Sense and reference
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Sinn and Bedeutung are usually translated, respectively, as sense and reference. Two different aspects of some terms' meanings, a term's reference is the object to which the term refers, while the term's sense is the way that the term refers to that object.
Sinn and Bedeutung were introduced by German philosopher and mathematician Gottlob Frege in his 1892 paper "Über Sinn und Bedeutung" ("On sense and reference"). Frege applied Bedeutung mainly to proper names and, in lesser extent, to sentences.
Motivation for and development of the distinction 
Frege's distinction rejects a view put forward by John Stuart Mill, according to which a proper name has no meaning above and beyond the object to which it refers (its referent or reference). That is, the word "Aristotle" just means Aristotle, that person, and no more. It does not mean "The writer of De Anima." Hence, the sentence Aristotle was Greek says only that that person was Greek. It does not say that the writer of De Anima was Greek. That is, it permits that Aristotle might not have written De Anima. More generally, for any given proposition about Aristotle, one can use the name without believing that proposition to be true of Aristotle.
Frege's central objection to the view that a name's meaning is no more than its referent is that, if a and b are names of the same object, then the identity statement a = b must mean the same as a = a. Yet clearly the first can convey information in a way that the second cannot; that Samuel Clemens is Samuel Clemens is just trivial, but that Samuel Clemens is Mark Twain is interesting. Why? Or, why is Cicero is Tully more significant than Cicero is Cicero? And, by the same token, Samuel Clemens wrote novels and Mark Twain wrote novels would have to mean the same thing but, again, the two sentences seem to convey different information.
Frege's distinction is meant to make sense of these phenomena. He postulates that, in addition to a reference (Bedeutung), a proper name possesses what he calls a sense (Sinn), some aspect of the way its reference is thought of that can differ, even between two names that refer to the same object. The important difference between Mark Twain and Samuel Clemens, for example, is a "difference in the mode of presentation of that which is designated". The sense of an expression is "that wherein the mode of presentation is contained". Thus, one can know both the names Mark Twain and Samuel Clemens without realizing that they are about the same object, because they present that object in different ways, that is, they have different senses. Another demonstrative example for this is the following: "The Leader of the Labour Party in October, 2006" and "the Prime Minister of the United Kingdom in October, 2006". These two linguistic expressions differ in sense, but they do have the same referent, that is Tony Blair.
- The reference is the object that the expression refers to. For instance, the name Mark Twain refers to Mark Twain, i.e. Samuel Clemens, the man who lived in the U.S. and wrote satires. The name Samuel Clemens also refers to that man. Hence the two have the same reference.
- The sense is the "cognitive significance" or "mode of presentation" of the referent.
- Linguistic Expressions with the same reference may have different senses.
Frege uses the following example to illustrate this view. Let a, b, and c be three lines, each of which joins one vertex of a triangle to the midpoint of the opposite side (each of a, b and c is thus a median). Then it is a theorem that
[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. Gottlob Frege, Über Sinn und Bedeutung
At one time, it was common to identify the sense of a name with an identifying description, which would put Frege's view close to the later Russell's description theory of names. For example, the name "Mark Twain" might just mean: The man who wrote Tom Sawyer, and Samuel Clemens might mean: The eldest son of John and Jane Clemens. Thus the reference would be determined as whatever fit the description. This interpretation is now almost unanimously rejected by scholars. Unfortunately, however, a detailed replacement has not been forthcoming. But what is clear is that Frege certainly did not mean that the sense of a name is merely a collection of ideas a particular user of a name happens to associate with it: Because they figure into the meanings of terms in a public language and can be communicated, senses must be objective.
Sense and reference (Sinn und Bedeutung) 
Broadly speaking, the reference (or referent) of a proper name is the object it denotes or indicates. The sense of a proper name is whatever meaning it has, when there is no object to be indicated.
What this article has called sense and reference are what Frege calls Sinn and Bedeutung, respectively, in the original German. Sometimes the pair of terms is translated as sense and meaning or as sense and nominatum. The precise meaning of these terms can vary quite significantly from writer to writer, so some caution is due.
Note that (confusingly) each expression has been translated as meaning by someone.
An expression's relation to sense or reference 
Terminology has also been applied to capture the relation between
- an expression and its sense
- an expression and its reference
Frege is typically translated as saying that an expression "expresses its sense" and "stands for or designates its reference". Yet earlier in the essay he offers another verb, refers, 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.
Sense without reference 
One application Frege saw for the distinction concerns what are called nonreferring, nondenoting, or empty, expressions. These expressions do not have a reference, for example "the greatest integer". Since there is not a greatest integer, the expression doesn't refer to anything. But it seems perfectly meaningful, since we seem to understand claims like "The greatest integer is larger than one million". Employing the sense-reference distinction, we can say that the expression has a sense but lacks a reference.
Although the term "the greatest integer" has no reference in the conventional arithmetic, in the ultra-intuitionistic arithmetic suggested by Alexander Esenin-Volpin (1960), it has a reference because one of the axioms of this arithmetic is that there is "the greatest integer." So, in one universe, an expression can have sense without reference, while in another universe, the same expression can have both sense and reference.
Another example is Odysseus. Since he is a fictional character, the name Odysseus does not appear to mean anyone at all; yet sentences like "Odysseus was set down on the beach at Ithaca" are meaningful, in that they can be true or false. If a sentence's meaning is a function of the meanings of its parts, then parts of the sentence, such as Odysseus, seemingly do have meaning.
