Language Truth and Logic in Mathematics

Language  Truth and Logic in Mathematics

As its title indicates, the essays included in the present volume represent the latter approach.

Author: Jaakko Hintikka

Publisher: Springer Science & Business Media

ISBN: 9789401720458

Category: Mathematics

Page: 250

View: 440

One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer. As its title indicates, the essays included in the present volume represent the latter approach. In most of them one of the fundamental concepts in the foundations of mathematics and logic is subjected to a scrutiny from a largely novel point of view. Typically, it turns out that the concept in question is in need of a revision or reconsideration or at least can be given a new twist. The results of such a re-examination are not primarily critical, however, but typically open up new constructive possibilities. The consequences of such deconstructions and reconstructions are often quite sweeping, and are explored in the same paper or in others.
Categories: Mathematics

Language Truth and Logic

Language  Truth and Logic

The basic thesis of this work is that philosophy should not squander its energies upon the unknowable, but should perform its proper function in criticism and analysis.

Author: Alfred Jules Ayer

Publisher: Courier Corporation

ISBN: 9780486113098

Category: Philosophy

Page: 160

View: 680

"A delightful book … I should like to have written it myself." — Bertrand Russell First published in 1936, this first full-length presentation in English of the Logical Positivism of Carnap, Neurath, and others has gone through many printings to become a classic of thought and communication. It not only surveys one of the most important areas of modern thought; it also shows the confusion that arises from imperfect understanding of the uses of language. A first-rate antidote for fuzzy thought and muddled writing, this remarkable book has helped philosophers, writers, speakers, teachers, students, and general readers alike. Mr. Ayers sets up specific tests by which you can easily evaluate statements of ideas. You will also learn how to distinguish ideas that cannot be verified by experience — those expressing religious, moral, or aesthetic experience, those expounding theological or metaphysical doctrine, and those dealing with a priori truth. The basic thesis of this work is that philosophy should not squander its energies upon the unknowable, but should perform its proper function in criticism and analysis.
Categories: Philosophy

Language Truth and Logic

Language  Truth and Logic

Ayer was only 24 when he finished LANGUAGE, TRUTH & LOGIC, yet it shook the foundations of Anglo-American philosophy and made its author notorious.

Author: A.J. Ayer

Publisher: Penguin UK

ISBN: 9780141911809

Category: Philosophy

Page: 224

View: 400

If you can't prove something, it is literally senseless - so argues Ayer in this irreverent and electrifying book. Statements are either true by definition (as in maths), or can be verified by direct experience. Ayer rejected metaphysical claims about god, the absolute, and objective values as completely nonsensical. Ayer was only 24 when he finished LANGUAGE, TRUTH & LOGIC, yet it shook the foundations of Anglo-American philosophy and made its author notorious. It became a classic text, cleared away the cobwebs in philosophical thinking, and has been enormously influential.
Categories: Philosophy

Logical Positivism in Perspective

Logical Positivism in Perspective

These essays offer a comprehensive appraisal of the influence and impact of Ayer's work and analyze the ways in which Ayer's arguments have been absorbed, modified, or rejected by various philosophers.

Author: Barry Gower

Publisher: Barnes & Noble Imports

ISBN: UOM:39076000605159

Category: Philosophy

Page: 129

View: 684

1986 is the fiftieth anniversary of the publication of A. J. Ayer's Language, Truth and Logic, which is commonly considered one of the most influential books in twentieth-century philosophy. These essays offer a comprehensive appraisal of the influence and impact of Ayer's work and analyze the ways in which Ayer's arguments have been absorbed, modified, or rejected by various philosophers. A noteworthy feature of the book is an original essay by A. J. Ayer that assesses the influence of his work in philosophy over the last fifty years.
Categories: Philosophy

The Historical and Philosophical Significance of Ayer s Language Truth and Logic

The Historical and Philosophical Significance of Ayer   s Language  Truth and Logic

79), and their truth is determined via formal criteria such as consistency. Although they are factually empty, they do not belong to the realm of metaphysics, as they govern the logic of our language. Chapter 4 does not contain many ...

Author: Adam Tamas Tuboly

Publisher: Springer Nature

ISBN: 9783030508845

Category:

Page:

View: 501

Categories:

Language Truth and Knowledge

Language  Truth and Knowledge

(2002) “Hyperclassical Logic (a.k.a.IF logic)and its Implications for Logical Theory”, Bulletin of Symbolic Logic, vol. 8, pp. 404–423. ... (1998) Language, Truth and Logic in Mathematics, Kluwer Academic, Dordrecht.

