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Author Topic: The Theory of Sense and Reference  (Read 379 times)

hubag bohol

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The Theory of Sense and Reference
« on: June 11, 2015, 11:11:04 PM »
from http://www.iep.utm.edu/frege/#H4


Frege's influential theory of meaning, the theory of sense (Sinn) and reference (Bedeutung) was first outlined, albeit briefly, in his article, "Funktion und Begriff" of 1891, and was expanded and explained in greater detail in perhaps his most famous work, "Über Sinn und Bedeutung" of 1892. In "Funktion und Begriff", the distinction between the sense and reference of signs in language is first made in regard to mathematical equations. During Frege's time, there was a widespread dispute among mathematicians as to how the sign, "=", should be understood. If we consider an equation such as, "4 x 2 = 11 - 3", a number of Frege's contemporaries, for a variety of reasons, were wary of viewing this as an expression of an identity, or, in this case, as the claim that 4 x 2 and 11 - 3 are one and the same thing. Instead, they posited some weaker form of "equality" such that the numbers 4 x 2 and 11 - 3 would be said to be equal in number or equal in magnitude without thereby constituting one and the same thing. In opposition to the view that "=" signifies identity, such thinkers would point out that 4 x 2 and 11 - 3 cannot in all ways be thought to be the same. The former is a product, the latter a difference, etc.
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hubag bohol

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Re: The Theory of Sense and Reference
« Reply #1 on: June 11, 2015, 11:11:31 PM »
In his mature period, however, Frege was an ardent opponent of this view, and argued in favor of understanding "=" as identity proper, accusing rival views of confusing form and content. He argues instead that expressions such as "4 x 2" and "11 - 3" can be understood as standing for one and the same thing, the number eight, but that this single entity is determined or presented differently by the two expressions. Thus, he makes a distinction between the actual number a mathematical expression such as "4 x 2" stands for, and the way in which that number is determined or picked out. The former he called the reference (Bedeutung) of the expression, and the latter was called the sense (Sinn) of the expression. In Fregean terminology, an expression is said to express its sense, and denote or refer to its reference.
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hubag bohol

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Re: The Theory of Sense and Reference
« Reply #2 on: June 11, 2015, 11:11:59 PM »
The distinction between reference and sense was expanded, primarily in "Über Sinn und Bedeutung" as holding not only for mathematical expressions, but for all linguistic expressions (whether the language in question is natural language or a formal language). One of his primary examples therein involves the expressions "the morning star" and "the evening star". Both of these expressions refer to the planet Venus, yet they obviously denote Venus in virtue of different properties that it has. Thus, Frege claims that these two expressions have the same reference but different senses. The reference of an expression is the actual thing corresponding to it, in the case of "the morning star", the reference is the planet Venus itself. The sense of an expression, however, is the "mode of presentation" or cognitive content associated with the expression in virtue of which the reference is picked out.
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hubag bohol

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Re: The Theory of Sense and Reference
« Reply #3 on: June 11, 2015, 11:12:31 PM »
Frege puts the distinction to work in solving a puzzle concerning identity claims. If we consider the two claims:

(1) the morning star = the morning star

(2) the morning star = the evening star

The first appears to be a trivial case of the law of self-identity, knowable a priori, while the second seems to be something that was discovered a posteriori by astronomers. However, if "the morning star" means the same thing as "the evening star", then the two statements themselves would also seem to have the same meaning, both involving a thing's relation of identity to itself. However, it then becomes to difficult to explain why (2) seems informative while (1) does not. Frege's response to this puzzle, given the distinction between sense and reference, should be apparent. Because the reference of "the evening star" and "the morning star" is the same, both statements are true in virtue of the same object's relation of identity to itself. However, because the senses of these expressions are different--in (1) the object is presented the same way twice, and in (2) it is presented in two different ways--it is informative to learn of (2). While the truth of an identity statement involves only the references of the component expressions, the informativity of such statements involves additionally the way in which those references are determined, i.e. the senses of the component expressions.
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hubag bohol