Whether this solution works, and whether it was even seriously intended by Frege, is disputed. In order for it to work, it must be possible for a term to have a sense without a reference, and this requires that sense cannot be defined simply as the mode of presentation of the reference, since sometimes there is no reference being presented. Thus the view that the sense-reference distinction solves the problem of empty names encourages the view that a sense is an individuating description (which could be understood with or without a reference satisfying it). This makes a sense equivalent to a Russellian description (see below), and makes Frege's position "descriptivist", leaving it prey to a number of difficulties raised against that view. Other philosophers[who?] have argued that Frege is not a descriptivist, and hence that the sense-reference distinction does not solve the problem of fictional names. Proponents of this view often claim that sentences using empty names do not in fact express propositions, hence are not literally meaningful, despite appearances. They face the difficulty of explaining the apparent meaningfulness of sentences using the word Odysseus. On one view, fictional names merely pretend to express propositions. Our understanding of sentences about Odysseus consists then in our "playing along" (see Gareth Evans, Saul Kripke).
Frege and Russell 
Propositions and senses 
Bertrand Russell famously rejected Frege's sense-reference distinction, though there is some possibility that the two were misinterpreting and 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.
For Russell, sense is wholly semantic. Reference by contrast is intimately connected with the named object. Mont Blanc is the referent of the name "Mont Blanc." Frege argues that the thought "Mont Blanc 'with its snowfields'" cannot be a component of the thought that "Mont Blanc is more than 4,000 meters high". If the same expression "Mont Blanc" is in both sentences then there is something common to each thought, and therefore something corresponding to the name "Mont Blanc." This common element, which cannot be the referent, must be the meaning or "sense."
Senses and descriptions 
Russell held the view that most of the apparent proper names in English are in fact "disguised definite descriptions". So "Aristotle" is understood as "The pupil of Plato and teacher of Alexander", or by some other unique description. Although Russell explicitly rejected Frege's notion of sense, he rejected it just for proper names. But Russell also held the view (not evident in the Mont Blanc example) that most of the "proper names" in English are not names at all, but descriptions in disguise. Possibly the only real proper names were demonstrative pronouns like this and that (directed at an object that can be immediately perceived). So in fact if Frege's view was "descriptivist", then he effectively agrees with Russell on most of the apparent "proper names" of ordinary language: Frege thinks that "Aristotle" is a name, with a sense, which is equivalent to some description. Russell thinks that Aristotle is not really a name, but is (in disguised form) just such a description.
Thus for most of the twentieth century the "Frege-Russell" descriptivist view was taken as something of an orthodoxy. In Saul Kripke's famous Naming and Necessity lectures, which largely turned the tide against descriptivism, he treats both Russell and Frege as opposed to Mill's view in the same way. Thus Kripke's argument that names are not equivalent to descriptions was widely construed as the view that names do not have senses; or as a rejection of the sense-reference distinction. (Tellingly, all of the three problems the distinction aimed to solve have subsequently re-emerged as important problems in the philosophy of language.)
This reading of Frege has been rejected by many scholars, most strongly by Gareth Evans in The Varieties of Reference and by John McDowell in "The Sense and Reference of a Proper Name", following lines developed by Michael Dummett. Dummett argues 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. '
Relation to connotation and denotation 
The sense-reference distinction is commonly confused with that between connotation and denotation, which predates Frege and is famously interpreted by Mill. This distinction is applied mainly to words (particularly predicates) expressing properties (e.g., red, dog, bachelor), rather than naming individuals, so the difference between the two distinctions can be hard to see. The connotation of a predicate is the concept it expresses, or more often, the set of properties that determine whether an individual falls under it. The denotation of a concept is the actual collection of entities that do fall under it. Thus the connotation of bachelor is perhaps "unmarried adult male human" and its denotation is all the bachelors in the world.
Under a descriptivist reading of Frege, sense and reference are probably the same as connotation and denotation.
Under a non-descriptivist reading, they are probably not. It is always possible to have a connotation without a denotation, which may not be the case with sense and reference. A given sense always determines the same reference, which might not be the case with connotation and denotation. Most clearly, a single concept—which by definition has only one connotation and denotation (at a time), might be expressed by terms having different senses. For example, cat and feline have precisely the same connotation (member of the Felidae family of carnivorous mammals), and obviously the same denotation (all the cats; that is, all the felines), but it is perfectly intelligible that someone should fail to realize that cat and feline mean the same—perhaps they have only heard one word applied to housecats, the other to tigers and lions. In that case, the words have different senses.
See also 
- Aliasing (computing), an example of "sense and reference" in computer programming, where two or more pointers or references point to the same memory location or object
- Dihydrogen monoxide hoax, that exploits the ignorance of many people that the two senses "dihydrogen monoxide" and "water" refer to the same chemical substance "H2O", similarly to Frege's example of Hesperus is Phosphorus
- Gottlob Frege
- Mediated reference theory
- On Denoting, which outlined Bertrand Russell's Philosophy of Language
- Quiddity and Haecceity, similar concepts from Medieval philosophy.
- Russell's Paradox, a puzzle-conflict between Russell and Frege
- Theory of descriptions
- Frege's example is "the least rapidly convergent series", and there is always "the present King of France".
- See Semantic composition
- This example is from a letter to Russell.
- Evans, Gareth (1982). In John McDowell. The Varieties of Reference. Oxford: Oxford University Press.
- McDowell, John (April 1977). "On the Sense and Reference of a Proper Name". Mind. New Series 86 (342).
- Gottlob Frege: Über Sinn und Bedeutung
- Gottlob Frege: On Sense and Reference (English translation by Max Black)
- Internet Encyclopedia of Philosophy: Frege and Language.
- Frege's Contribution to the Philosophy of Language by Richard G. Heck and Robert May, published in the Oxford Handbook to the Philosophy of Language