" mean different things, since sentences using them convey different information. At the same time, Cicero is Tully, and so in a way they clearly mean the same thing.

Frege's earlier attempt to solve this problem, in his Begriffsschrift, was to claim that identity statements are not about their objects, but rather are about the names they use for those objects. (Something of this approach recurs in Donald Davidson's treatment, not of names but of quotation and indirect discourse.)

  1. Sentences using empty names appear to be capable of conveying information. For example, if Odysseus is fictional, then the name Odysseus does not appear to mean anyone; yet sentences like "Odysseus was set down on the beach at Ithaca" (or the present sentence) are meaningful and are true or false. If, as seems reasonable, a sentence's meaningfulness, its ability to be true or false, is a function of the meanings of its parts (see Semantic composition), then the parts of this sentence, such as Odysseus, seemingly do have meaning.

Exactly which names really are empty was in Frege's time, and still is, a matter of dispute. Some philosophers claim that sentences using empty names never express propositions (see Gareth Evans, John McDowell); some of these still maintain the sense-reference distinction for names.

Proper names

Broadly speaking, the reference (or referent) of a proper name is the object it means or indicates. The sense of a proper name is whatever meaning it has, when there is no object to be indicated. Frege justifies 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. Sense is wholly semantic. Reference by contrast, though semantic, is intimately (and puzzingly) connected with the named object. Mont Blanc is the referent of the name "Mont Blanc." But Frege argues that Mont Blanc "with its snowfields" cannot be a component of the thought that Mont Blanc is more than 4,000 metres high (letter to Russell). But if we find the same expression in two sentences, e.g. "Mont Blanc," then we also we recognise something common to the corresponding thoughts, something corresponding to the name "Mont Blanc." This common element, which cannot be the referent, must be the meaning or "sense."

3. The sense of different names is different, even when their reference is the same. Frege argues, in what is probably his most famous philosophical essay, that if an identity statement ("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.

Points of dispute

Bertrand Russell famously rejected Frege's sense-reference distinction, though there is some question as to how clearly he understood it. One possibility is that the two were arguing past one another: Frege talks about (for example) sentences, which have both a sense (a proposition) and a reference (a truth value); Russell on the other hand deals directly with propositions, but construes these not as abstract para-linguistic items but as tuples, or sets, of objects and concepts.

(Something like the Fregean view of propositions is most common among contemporary philosophers (John McDowell, e.g.) who countenance them; something like the Russellian view has been revived by David Kaplan).

Gareth Evans, for example, has argued that Frege held a Russellian theory of names, according to which there are no thoughts corresponding to empty names. His argument faces the difficulty that Frege did indeed hold that we can express a thought using the name "Odysseus."

The distinction is commonly confused with that between connotation and denotation. (A distinction which predates Frege, famously interpreted by Mill). The "connotation" of a concept-word like "planet" is the concept that the concept-word refers to. Denotation is any object (such as Venus or Mars) which, in Frege's terminology, falls under or satisfies the concept.

Portion of "Larry's text" not yet incorporated into the article

I suppose this looks like a very reasonable theory. But consider now the following objection, which is due to the extremely influential German philosopher and logician, Gottlob Frege, who worked mainly in the late nineteenth century. He wrote a famous article called "On Sense and Reference," in which he said that proper names have two different kinds of meaning: not only their reference, but also their sense. So Frege said that there was more to the meaning of proper names than what they referred to. You also have to consider their sense, he said.

Consider examples like the following. Suppose you know that the name "Cicero" refers to a famous ancient Roman statesman. Well if you didn't know that then you do now. Suppose I tell you next that the name "Tully" refers to an ancient philosopher who was also an orator. I'm sure most of you didn't know that. But now consider. If I were to tell you, "Cicero is Cicero," you'd say, "Yeah, so?" You haven't learned anything then. But if I tell you, "Cicero is Tully," then you have learned something -- and that's a matter of fact, indeed Cicero is Tully; the man's full name was Marcus Tullius Cicero. Well, the argument goes, the only way it can be informative to say that Cicero is Tully is if the two names, "Cicero" and "Tully," differ somehow in their meanings. They have, as Frege said, different senses.

Let me give you another example. Both of the examples are totally hackneyed but if you're going to get a traditional introduction to the theory of meaning then you've got to be exposed to them! There is bright point of light which appears in the morning sky, just before sunrise, called "the Morning Star"; and similarly, just after sunset sometimes you can see a bright point of light in the sky, and this has been called "the Evening Star." And so the proper name, "the Morning Star," refers to a particular celestial object that appears the morning; and the proper name, "the Evening Star," refers to a particular celestial object that appears in the evening. And well, you've probably guessed it -- in fact the Morning Star is the Evening Star, and they are both the planet Venus and not a star at all.

So you've been informed and enlightened; you've been told that the two different names actually refer to the same thing, and you (probably) didn't know that before. If the two names had exactly the same meaning, though, how could it be informative or enlightening to be told that the two names refer to the same thing? They couldn't. So "the Evening Star" must differ somehow in its meaning from "the Morning Star." Since they refer to the same thing, namely Venus, it must be something else about their meaning that differs. And this other thing we call sense. So the sense of "the Morning Star" differs from the sense of the "Evening Star." Frege then said that a proper name denotes its reference and expresses its sense.

So then what sort of thing is a sense? It's basically like a description of a thing the word refers to; you can regard the following as a definition of "sense":

The sense of a proper name is a set of properties that can be expressed as a description that picks out the reference of the name.

To take an example: the sense of "the Morning Star" would be a set of properties that can be expressed as a description; and that description would pick out the planet Venus from among all the other stars and planets in the sky. So the description might be: "the brightest natural object in the sky, aside from the sun and the moon, which appears occasionally before sunrise." Something like that description would express the sense of "the Morning Star." And then how would the description of the sense of "the Evening Star" go? Maybe like this: "the brightest natural object in the sky, aside from the sun and the moon, which appears occasionally after sunset."

Now remember, we started out our discussion of proper names with the referential theory, the "Fido"-Fido Theory, which says that the meaning of a proper name is simply the thing to which it refers. But now if we say, with Frege and some others, that proper names have a sense as well as a reference, then we have to change our theory. So here's the new theory:

External links

fr:Sens et dÚnotation


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