the reason s proper study essays towards a neo fregean philosophy of mathematics

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The Reason S Proper Study

Author : Bob Hale
ISBN : 0199266328
Genre : Philosophy
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Bob Hale and Crispin Wright draw together here the key writings in which they have worked out their distinctive neo-Fregean approach to the philosophy of mathematics. The two main components in Frege's mathematical philosophy were his platonism and his logicism - the claims, respectively, that mathematics is a body of knowledge about independently existing objects, and that this knowledge may be acquired on the basis of general logical laws and suitable definitions. The central thesis ofthis collection is that Frege was - his own eventual recantation notwithstanding - substantially right in both claims. Where neo-Fregeanism principally differs from Frege is in taking a more optimistic view of the kind of contextual explanation (proceeding via what are now commonly called abstraction principles) of the fundamental concepts of arithmetic and analysis which Frege considered and rejected. On this basis, neo-Fregeanism promises defensible and attractive answers to some of the most important ontological and epistemological questions in the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the programme and the contributions made to it by the various papers; a postscript explaining which issues most require further attention; and bibliographies both of references and of further useful sources. The Reason's Proper Study will be recognized as the most powerful presentation yet of the neo-Fregean programme; it will prove indispensable reading not just to philosophers of mathematics but to all who are interested in the fundamental metaphysical and epistemological issues on which the programme impinges.

Existence And Nature

Author : Camposampiero, Matteo Favaretti
ISBN : 9783110321807
Genre : Philosophy
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Is all that exists part of the natural world? If there are non-natural entities, what is their difference from natural things? Is the human-independent realm of nature the only paradigm for ontological respectability, as naturalism claims? Can existence be simply explained away by means of formal devices? Philosophers keep struggling with such questions. Still, the two basic notions involved, that of existence and that of nature, have not yet been fully explored. The four essays collected here address the issue from the points of view of the philosophy of mathematics, of analytic ontology, of early modern philosophy, and of contemporary phenomenology. The results will surprise the reader: difficult topics are unlocked, long-received views are called into question, and new perspectives are opened.

Introducing Philosophy Of Mathematics

Author : Michele Friend
ISBN : 9781317493792
Genre : Philosophy
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What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

The Routledge Companion To Metaphysics

Author : Robin Le Poidevin
ISBN : 9781134155866
Genre : Philosophy
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The Routledge Companion to Metaphysics is an outstanding, comprehensive and accessible guide to the major themes, thinkers, and issues in metaphysics. The Companion features over fifty specially commissioned chapters from international scholars which are organized into three clear parts: History of Metaphysics Ontology Metaphysics and Science. Each section features an introduction which places the range of essays in context, while an extensive glossary allows easy reference to key terms and definitions. The Routledge Companion to Metaphysics is essential reading for students of philosophy and anyone interested in surveying the central topics and problems in metaphysics from causation to vagueness and from Plato and Aristotle to the present-day.


Author : Michael A. E. Dummett
ISBN : 0674319354
Genre : Philosophy
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No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.

The Philosophy Of Michael Dummett

Author : Randall E. Auxier
ISBN : 0812696220
Genre : Philosophy
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For over 50 years, Sir Michael Dummett has been a major philosophical voice in a wide range of fields, including epistemology, ontology, and the philosophy of language. This comprehensive volume treats all of these subjects and more in detail. It contains Dummett’s intellectual autobiography, 27 previously unpublished critical and descriptive essays by famous scholars, a reply to each essay by Dummett, and a complete bibliography of his published works.

International Journal Of Philosophical Studies

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ISBN : UCAL:B4938999
Genre :
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The Limits Of Abstraction

Author : Kit Fine
ISBN : 9780191567261
Genre : Philosophy
File Size : 48. 71 MB
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What is abstraction? To what extent can it account for the existence and identity of abstract objects? And to what extent can it be used as a foundation for mathematics? Kit Fine provides rigorous and systematic answers to these questions along the lines proposed by Frege, in a book concerned both with the technical development of the subject and with its philosophical underpinnings. Fine proposes an account of what it is for a principle of abstraction to be acceptable, and these acceptable principles are exactly characterized. A formal theory of abstraction is developed and shown to be capable of providing a foundation for both arithmetic and analysis. Fine argues that the usual attempts to see principles of abstraction as forms of stipulative definition have been largely unsuccessful but that there may be other, more promising ways of vindicating the various forms of contextual definition. The Limits of Abstraction breaks new ground both technically and philosophically, and is essential reading for all those working on the philosophy of mathematics.

The Harvard Review Of Philosophy

Author :
ISBN : STANFORD:36105122322774
Genre : Philosophy
File Size : 69. 34 MB
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International Philosophical Quarterly

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ISBN : STANFORD:36105113210178
Genre : Philosophy
File Size : 29. 60 MB
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