scholarly journals SELF-REFERENCE, THEORY OF TYPES, AND CATEGORIZATION IN WITTGENSTEIN’S PICTURE THEORY OF STATEMENTS

2021 ◽  
pp. 213-233
Author(s):  
Валерий Александрович Суровцев
Keyword(s):  
Bertrand Russell ◽  
Gottlob Frege ◽  
Foundations Of Mathematics ◽  
Picture Theory ◽  
Reference Theory ◽  
Logical Paradoxes ◽  
Self Reference

Рассматривается источник логических парадоксов, выявленных Б. Расселом в системе обоснования математики, предложенной Г. Фреге. Самореферентность выражений, предложенная Б. Расселом как объяснение возникновения парадоксов, рассматривается с точки зрения разработанной им простой и разветвленной теории типов. Обосновывается, что теория типов, предложенная Б. Расселом, основана на онтологических предпосылках. Онтологические предпосылки зависят от предпочтения семантическому перед синтаксическим подходом, который принимается Б. Расселом. Рассмотрены синтаксические подходы к логическому символизму, которые позволяют устранить парадоксы с точки зрения языка современной символической логики. Анализируется подход к решению парадоксов Л. Витгенштейна, который основан на синтаксическом подходе. Показано, что этот подход отличается от способов построения языка, принятых в современной логике. The article analyzes the source of logical paradoxes Bertrand Russell identified in the foundations of mathematics proposed by Gottlob Frege. Russell proposed self-reference of expressions as the source of paradoxes. To solve paradoxes, he developed the simple and ramified theory of types. Ontological presuppositions are well substantiated for his theory; they depend on semantic, but not syntactic, preference. Contemporary approaches in symbolical logic prefer syntactic methods. But Wittgenstein’s approach in his Tractatus Logico-Philosophicus is more interesting, especially from the perspective of his picture theory of statements.

The Analytic Revolution

2016 ◽  
Vol 78 ◽  
pp. 227-249 ◽  
Author(s):  
Michael Beaney
Keyword(s):  
Twentieth Century ◽  
Analytic Philosophy ◽  
Logical Analysis ◽  
Bertrand Russell ◽  
Gottlob Frege ◽  
Foundations Of Mathematics ◽  
Logical Theory

AbstractAnalytic philosophy, as we recognize it today, has its origins in the work of Gottlob Frege and Bertrand Russell around the turn of the twentieth century. Both were trained as mathematicians and became interested in the foundations of mathematics. In seeking to demonstrate that arithmetic could be derived from logic, they revolutionized logical theory and in the process developed powerful new forms of logical analysis, which they employed in seeking to resolve certain traditional philosophical problems. There were important differences in their approaches, however, and these approaches are still pursued, adapted, and debated today. In this paper I shall elucidate the origins of analytic philosophy in the work of Frege and Russell and explain the revolutionary significance of their methods of logical analysis.

scholarly journals Frege and Wittgenstein: The Limits of the Analytic Style

Elements ◽  
2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Christopher Sheridan
Keyword(s):  
Twentieth Century ◽  
Logical Analysis ◽  
Linguistic Meaning ◽  
Bertrand Russell ◽  
Gottlob Frege ◽  
Symbolic Logic ◽  
Scientific Language ◽  
German Mathematician ◽  
Broad Application ◽  
Analytic Tradition

The analytic tradition in philosophy stems from the work of German mathematician and logician Gottlob Frege. Bertrand Russell brough Frege's program to render language-particularly scientific language-in formal logical terms to the forefront of philosophy in the early twentieth century. The quest to clarify language and parse out genuine philosophical problems remains a cornerstone of analytic philosophy, but investigative programs involving the broad application of formal symbolic logic to language have largely been abandoned due to the influence of Ludwig Wittgenstein's later work. This article identifies the key philosophical moves that must be performed successfully in order for Frege's "conceptual notation" and other similar systems to adequately capture syntax and semantics. These moves ultimately fail as a result of the nature of linguistic meaning. The shift away from formal logical analysis of language and the emergence of the current analytic style becomes clearer when this failure is examined critically.

