This might even entail that we could not truthfully deny the existence of anything of which we could conceive, which seems implausible. The second serious problem for referential theories of meaning, noted by Frege , was the informativeness of some identity sentences. Sentences of self-identity are true purely in virtue of their logical form, and we may affirm them even when we do not know what the expression refers to. For instance, anyone could affirm.
Kilimanjaro is. Making this statement in such a case would not inform our understanding of the world in any significant way. However, a sentence like. But remember that according to referential theories of meaning, "Mt. Kilimanjaro" and "the tallest mountain in Africa" refer to the same thing and hence mean the same thing according to these theories; therefore, 5 and 6 say the same thing and one should be no more or less informative than the other.
Where we grasp the meaning of an expression or a sentence, philosophers have traditionally taken it that this should make some sort of cognitive difference, for example, we should be able to perform an action, make an inference, recognize something, and so on. Thus differences in the meanings of expressions should be reflected by some difference in cognitive significance between the expressions. But if expressions refer to the same thing, and their meaning consists solely in their picking out a referent, then there should be no such cognitive difference even if there is apparently a difference in meaning.
Simple referential theories do not offer us an obvious solution to this problem and therefore fail to capture important intuitions about meaning. To address these problems, Frege proposed that we should think of expressions as having two semantic aspects: a sense and a reference. The sense of an expression would be its "mode of presentation," as Frege put it, that conveyed information to us in its own distinct way.
That information would in turn determine a referent for each expression. This led to a credo pervasive in analytical philosophy : sense determines reference. This solved problems of reference by shifting the emphasis to the sense of expressions first and to their reference later. Negative existential sentences were intelligible because the sense of an expression like "largest prime number" or "Atlantis" could be logically analyzed or made explicit in terms of other descriptions, even if the set of things specified by this information was, in fact, empty.
Our belief that these sentences and expressions were meaningful was a consequence of grasping their senses, even when we realized this left them without a referent.
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As Frege put it:. It can perhaps be granted that an expression has a sense if it is formed in a grammatically correct manner and stands for a proper name.
But as to whether there is a denotation corresponding to the connotation is hereby not decided… [T]he grasping of a sense does not with certainty warrant a corresponding nominatum. The informativeness of some identity claims also became clearer. In a sentence like 5 , we are simply stating self-identity, but in a sentence like 6 , we express something of real cognitive significance, containing extensions of our knowledge that cannot generally be shown a priori.
Even if "Mt. Kilimanjaro" and "the tallest mountain in Africa" refer to the same thing, it would be informative to learn that they do, and we would augment our understanding of the world by learning this. Frege also noted that expressions which shared their referents could generally be substituted for one another without changing the truth value of a sentence. However, Frege realized that there were certain contexts in which this substitutability failed, or at least could not be guaranteed.
What has happened here? Note that 7 and 8 both include strings of words that could be sentences in their own right "Elvis Costello was born in Liverpool" and "Declan McManus was born in Liverpool". Frege suggested that in these cases, the reference of those embedded sentences is not a truth value, as it would customarily be, but is rather the sense of the sentence itself. Someone might grasp the sense of one sentence but not another, and hence sentences like 7 and 8 could vary in their truth values.
Frege called these "indirect" contexts, and Quine would later dub such cases "opaque" contexts. Rudolf Carnap would later replace the term "sense" with "intension" and "reference" with "extension. Significant worries remained for the Fregean notion of sense, however. Names and other expressions in natural languages rarely have fixed sets of descriptions that are universally acknowledged as Frege's senses would have to be. Frege might reply that he had no intention of making sense a matter of public consensus or psychological regularity, but this makes the status of a sense all the more mysterious, as well as our capacity to grasp them.
Analytical philosophers of language would struggle with this for decades to come. Still, Frege had effectively redrawn the map for philosophy. By introducing senses as a focal point of analysis, he had carved out a distinct territory for philosophical inquiry. Senses were not simply psychological entities, since they were both commonly accessible by different speakers and had a normative dimension to them, prescribing correct usage rather than simply describing performance.
See Frege for a thorough attack on psychologistic accounts of meaning. Nor were they the causal and mechanical objects of natural science, reducible to accounts of lawlike regularity. They were entities playing a logical and cognitive role, and would be both explanatory of conceptual content and universal across natural languages, unlike the empirical details of linguistics and anthropology. Thus, there was a project for philosophy to undertake, separate from the natural sciences, and it was the logical analysis of the underlying structure of meaning.
Though naturalistic concerns would be reasserted in the development of analytical philosophy, Frege's project would come to dominate Anglo-American philosophy for much of the next century.