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Re: The Theory of Sense and Reference
« Reply #4 on: June 11, 2015, 11:13:00 PM »
So far we have only considered the distinction as it applies to expressions that name some object (including abstract objects, such as numbers). For Frege, the distinction applies also to other sorts of expressions and even whole sentences or propositions. If the sense/reference distinction can be applied to whole propositions, it stands to reason that the reference of the whole proposition depends on the references of the parts and the sense of the proposition depends of the senses of the parts. (At some points, Frege even suggests that the sense of a whole proposition is composed of the senses of the component expressions.) In the example considered in the previous paragraph, it was seen that the truth-value of the identity claim depends on the references of the component expressions, while the informativity of what was understood by the identity claim depends on the senses. For this and other reasons, Frege concluded that the reference of an entire proposition is its truth-value, either the True or the False. The sense of a complete proposition is what it is we understand when we understand a proposition, which Frege calls "a thought" (Gedanke). Just as the sense of a name of an object determines how that object is presented, the sense of a proposition determines a method of determination for a truth-value. The propositions, "2 + 4 = 6" and "the Earth rotates", both have the True as their references, though this is in virtue of very different conditions holding in the two cases, just as "the morning star" and "the evening star" refer to Venus in virtue of different properties.
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hubag bohol

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Re: The Theory of Sense and Reference
« Reply #5 on: June 11, 2015, 11:13:50 PM »
In "Über Sinn und Bedeutung", Frege limits his discussion of the sense/reference distinction to "complete expressions" such as names purporting to pick out some object and whole propositions. However, in other works, Frege makes it quite clear that the distinction can also be applied to "incomplete expressions", which include functional expressions and grammatical predicates. These expressions are incomplete in the sense that they contain an "empty space", which, when filled, yields either a complex name referring to an object, or a complete proposition. Thus, the incomplete expression "the square root of ( )" contains a blank spot, which, when completed by an expression referring to a number, yields a complex expression also referring to a number, e.g., "the square root of sixteen". The incomplete expression, "( ) is a planet" contains an empty place, which, when filled with a name, yields a complete proposition. According to Frege, the references of these incomplete expressions are not objects but functions. Objects (Gegenstände), in Frege's terminology, are self-standing, complete entities, while functions are essentially incomplete, or as Frege says, "unsaturated" (ungesättigt) in that they must take something else as argument in order to yield a value. The reference of the expression "square root of ( )" is thus a function, which takes numbers as arguments and yields numbers as values. The situation may appear somewhat different in the case of grammatical predicates. However, because Frege holds that complete propositions, like names, have objects as their references, and in particular, the truth-values the True or the False, he is able to treat predicates also as having functions as their references. In particular, they are functions mapping objects onto truth-values. The expression, "( ) is a planet" has as its reference a function that yields as value the True when saturated by an object such as Saturn or Venus, but the False when saturated by a person or the number three. Frege calls such a function of one argument place that yields the True or False for every possible argument a "concept" (Begriff), and calls similar functions of more than one argument place (such as that denoted by "( ) > ( )", which is doubly in need of saturation), "relations".
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hubag bohol

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Re: The Theory of Sense and Reference
« Reply #6 on: June 11, 2015, 11:14:17 PM »
It is clear that functions are to be understood as the references of incomplete expressions, but what of the senses of such expressions? Here, Frege tells us relatively little save that they exist. There is some amount of controversy among interpreters of Frege as to how they should be understood. It suffices here to note that just as the same object (e.g. the planet Venus), can be presented in different ways, so also can a function be presented in different ways. While "identity", as Frege uses the term, is a relation holding only between objects, Frege believes that there is a relation similar to identity that holds between functions just in case they always share the same value for every argument. Since all and only those things that have hearts have kidneys, strictly speaking, the concepts denoted by the expressions "( ) has a heart", and "( ) has a kidney" are one and the same. Clearly, however, these expressions do not present that concept in the same way. For Frege, these expressions would have different senses but the same reference. Frege also tells us that it is the incomplete nature of these senses that provides the "glue" holding together the thoughts of which they form a part.
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hubag bohol