Author: Thomas Bonk

Publisher: Springer Science & Business Media

ISBN: 9789401701518

Category: Philosophy

Page: 194

View: 207

This collection will prove a valuable resource for our understanding of the historic Carnap and the living philosophical issues with which he grappled. It arose out of a symposium on Carnap's work (Vienna, 2001). With essays by Graham H. Bird, Jaakko Hintikka, Ilkka Niiniluoto, Jan Wolenski, this volume will interest graduate students of the philosophy of language and logic, as well as professional philosophers, historians of analytic philosophy, and philosophically inclined logicians.
Categories: Philosophy

Alfred Tarski Philosophy of Language and Logic

Alfred Tarski  Philosophy of Language and Logic

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, ...

Author: Douglas Patterson

Publisher: Springer

ISBN: 9780230367227

Category: Mathematics

Page: 262

View: 332

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.
Categories: Mathematics

Briefly Ayer s Language Truth and Logic

Briefly  Ayer s Language Truth and Logic

Language,. Truth. and. Logic. Preface to First Edition (pp. 9–11) The views expressed below derive from those of Russell and ... comprising the 'a priori propositions of logic and pure mathematics', which are 'necessary and certain', ...

Author: David Mills Daniel

Publisher: SCM Press

ISBN: 9780334048305

Category: Religion

Page: 96

View: 201

Part of the "SCM Briefly" series, which summarizes books by philosophers and theologians, this book provides a summary of Language, Truth and Logic. It also includes line by line analysis, short quotes, and a glossary of terms to help students with definitions of philosophical terms.
Categories: Religion

The Principles of Mathematics Revisited

The Principles of Mathematics Revisited

listed are essentially restrictive , including theorems as to what cannot be done in logic or in mathematics . ... Nonetheless , objectively speaking a study of the roles of language , truth and logic in mathematics seems to me by far ...

Author: Jaakko Hintikka

Publisher: Cambridge University Press

ISBN: 0521624983

Category: Mathematics

Page: 304

View: 619

Hintikka proposes a new logic and uses it to explore the foundations of mathematics.
Categories: Mathematics

Philosophy of Language

Philosophy of Language

See his “Review of Language, Truth, and Logic”. ... Readers completely new to the philosophy of language may wish to skip the section, move directly to §3.4, and return to the ... “Logic, Mathematics, and Knowledge of Nature”, p.148.

Author: Alex Miller

Publisher: Routledge

ISBN: 9781134271146

Category: Philosophy

Page: 416

View: 788

This engaging and accessible introduction to the philosophy of language provides an important guide to one of the liveliest and most challenging areas of study in philosophy. Interweaving the historical development of the subject with a thematic overview of the different approaches to meaning, the book provides students with the tools necessary to understand contemporary analytical philosophy. The second edition includes new material on: Chomsky, Wittgenstein and Davidson as well as new chapters on the causal theory of reference, possible worlds semantics and semantic externalism.
Categories: Philosophy

Philosophy of Language

Philosophy of Language

14 Ayer, Language, Truth, and Logic, p.13. 15 Ibid. 16 See Church, “Review of Language, Truth, and Logic”. 17 The material in this section is more ... 30 Hahn, “Logic, Mathematics”, p.148. 31 Ayer, Language, Truth, and Logic, p.75.

Author: Alexander Miller

Publisher: Routledge

ISBN: 9781351265508

Category: Philosophy

Page: 448

View: 713

Philosophy of Language provides a comprehensive, meticulous survey of twentieth-century and contemporary philosophical theories of meaning. Interweaving the historical development of the subject with a thematic overview of the different approaches to meaning, the book provides students with the tools necessary to understand contemporary analytic philosophy. Beginning with a systematic look at Frege’s foundational theories on sense and reference, Alexander Miller goes on to offer a clear exposition of the development of subsequent arguments in the philosophy of language. Communicating a sense of active philosophical debate, the author confronts the views of the early theorists, taking in Frege, Russell, and logical positivism and going on to discuss the scepticism of Quine, Kripke, and Wittgenstein. The work of philosophers such as Davidson, Dummett, Searle, Fodor, McGinn, Wright, Grice, and Tarski is also examined in depth. The third edition has been fully revised for enhanced clarity and includes: · a short introduction for students, outlining the importance of the philosophy of language and the aims of the book; · two substantial new sections on Philip Pettit’s "ethocentric" account of rule-following and on Hannah Ginsborg’s "partial reductionism" about rule-following and meaning; · the addition of chapter summaries and study questions throughout, designed to promote greater understanding and engagement; · updated guides to further reading at the end of every chapter. This well-established and sophisticated introduction to the philosophy of language is an unrivalled guide to one of the liveliest and most challenging areas of philosophy and is suitable for use on undergraduate degrees and in postgraduate study.
Categories: Philosophy

Jaakko Hintikka Selected Papers Set

Jaakko Hintikka Selected Papers  Set

Vol. 6: Analyses of Aristotle This collection comprises several striking interpretations of Aristotle's logic and methodology that Jaakko Hintikka has put forward over the years, constituting a challenge not only to Aristotelian scholars ...

