Language Truth And Logic In Mathematics
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Language Truth And Logic In Mathematics
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Author : Jaakko Hintikka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Language Truth And Logic In Mathematics written by Jaakko Hintikka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Language Truth And Logic
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Author : Alfred Jules Ayer
language : en
Publisher: Courier Corporation
Release Date : 2012-04-18
Language Truth And Logic written by Alfred Jules Ayer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-18 with Philosophy categories.
"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.
The Principles Of Mathematics Revisited
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Author : Jaakko Hintikka
language : en
Publisher: Cambridge University Press
Release Date : 1998-04-28
The Principles Of Mathematics Revisited written by Jaakko Hintikka and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-28 with Mathematics categories.
This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities.
Shadows Of Syntax
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Author : Jared Warren
language : en
Publisher: Oxford University Press
Release Date : 2020-07-20
Shadows Of Syntax written by Jared Warren and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-20 with Mathematics categories.
What is the source of logical and mathematical truth? This volume revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. In Shadows of Syntax, Jared Warren offers the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. He argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims. In Part I, Warren explains exactly what conventionalism amounts to and what linguistic conventions are. Part II develops an unrestricted inferentialist theory of the meanings of logical constants that leads to logical conventionalism. This conventionalist theory is elaborated in discussions of logical pluralism, the epistemology of logic, and of the influential objections that led to the historical demise of conventionalism. Part III aims to extend conventionalism from logic to mathematics. Unlike logic, mathematics involves both ontological commitments and a rich notion of truth that cannot be generated by any algorithmic process. To address these issues Warren develops conventionalist-friendly but independently plausible theories of both metaontology and mathematical truth. Finally, Part IV steps back to address big picture worries and meta-worries about conventionalism. This book develops and defends a unified theory of logic and mathematics according to which logical and mathematical truths are reflections of our linguistic rules, mere shadows of syntax.
Philosophy Of Language
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Author : Alexander Miller
language : en
Publisher: Routledge
Release Date : 2018-01-17
Philosophy Of Language written by Alexander Miller and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-17 with Philosophy categories.
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.
Philosophy Of Science Logic And Mathematics In The 20th Century
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Author : Stuart G. Shanker
language : en
Publisher: Taylor & Francis
Release Date : 2023-05-09
Philosophy Of Science Logic And Mathematics In The 20th Century written by Stuart G. Shanker and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-09 with Philosophy categories.
The twentieth century witnessed the birth of analytic philosophy. This volume covers some of its key movements and philosophers, including Frege and Wittgenstein's Tractatus.
Philosophy Of Language
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Author : Alex Miller
language : en
Publisher: Routledge
Release Date : 2007-09-12
Philosophy Of Language written by Alex Miller and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-12 with Philosophy categories.
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.
The Philosophy Of Mathematics And Natural Laws
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Author : Noel Curran
language : en
Publisher: Routledge
Release Date : 2019-07-23
The Philosophy Of Mathematics And Natural Laws written by Noel Curran and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Philosophy categories.
First published in 1997, this title is a sequel to Dr Noel Curran's first book The Logical Universe: The Real Universe (published by Ashgate under the Avebury imprint, 1994). The philosophy of mathematics in this book is based on ideas of Sir William Rowan Hamilton on the ordinal character of numbers, the real numbers, the measure numbers, scalar numbers and the extension to vectors. The final extension is to Hamilton’s quaternions. This algebra is interpreted as the mathematics of spin. This led to a a new theory of time and space which is Euclidian. The motion of spin is absolute, no frame of reference is required. If time is assumed to have a beginning it would be asymmetric with an arrow. This concept is applied to the laws of nature, which are symmetrical. This is another Copernican Revolution in three aspects: absolute time is restored, time has an arrow - is asymmetric, and thirdly the theory is based on the motion of spin which is absolute and more fundamental than the motion of translation. This opens the way to the final unification of physics.
Mathematics As A Science Of Patterns
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Author : Michael D. Resnik
language : en
Publisher: Oxford University Press
Release Date : 1997
Mathematics As A Science Of Patterns written by Michael D. Resnik and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism about the metaphysics of mathematics--the view that mathematics is about things that really exist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism, and epistemology.
Wittgenstein And The Turning Point In The Philosophy Of Mathematics
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Author : S.G. Shanker
language : en
Publisher: Routledge
Release Date : 2013-12-19
Wittgenstein And The Turning Point In The Philosophy Of Mathematics written by S.G. Shanker and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-19 with Philosophy categories.
First published in 2005. This study seeks to identify the specific mistakes that critics were alluding to in their passing asides on Wittgenstein's failure to grasp the mechanics of Godel's second incompleteness theorem. It also includes an understanding of his attack on meta-mathematics and Hilbert's Programme.