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Re: The Theory of Sense and Reference
« Reply #7 on: June 11, 2015, 11:15:03 PM »
Frege also uses the distinction to solve what appears to be a difficulty with Leibniz's law with regard to identity. This law was stated by Leibniz as, "those things are the same of which one can be substituted for another without loss of truth," a sentiment with which Frege was in full agreement. As Frege understands this, it means that if two expressions have the same reference, they should be able to replace each other within any proposition without changing the truth-value of that proposition. Normally, this poses no problem. The inference from:

(3) The morning star is a planet.

to the conclusion:

(4) The evening star is a planet.

in virtue of (2) above and Leibniz's law is unproblematically valid. However, there seem to be some serious counterexamples to this principle. We know for example that "the morning star" and "the evening star" have the same customary reference. However, it is not always true that they can replace one another without changing the truth of a sentence. For example, if we consider the propositions:

(5) Gottlob believes that the morning star is a planet.

(6) Gottlob believes that the evening star is a planet.

If we assume that Gottlob does not know that the morning star is the same heavenly body as the evening star, (5) may be true while (6) false or vice versa.
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hubag bohol

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Re: The Theory of Sense and Reference
« Reply #8 on: June 11, 2015, 11:15:33 PM »
Frege meets this challenge to Leibniz's law by making a distinction between what he calls the primary and secondary references of expressions. Frege suggests that when expressions appear in certain unusual contexts, they have as their references what is customarily their senses. In such cases, the expressions are said to have their secondary references. Typically, such cases involve what Frege calls "indirect speech" or "oratio obliqua", as in the case of statements of beliefs, thoughts, desires and other so-called "propositional attitudes", such as the examples of (5) and (6). However, expressions also have their secondary references (for reasons which should already be apparent) in contexts such as "it is informative that..." or "... is analytically true".
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Re: The Theory of Sense and Reference
« Reply #9 on: June 11, 2015, 11:16:00 PM »
Let us consider the examples of (5) and (6) more closely. To Frege's mind, these statements do not deal directly with the morning star and the evening star itself. Rather, they involve a relation between a believer and a thought believed. Thoughts, as we have seen, are the senses of complete propositions. Beliefs depend for their make-up on how certain objects and concepts are presented, not only on the objects and concepts themselves. The truth of belief claims, therefore, will depend not on the customary references of the component expressions of the stated belief, but their senses. Since the truth-value of the whole belief claim is the reference of that belief claim, and the reference of any proposition, for Frege, depends on the references of its component expressions, we are lead to the conclusion that the typical senses of expressions that appear in oratio obliqua are in fact the references of those expressions when they appear in that context. Such contexts can be referred to as "oblique contexts", contexts in which the reference of an expression is shifted from its customary reference to its customary sense.
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Re: The Theory of Sense and Reference
« Reply #10 on: June 11, 2015, 11:16:25 PM »
In this way, Frege is able to actually retain his commitment in Leibniz's law. The expressions "the morning star" and "the evening star" have the same primary reference, and in any non-oblique context, they can replace each other without changing the truth-value of the proposition. However, since the senses of these expressions are not the same, they cannot replace each other in oblique contexts, because in such contexts, their references are non-identical.

Frege ascribes to senses and thoughts objective existence. In his mind, they are objects every bit as real as tables and chairs. Their existence is not dependent on language or the mind. Instead, they are said to exist in a timeless "third realm" of sense, existing apart from both the mental and the physical. Frege concludes this because, although senses are obviously not physical entities, their existence likewise does not depend on any one person's psychology. A thought, for example, has a truth-value regardless of whether or not anyone believes it and even whether or not anyone has grasped it at all. Moreover, senses are interpersonal. Different people are able to grasp the same senses and same thoughts and communicate them, and it is even possible for expressions in different languages to express the same sense or thought. Frege concludes that they are abstract objects, incapable of full causal interaction with the physical world. They are actual only in the very limited sense that they can have an effect on those who grasp them, but are themselves incapable of being changed or acted upon. They are neither created by our uses of language or acts of thinking, nor destroyed by their cessation.
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