Author: Jaakko Hintikka

Publisher: Springer

ISBN: 1402033303

Category: Philosophy

Page: 1784

View: 260

Vol. 1: Ludwig Wittgenstein: Half-Truths and One-and-a-Half-Truths Because of his legendary impatience, Wittgenstein's published books are focused on his solutions to his latest problems and consequently often fail to explain not only his earlier solutions but also his problem situation. In the essays collected in this volume, Jaakko Hintikka counteracts the difficulty which this peculiarity of Wittgenstein's poses to his readers by analysing in depth the crucial stages of Wittgenstein's philosophical career and the relation of his ideas to those of other philosophers, especially Russell, Carnap and Husserl, with sometimes surprising results. Vol. 2: Lingua Universalis vs. Calculus Ratiocinator Twentieth-century philosophy has tacitly been dominated by a deep contrast between universalist and model-theoretical visions of language. The role of this contrast is studied here in Peirce, Frege, Wittgenstein, Carnap, Quine, Husserl, Heidegger and in the development of logical theory. Hintikka also develops a new approach to truth-definitions which strongly supports the model-theoretical view. Vol. 3: Language, Truth and Logic in Mathematics The foundations of mathematics are examined by reference to such crucial concepts as the informational independence of quantifiers, the standard-nonstandard distinction, completeness, computability, parallel processing and the extremality of models. Vol. 4: Paradigms for Language Theory and Other Essays Several of the basic ideas of current language theory are subjected to critical scrutiny and found wanting, including the concept of scope, the hegemony of generative syntax, the Frege-Russell claim that verbs like `is' are ambiguous, and the assumptions underlying the so-called New Theory of Reference. In their stead, new constructive ideas are proposed. Vol. 5: Inquiry as Inquiry: A Logic of Scientific Discovery/STRONG In the essays collected here, Hintikka both defends and outlines a genuine logic of scientific discovery, the logic of questions and answers. Thus inquiry in the sense of knowledge-seeking becomes inquiry in the sense of interrogation. Using this new logic, Hintikka establishes a result that will undoubtedly be considered the fundamental theorem of all epistemology, viz., the virtual identity of optimal strategies of pure discovery with optimal deductive strategies. Vol. 6: Analyses of Aristotle This collection comprises several striking interpretations of Aristotle's logic and methodology that Jaakko Hintikka has put forward over the years, constituting a challenge not only to Aristotelian scholars and historians of ideas, but to everyone interested in logic, epistemology or metaphysics and in their history.
Categories: Philosophy

Logicism and the Philosophy of Language

Logicism and the Philosophy of Language

This is a collection for anyone interested in questions about truth, meaning, reference, and logic, and in the application of formal analysis to these concepts.

Author: Arthur Sullivan

Publisher: Broadview Press

ISBN: 9781551114712

Category: Philosophy

Page: 304

View: 924

Logicism and the Philosophy of Language brings together the core works by Gottlob Frege and Bertrand Russell on logic and language. In their separate efforts to clarify mathematics through the use of logic in the late nineteenth and early twentieth century, Frege and Russell both recognized the need for rigorous and systematic semantic analysis of language. It was their turn to this style of analysis that would establish the philosophy of language as an autonomous area of inquiry. This anthology gathers together these foundational writings, and frames them with an extensive historical introduction. This is a collection for anyone interested in questions about truth, meaning, reference, and logic, and in the application of formal analysis to these concepts.
Categories: Philosophy

The Lvov Warsaw School Past and Present

The Lvov Warsaw School  Past and Present

His most important result in logic was his conjecture that any propositional calculus can be characterized by a ... the Italians Giuseppe Peano, Alessandro Padoa and Mario Pieri) to reduce mathematics to language, truth and logic, ...