Language, Meaning, and Information

2014 ◽  
Author(s):  
Scott Soames
Keyword(s):  
Modal Logic ◽  
Philosophy Of Language ◽  
Possible Worlds ◽  
Philosophy Of Mathematics ◽  
Scientific Study ◽  
Bertrand Russell ◽  
Gottlob Frege ◽  
Possible Worlds Semantics ◽  
Language Meaning

This chapter is a case study of the process by which the attempt to solve philosophical problems sometimes leads to the birth of new domains of scientific inquiry. It traces how advances in logic and the philosophy of mathematics, starting with Gottlob Frege and Bertrand Russell, provided the foundations for what became a rigorous and scientific study of language, meaning, and information. After sketching the early stages of the story, it explains the importance of modal logic and “possible worlds semantics” in providing the foundation for the last half century of work in linguistic semantics and the philosophy of language. It argues that this foundation is insufficient to support the most urgently needed further advances. It proposes a new conception of truth-evaluable information as inherently representational cognitive acts of certain kinds. The chapter concludes by explaining how this conception of propositions can be used to illuminate the notion of truth; vindicate the connection between truth and meaning; and fulfill a central, but so far unkept, promise of possible worlds semantics.

Charles Sanders Peirce: An Overview

1996 ◽  
pp. 1-16
Author(s):  
Vincent G. Potter
Keyword(s):  
Nineteenth Century ◽  
Charles Sanders Peirce ◽  
Alfred North Whitehead ◽  
Bertrand Russell ◽  
Gottlob Frege ◽  
Georg Cantor ◽  
Academic World ◽  
American Pragmatism ◽  
George Boole

This chapter provides an overview of the life of Charles Sander Peirce—philosopher, logician, scientist, and father of American pragmatism. This man, unappreciated in his lifetime, virtually ignored by the academic world of his day, is now recognized as perhaps America's most original philosopher and her greatest logician. Indeed, on the latter score, he is surely one of the logical giants of the nineteenth century, which produced such geniuses as Georg Cantor, Gottlob Frege, George Boole, Augustus De Morgan, Bertrand Russell, and Alfred North Whitehead. Today, more than eighty years after his death, another generation of scholars is beginning to pay him the attention he deserves. The chapter shows the brilliant and tragic career of Peirce. Though he never published a book on philosophy, his articles and drafts fill volumes.

The Predicate of Existence

2019 ◽  
pp. 14-37
Author(s):  
Palle Yourgrau
Keyword(s):  
Bertrand Russell ◽  
Gottlob Frege ◽  
Order Property ◽  
Saul Kripke ◽  
Existential Quantifier ◽  
Modern Logic ◽  
First Order ◽  
David Kaplan ◽  
Theory Of Descriptions ◽  
Nathan Salmon

Kant famously declared that existence is not a (real) predicate. This famous dictum has been seen as echoed in the doctrine of the founders of modern logic, Gottlob Frege and Bertrand Russell, that existence isn’t a first-order property possessed by individuals, but rather a second-order property expressed by the existential quantifier. Russell in 1905 combined this doctrine with his new theory of descriptions and declared the paradox of nonexistence to be resolved without resorting to his earlier distinction between existence and being. In recent years, however, logicians and philosophers like Saul Kripke, David Kaplan, and Nathan Salmon have argued that there is no defensible reason to deny that existence is a property of individuals. Kant’s dictum has also been re-evaluated, the result being that the paradox of nonexistence has not, after all, disappeared. Yet it’s not clear how exactly Kripke et al. propose to resolve the paradox.

Propositions and Truth-Bearers

2018 ◽  
Author(s):  
Jeffrey C. King
Keyword(s):  
Bertrand Russell ◽  
Gottlob Frege ◽  
The 1960S

The chapter begins by reviewing the roles that advocates of propositions take them to play. Then it turns to the question of the nature of the things that play these roles. What is the correct metaphysics of propositions? Since most contemporary thought about the nature of propositions is traceable in some way to the classical theories of propositions of Gottlob Frege and Bertrand Russell, those theories are discussed in some detail. Then accounts of the metaphysics of propositions developed in 1960s are discussed. The chapter concludes by reviewing other accounts of propositions developed between the 1960s and the present.

