Frege: Descriptions

Fregean theories of descriptions as terms have to deal with improper descriptions. To save bivalence various proposals have been made that involve assigning referents to improper descriptions. While bivalence is indeed saved, there is a price to be paid. Instantiations of the same general scheme, viz. the one and only individual that is F and G is G, are not only allowed but even required to have different truth values.

Bertrand Russell in his essay On Denoting [1905] presented a theory of description developed in response to the one proposed by Gottlob Frege in his paper Über Sinn und Bedeutung [1892]. The aim of our work will be to show that Russell underestimated Frege three times over in presenting the latter’s work: in relation to the Gray’s Elegy argument, to the Ferdinand argument, and to puzzles discussed by Russell. First, we will discuss two claims of Russell’s which do not do (...) justice to Frege: that we speak of a sense by means of quotation marks, and that all Frege does to cope with phrases that might denote nothing is define an arbitrary object as their reference. Second, we will show that Russell omitted the fact that Frege’s theory provided some answers for the puzzles presented by Russell in his essay. (shrink)

It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his rejection (...) of similar “semantic dualisms” such as Frege’s theory of sense and reference—at least in “On Denoting”—made no explicit mention of any Cantorian paradox. My aim in this paper is to argue that such paradoxes do pose a problem for certain theories such as Frege’s, and early Russell’s, about how definite descriptions are meaningful. My first aim is simply to lay out the problem I have in mind. Next, I shall turn to arguing that the theories of descriptions endorsed by Frege and by Russell prior to “On Denoting” are susceptible to the problem. Finally, I explore what responses a.. (shrink)

In ‘On Denoting’ and to some extent in ‘Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie’, published in the same issue of Mind (Russell, 1905a,b), Russell presents not only his famous elimination (or contextual defi nition) of defi nite descriptions, but also a series of considerations against understanding defi nite descriptions as singular terms. At the end of ‘On Denoting’, Russell believes he has shown that all the theories that do treat defi nite descriptions as singular terms fall (...) logically short: Meinong’s, Mally’s, his own earlier (1903) theory, and Frege’s. (He also believes that at least some of them fall short on other grounds—epistemological and metaphysical—but we do not discuss these criticisms except in passing). Our aim in the present paper is to discuss whether his criticisms actually refute Frege’s theory. We fi rst attempt to specify just what Frege’s theory is and present the evidence that has moved scholars to attribute one of three different theories to Frege in this area. We think that each of these theories has some claim to be Fregean, even though they are logically quite different from each other. This raises the issue of determining Frege’s attitude towards these three theories. We consider whether he changed his mind and came to replace one theory with another, or whether he perhaps thought that the different theories applied to different realms, for example, to natural language versus a language for formal logic and arithmetic. We do not come to any hard and fast conclusion here, but instead just note that all these theories treat defi nite descriptions as singular terms, and that Russell proceeds as if he has refuted them all. After taking a brief look at the formal properties of the Fregean theories (particularly the logical status of various sentences containing nonproper defi - nite descriptions) and comparing them to Russell’s theory in this regard, we turn to Russell’s actual criticisms in the above-mentioned articles to examine the extent to which the criticisms hold.. (shrink)

In the case of an actual proper name such as ‘Aristotle’ opinions as to the Sinn may differ. It might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the Great. Anybody who does this will attach another Sinn to the sentence ‘Aristotle was born in Stagira’ than will a man who takes as the Sinn of the name: the teacher of Alexander the Great who was born in Stagira. So long as the (...) Bedeutung remains the same, such variations of Sinn may be tolerated, although they are to be avoided.. (shrink)

According to the principle of compositionality, the meaning of a composed expression depends only on its logical form and the meaning of its descriptive sub-expressions. This dependence can be understood as the substitutivity of expressions that have the same meaning without changing the meaning of the composed expression. In this book the hidden complexity of Frege's and Quine's conceptions of extensionality is revealed. The insights gained by this analysis as well as two versions of the principle of compositionality are used (...) in a formal reconstruction of Gödel's and Quine's versions of the slingshot argument. (shrink)

The main thesis of this paper is that some of the most important ideas and symbolic devices that made Russell's theory of descriptions possible were already present in writings by Frege and especially Peano that Russell knew well. The paper contains a detailed comparison between the relevant parts of Russell's theory--including manuscripts recently published--and some of Frege and Peano's insights, as well as a discussion of numerous possible objections that could be posed to the main claim. Even if Russell was (...) not actually influenced by those insights, the parallelism is close enough to be worth analyzing, especially in the case of Peano, whose writings are not very well known. (shrink)

......Mathematics coincides with Frege's theory of Sinn and Bedeutung...argued that in cases where Frege would say we recognize over...successful.) With this sort of elucidation, then, I indeed proposed to...use of . . .', or between Frege's 'einen Sinn ausdruckeri.....

The paper analyzes the famous passage in "on denoting" where russell appears to be attacking frege's theory of the sense and reference of proper names. We argue that russell's attack has been misinterpreted and unjustly condemned. The strategy is to show what difficulties do genuinely face a two-Part theory, And then to show that it is quite easy to interpret russell as having perceived them.

Gödel’s slingshot-argument proceeds from a referential theory of definite descriptions and from the principle of compositionality for reference. It outlines a metasemantic proof of Frege’s thesis that all true sentences refer to the same object—as well as all false ones. Whereas Frege drew from this the conclusion that sentences refer to truth-values, Gödel rejected a referential theory of definite descriptions. By formalising Gödel’s argument, it is possible to reconstruct all premises that are needed for the derivation of Frege’s thesis. For (...) this purpose, a reference-theoretical semantics for a language of first-order predicate logic with identity and referentially treated definite descriptions will be defined. Some of the premises of Gödel’s argument will be proven by such a reference-theoretical semantics, whereas others can only be postulated. For example, the principle that logically equivalent sentences refer to the same object cannot be proven but must be assumed in order to derive Frege’s thesis. However, different true (or false) sentences can refer to different states of affairs if the latter principle is rejected and the other two premises are maintained. This is shown using an identity criterion for states of affairs according to which two states of affairs are identical if and only if they involve the same objects and have the same necessary and sufficient condition for obtaining. (shrink)