Author: Ángel Garrido

Publisher: Birkhäuser

ISBN: 9783319654300

Category: Mathematics

Page: 815

View: 888

This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.
Categories: Mathematics

Analytic Philosophy in Finland

Analytic Philosophy in Finland

Language, Truth and Logic in Mathematics. Jaakko Hintikka Selected Papers 3. Dordrecht: Kluwer Academic Publishers. Hintikka, J. and M. B. Hintikka (1982). Towards a general theory of individuation and identification.

Author:

Publisher: BRILL

ISBN: 9789004333888

Category: Philosophy

Page: 596

View: 313

Finland is internationally known as one of the leading centers of twentieth century analytic philosophy. This volume offers for the first time an overall survey of the Finnish analytic school. The rise of this trend is illustrated by original articles of Edward Westermarck, Eino Kaila, Georg Henrik von Wright, and Jaakko Hintikka. Contributions of Finnish philosophers are then systematically discussed in the fields of logic, philosophy of language, philosophy of science, history of philosophy, ethics and social philosophy. Metaphilosophical reflections on the nature of philosophy are highlighted by the Finnish dialogue between analytic philosophy, phenomenology, pragmatism, and critical theory.
Categories: Philosophy

Logic Language and Mathematics

Logic  Language  and Mathematics

This volume is a collective exploration of the major themes of his work in philosophy of language, philosophical logic, and philosophy of mathematics.

Author: Alexander Miller

Publisher: Oxford University Press, USA

ISBN: 9780199278343

Category: Mathematics

Page: 464

View: 704

Crispin Wright is widely recognised as one of the most important and influential analytic philosophers of the twentieth and twenty-first centuries. This volume is a collective exploration of the major themes of his work in philosophy of language, philosophical logic, and philosophy of mathematics. It comprises specially written chapters by a group of internationally renowned thinkers, as well as four substantial responses from Wright. In these thematically organized replies, Wright summarizes his life's work and responds to the contributory essays collected in this book. In bringing together such scholarship, the present volume testifies to both the enormous interest in Wright's thought and the continued relevance of Wright's seminal contributions in analytic philosophy for present-day debates;
Categories: Mathematics

Wittgenstein and the Turning Point in the Philosophy of Mathematics

Wittgenstein and the Turning Point in the Philosophy of Mathematics

143, both in Logical Positivism, A.J.Ayer (ed.) (New York, The Free Press, 1959);HansHahn, 'Logic, Mathematics and Knowledge of Nature', p.158in Logical Positivism;and A.J. Ayer, Language, Truth and Logic (London,Victor Gollancz,1970) ...

Author: S.G. Shanker

Publisher: Routledge

ISBN: 9781317832034

Category: Philosophy

Page: 376

View: 149

First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.
Categories: Philosophy

Kant s Philosophy of Mathematics

Kant s Philosophy of Mathematics

(1984): “Kant's Transcendental Method and His Theory of Mathematics,” Topoi 3, 99–108. Reprinted in Posy (ed.) (1992), 341–360. (1998): Language, Truth and Logic in Mathematics. Selected Papers, Vol. 3. Dordrecht: Kluwer.

Author: Carl Posy

Publisher: Cambridge University Press

ISBN: 9781107042902

Category: Philosophy

Page: 328

View: 704

Essential for students and scholars, this book brings contemporary Kantian scholarship together with the history of philosophy of mathematics.
Categories: Philosophy

The Philosophy of Mathematics Today

The Philosophy of Mathematics Today

Of course , everyone knew nothing was ever as simple as Ayer made it out to be - Language , Truth , and Logic was the Manifesto , not Das Kapital . But didn't he have it approximately right ? Wasn't the basic point correct , even if he ...

Author: Matthias Schirn

Publisher: Oxford University Press

ISBN: 0199262624

Category: Philosophy

Page: 638

View: 360

Representing the state of the art in the field of the philosophy of mathematics, this collection of 20 essays deals with fundamental issues, ranging from the nature of mathematical knowledge to sets and natural 'number'.
Categories: Philosophy

Kant s Philosophy of Mathematics Volume 1 The Critical Philosophy and its Roots

Kant s Philosophy of Mathematics  Volume 1  The Critical Philosophy and its Roots

(1984): “Kant's Transcendental Method and His Theory of Mathematics,” Topoi 3, 99–108. Reprinted in Posy (ed.) (1992), 341–360. (1998): Language, Truth and Logic in Mathematics. Selected Papers, Vol. 3. Dordrecht: Kluwer.

Author: Carl Posy

Publisher: Cambridge University Press

ISBN: 9781108669535

Category: Philosophy

Page:

View: 860

The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical philosophy, and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant.
Categories: Philosophy