The Metaphysics of Propositions

2017 ◽  
Author(s):  
Jeffrey C. King
Keyword(s):  
Possible Worlds ◽  
Direct Reference ◽  
Bertrand Russell ◽  
Gottlob Frege ◽  
Modal Properties

Propositions have been long thought by many philosophers to play a number of important roles. These include being the information conveyed by an utterance of a sentence, being the primary bearers of truth and falsity, being the possessors of modal properties like being possible and necessary, and being the things we assume, believe, and doubt. This article canvases significant attempts by philosophers to say what sorts of things propositions are. First, the classical views of propositions advanced by Gottlob Frege and Bertrand Russell are considered. Second, the view of propositions as sets of possible worlds is discussed. Next, views of propositions arising out of work on direct reference are discussed. The article closes with a discussion of more recent views of propositions.

Paul Benacerraf and Hilary Putnam. Introduction. Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle-wood Cliffs, New Jersey, 1964, pp. 1–27. - Rudolf Carnap. The logicist foundations of mathematics. English translation of 3528 by Erna Putnam and Gerald E. Massey. Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle-wood Cliffs, New Jersey, pp. 31–41. - Arend Heyting. The intuitionist foundations of mathematics. English translation of 3856 by Erna Putnam and Gerald E. Massey. Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle-wood Cliffs, New Jersey, pp. 42–49. - Johann von Neumann. The formalist foundations of mathematics. English translation of 2998 by Erna Putnam and Gerald E. Massey. Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle-wood Cliffs, New Jersey, pp. 50–54. - Arend Heyting. Disputation. A reprint of pages 1-12 (the first chapter) and parts of the bibliography of XXI 367. Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle-wood Cliffs, New Jersey, pp. 55–65. - L. E. J. Brouwer. Intuitionism and formalism. A reprint of 1557. Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle-wood Cliffs, New Jersey, pp. 66–77. - L. E. J. Brouwer. Consciousness, philosophy, and mathematics. A reprint of pages 1243-1249 of XIV 132. Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle-wood Cliffs, New Jersey, pp. 78–84. - Gottlob Frege. The concept of number. English translation of pages 67-104, 115-119, of 495 (1884 edn.) by Michael S. Mahoney. Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle-wood Cliffs, New Jersey, pp. 85–112. - Bertrand Russell. Selections from Introduction to mathematical philosophy. A reprint of pages 1-19, 194-206, of 11126 (1st edn., 1919). Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle-wood Cliffs, New Jersey, pp. 113–133. - David Hilbert. On the infinite. English translation of 10813 by Erna Putnam and Gerald E. Massey. Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle-wood Cliffs, New Jersey, pp. 134–151.

1969 ◽  
Vol 34 (1) ◽  
pp. 107-110
Author(s):  
Alec Fisher
Keyword(s):  
New Jersey ◽  
English Translation ◽  
Philosophy Of Mathematics ◽  
Bertrand Russell ◽  
Hilary Putnam ◽  
Foundations Of Mathematics ◽  
Rudolf Carnap ◽  
Von Neumann ◽  
David Hilbert ◽  
And Mathematics

Necessity Lost

2019 ◽  
Author(s):  
Sanford Shieh
Keyword(s):  
Analytic Philosophy ◽  
Logical Positivism ◽  
Bertrand Russell ◽  
Gottlob Frege ◽  
Deductive Argument ◽  
Analytic Tradition

A long tradition, going back to Aristotle, conceives of logic in terms of necessity and possibility: a deductive argument is correct if the truth of its conclusion follows necessarily from the truth of its premises or, put differently, if it is not possible for the conclusion to be false when the premises are true. A relatively unknown feature of the analytic tradition in philosophy is that, at its very inception, this venerable conception of the relation between logic and modality was put into question. The founders of analytic philosophy, Gottlob Frege and Bertrand Russell, held that there are no genuine distinctions among the necessary, the possible and the actual. In this first of a two-volume book, I investigate the grounds and consequences of this anti-modal position. The grounds lie in doctrines on truth, thought, and knowledge, as well as on the relation between mind and reality, that are central to the philosophies of Frege and Russell, and are of enduring philosophical interest. The main consequence is that logic is fundamental, and, to be coherent, modal concepts would be reconstructed in logical terms. This rejection of modality in early analytic philosophy remains of contemporary significance. The coherence of modal concepts is rarely questioned nowadays, because it is assumed that suspicion of modality derives from logical positivism, which has not survived philosophical scrutiny. The anti-modal arguments of Frege and Russell, however, have nothing to do with positivism, and remain a challenge to the contemporary acceptance of modal notions.

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