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Both men were mathematicians by training and shared a concern with the foundations of arithmetic. However, Russell shared a sense with some earlier philosophers that at least some expressions were meaningful in virtue of direct reference, contra Frege. Still, Russell saw the potential in Frege's work and undertook an analysis of singular definite descriptions. These are complex expressions that purport to single out a particular referent by providing a description, for example, "the President of the USA," or "the tallest person in this room right now. Russell's solution was to analyze the logical role of such descriptions.
Although a select few expressions referred directly to objects, most were either descriptions that picked out a referent by offering a list of properties, or disguised abbreviations of such descriptions. Russell even suggested that most proper names were abbreviated descriptions. Strictly speaking, descriptions would not refer at all; they would be quantified phrases that had or lacked extensions. What was needed was an account that could explain the meaning of descriptions in terms of the propositions that they abbreviated. Russell analyzed sentence 9 as implying three things that jointly gave us a definition of propositions involving descriptions.
A more succinct presentation comes in Russell A sentence like "The author of Waverley was Scotch" involves three logical constituents:. The first two here effectively assert the existence and uniqueness of the referent of this expression, respectively.
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We may generalize them and express them as a single proposition of the form "There is a term c such that Fx is true when x is c, and Fx is false when x is not c. This asserts that there is a unique satisfier of the description given or implied by an expression, and this may be true or false depending on the expression at hand. We can then tack on an additional condition expressing whatever property is attributed to the referent being bald, Scotch, and so on in the form "c has the property Y. Such expressions are actually to be understood as quantified phrases and we may understand them as having objects over which they quantify or lacking such objects; the grasp of the logical structure of those phrases is what constitutes our understanding of them.
While we grasp each of the parts abbreviated by the expression, we also understand that one of them is false—there is no unique satisfier of "the present King of France"—and thus we can understand the sentence "The present king of France is bald" even though one of its terms does not refer.
That expression can have a significant occurrence once we understand it as an "incomplete" or "complex" symbol whose meaning is derived from its constituents. Most proper names, and indeed almost all expressions in a natural language, would submit to such an analysis, and Russell's work thus kick-started analytical philosophy in the English-speaking world.
Significant contributions were also made by G. Moore in the fields of epistemology and ethics and hence he is often mentioned along with Russell, but Moore's achievements are largely outside the scope of our focus here. The achievements of Russell and Frege, in setting an agenda for analytical philosophers that promised to both resolve longstanding philosophical difficulties and preserve a role for philosophy on an equal footing with the natural sciences, electrified European and American academic philosophers.
The following section focuses on three points of interest in the early phases of this tradition: 1 the early work of Ludwig Wittgenstein ; 2 the Logical Positivists ; and 3 Tarski 's theory of truth. Ludwig Wittgenstein came to read Frege and Russell out of an interest in the foundations of mathematics and went to Cambridge to study with Russell.
He studied there, but left to serve in the Austro-Hungarian army in While being held as a prisoner of war, he wrote drafts of a text that many saw as the high-water mark of early analytical philosophy, the Tractatus Logico-Philosophicus. In it, he wrote seven propositions and made extensive comments on six of them, with extensive comments on the comments, and so forth. He laid out a parsimonious and ambitious plan to systematically realize Frege and Russell's aspirations of analyzing the logical structure of language and thought.
Through logical analysis, Wittgenstein held that we could arrive at a conception of language as consisting of elementary propositions related by the now-familiar elements of first-order logic. Any sentence with a sense could have that sense perspicuously rendered in such a system, and any sentence that did not yield to such analysis would not have a sense at all.
Everything that can be said can be said clearly.
Rather, in doing so, we do not express anything that has a sense. What we say may get nods of approval from fellow speakers, and we may even be grasping at something important, but what we say does not convey anything meaningful. In part, this reflects Wittgenstein's early view that propositions "pictured" the world. This is not to say that a written inscription or a verbal utterance of a sentence visually resembles that state of affairs it expresses. Rather, the form of a proposition resembled the form of some fact of the world. What was required to understand this as a picture of the world was just what was needed in the case of actual pictures—a coordination of the elements in the picture with objects outside itself.
Logical truths would be true in virtue of relations among their propositions. Where we could do this, the language was stating something clearly; where we could not, despite our best efforts, the words were not saying anything at all. However, this was not to say that everything about meaning and our understanding of the world was a matter of explicit definition, that is, something we could say.
Related Naming and Reference: The Link of Word to Object (Problems of Philosophy)
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