Conceptions of Set and the Foundations of Mathematics PDF Download
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Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108497829
Category : History
Languages : en
Pages : 255
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Book Description
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108497829
Category : History
Languages : en
Pages : 255
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Book Description
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author: Neil Barton
Publisher: Cambridge University Press
ISBN: 1009227254
Category : Philosophy
Languages : en
Pages : 122
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Book Description
Many philosophers are aware of the paradoxes of set theory (e.g. Russell's paradox). For many people, these were solved by the iterative conception of set which holds that sets are formed in stages by collecting sets available at previous stages. This Element will examine possibilities for articulating this solution. In particular, the author argues that there are different kinds of iterative conception, and it's open which of them (if any) is the best. Along the way, the author hopes to make some of the underlying mathematical and philosophical ideas behind tricky bits of the philosophy of set theory clear for philosophers more widely and make their relationships to some other questions in philosophy perspicuous.
Author: Michael D. Potter
Publisher: Clarendon Press
ISBN: 9780199269730
Category : Mathematics
Languages : en
Pages : 345
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Book Description
A wonderful new book ... Potter has written the best philosophical introduction to set theory on the market - Timothy Bays, Notre Dame Philosophical Reviews.
Author: Sean Morris
Publisher: Cambridge University Press
ISBN: 110715250X
Category : History
Languages : en
Pages : 221
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Book Description
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author: Neil Barton
Publisher: Cambridge University Press
ISBN: 9781009227261
Category : Philosophy
Languages : en
Pages : 0
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Book Description
Many philosophers are aware of the paradoxes of set theory (e.g. Russell's paradox). For many people, these were solved by the iterative conception of set which holds that sets are formed in stages by collecting sets available at previous stages. This Element will examine possibilities for articulating this solution. In particular, the author argues that there are different kinds of iterative conception, and it's open which of them (if any) is the best. Along the way, the author hopes to make some of the underlying mathematical and philosophical ideas behind tricky bits of the philosophy of set theory clear for philosophers more widely and make their relationships to some other questions in philosophy perspicuous.
Author: Paul Benacerraf
Publisher: Cambridge University Press
ISBN: 1107268133
Category : Science
Languages : en
Pages : 604
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Book Description
The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.
Author: Hao Wang
Publisher: Routledge
ISBN: 1134884338
Category : Philosophy
Languages : en
Pages : 445
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Book Description
First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge.
Author: George Boolos
Publisher: Harvard University Press
ISBN: 9780674537675
Category : Mathematics
Languages : en
Pages : 458
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Book Description
George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.
Author: Jens Allwood
Publisher: Cambridge University Press
ISBN: 9780521291743
Category : Language Arts & Disciplines
Languages : en
Pages : 200
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Book Description
The authors offer a clear, succinct and basic introduction to set theory and formal logic for linguists.
Author: C. Anthony Anderson
Publisher: Springer Science & Business Media
ISBN: 9401005265
Category : Philosophy
Languages : en
Pages : 632
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Book Description
This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.
