Equality1 gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A relation between objects, or between names or signs of objects? In my Begriffsschrift I assumed the latter. The reasons which seem to favour this are the following: a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = (...) b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names ‘a’ and ‘b’ designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. What is intended to be said by a = b seems to be that the signs or names ‘a’ and ‘b’ designate the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only in so far as they named or designated something. It would be mediated by the connexion of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a = b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means. But in many cases this is just what we want to do. If the sign ‘a’ is distinguished from the sign ‘b’ only as object (here, by means of its shape), not as sign (i.e. not by the manner in which it designates something), the cognitive value of a = a becomes essentially equal to that of a = b, provided a = b is true.. (shrink)

This is identical with the first edition (see 21: 2716) except for the addition of a Supplement containing 5 previously published articles and the bringing of the bibliography (now 73 items) up to date. The 5 added articles present clarifications or modifications of views expressed in the first edition. (PsycINFO Database Record (c) 2009 APA, all rights reserved).

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.

In this investigation into Frege's philosophical views as a whole, the central focus is on his notion of sense, the conception that has proved most influential in the development of analytical philosophy, and around which the main problems of interpretation revolve.

Frege's notion of 'bedeutung' (b.) is here interpreted not as the object for which an expression stands but as its truth-Value potential. This is achieved by beginning with the b. Of sentences and defining the b. Of names as that property of them which remains constant when they are substituted in sentences without a change in truth-Value. This interpretation is shown to receive confirmation from what frege says in a recently published manuscript about the b. Of predicates; finally, It is (...) applied to frege's doctrine of oblique b. (shrink)

Chapter One: Constructions. Entities, constructions, and functions When one travels from Los Angeles to New York, going, say, by way of St. Louis, Chicago, ...

Michael Dummett, following an established line of reasoning, has interpreted Frege as a realist. But his claim that Frege was arguing against a dominant idealism is untenable. While there are passages in Frege's writings that seem to support a realistic interpretation, others are irreconcilable with it. The issue can be resolved only by examining the historical context. Frege's thought is, in fact, related to the philosophy of Hermann Lotze. Frege is best regarded as a transcendental idealist in the Lotze-Kant tradition. (...) His contextual principle is a linguistic version of Kant's principle of the transcendental unity of judgment. By ignoring the historical context Dummett has been led to misinterpret the precise role of the contextual principle in Frege's thought. (shrink)

The concept ofsemantic interpretation is a source of chronic confusion: the introduction of a notion ofinterpretation can be the result of several quite different kinds of considerations.Interpretation can be understood in at least three ways: as a process of dis-abstraction of formulas, as technical tool for the sake of characterizing truth, or as a reconstruction of meaning-assignment. However essentially different these motifs are and however properly they must be kept apart, these can all be brought to one and the same (...) notion of interpretation: to the notion of a compositional evaluation of expressions inducing a possible distribution of truth values among statements. (shrink)

The Principle of Semantic Compositionality (sometimes called Frege''s Principle) is the principle that the meaning of a (syntactically complex) whole is a function only of the meanings of its (syntactic) parts together with the manner in which these parts were combined. This principle has been extremely influential throughout the history of formal semantics; it has had a tremendous impact upon modern linguistics ever since Montague Grammars became known; and it has more recently shown up as a guiding principle for a (...) certain direction in cognitive science.Despite the fact that The Principle is vague or underspecified at a number of points — such as what meaning is, what counts as a part, what counts as a syntactic complex, what counts as combination — this has not stopped some people from viewing The Principle as obviously true, true almost by definition. And it has not stopped other people from viewing The Principle as false, almost pernicious in its effect. And some of these latter theorists think that it is an empirically false principle while others think of it as a methodologically wrong-headed way to proceed. (shrink)

Frege has one magnificent achievement to his credit, viz. the creation of modern formal logic. As a philosopher and as a theoretical logician, he was nevertheless as parochial as he was, geographically speaking. Hence Frege’s concepts and problems offer singularly unfortunate starting points for constructive work in the foundations of logic and mathematics. Even if he is right in some of his views, they depend on severely restrictive assumptions that have to be noted and eliminated. These restrictive assumptions have not (...) been sufficiently acknowledged in most of the recent discussions of Frege’s ideas. This has given rise to wild overstatements of Frege’s achievements. To give only two examples, Frege is sometimes said to have had within his reach “the concepts necessary to frame the notion of the completeness of a formalization of logic as well as soundness.” Or, he is credited with the creation of mathematical logic “issuing in a formal system logic incorporating propositional calculus, first- and second-order quantification theory, and a theory of sets developed within second-order quantification theory.” We will soon see that both these claims are not only severely exaggerated but that they miss some of the most characteristic features of Frege’s entire way of thinking about logical and semantical matters. (shrink)

Bob Hale; XII*—Grundlagen §64, Proceedings of the Aristotelian Society, Volume 97, Issue 1, 1 June 1997, Pages 243–262, https://doi.org/10.1111/1467-9264.00015.

Bob Hale; XII*—Grundlagen §64, Proceedings of the Aristotelian Society, Volume 97, Issue 1, 1 June 1997, Pages 243–262, https://doi.org/10.1111/1467-9264.00015.

[Translation of Frege's 'Gedankengefüge' (1923)].

Originally published in 1973, this book shows that methods developed for the semantics of systems of formal logic can be successfully applied to problems about the semantics of natural languages; and, moreover, that such methods can take account of features of natural language which have often been thought incapable of formal treatment, such as vagueness, context dependence and metaphorical meaning. Parts 1 and 2 set out a class of formal languages and their semantics. Parts 3 and 4 show that these (...) formal languages are rich enought to be used in the precise description of natural languages. Appendices describe some of the concepts discussed in the text. (shrink)

At the age of eight, Karl Popper was puzzling over the idea of infinity and by fifteen was beginning to take a keen interest in his father's well-stocked library of books. Unended Quest recounts these moments and many others in the life of one of the most influential thinkers of the twentieth century, providing an indispensable account of the ideas that influenced him most. As an introduction to Popper's philosophy, Unended Quest also shines. Popper lucidly explains the central ideas in (...) his work, making this book ideal for anyone coming to Popper's life and work for the first time. (shrink)

A brilliant account of the life of one of the most influential thinkers of the twentieth century. Popper also explains some of the central ideas in his work, making this ideal reading for anyone coming to his life and work for the first time.

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.