Iterative Conceptions Of Set
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Author |
: Luca Incurvati |
Publisher |
: Cambridge University Press |
Total Pages |
: 255 |
Release |
: 2020-01-23 |
ISBN-10 |
: 9781108497824 |
ISBN-13 |
: 1108497829 |
Rating |
: 4/5 (24 Downloads) |
Synopsis Conceptions of Set and the Foundations of Mathematics by : Luca Incurvati
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.
Author |
: Neil Barton |
Publisher |
: Cambridge University Press |
Total Pages |
: 122 |
Release |
: 2024-06-30 |
ISBN-10 |
: 9781009227254 |
ISBN-13 |
: 1009227254 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Iterative Conceptions of Set by : Neil Barton
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 Potter |
Publisher |
: Clarendon Press |
Total Pages |
: 362 |
Release |
: 2004-01-15 |
ISBN-10 |
: 9780191556432 |
ISBN-13 |
: 0191556432 |
Rating |
: 4/5 (32 Downloads) |
Synopsis Set Theory and its Philosophy by : Michael Potter
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Author |
: Sean Morris |
Publisher |
: Cambridge University Press |
Total Pages |
: 221 |
Release |
: 2018-12-13 |
ISBN-10 |
: 9781107152502 |
ISBN-13 |
: 110715250X |
Rating |
: 4/5 (02 Downloads) |
Synopsis Quine, New Foundations, and the Philosophy of Set Theory by : Sean Morris
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author |
: Jose Ferreiros |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 472 |
Release |
: 2001-11-01 |
ISBN-10 |
: 3764357495 |
ISBN-13 |
: 9783764357498 |
Rating |
: 4/5 (95 Downloads) |
Synopsis Labyrinth of Thought by : Jose Ferreiros
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
Author |
: Alfred North Whitehead |
Publisher |
: |
Total Pages |
: 688 |
Release |
: 1910 |
ISBN-10 |
: UOM:39015002922881 |
ISBN-13 |
: |
Rating |
: 4/5 (81 Downloads) |
Synopsis Principia Mathematica by : Alfred North Whitehead
Author |
: Juliette Kennedy |
Publisher |
: Cambridge University Press |
Total Pages |
: 293 |
Release |
: 2014-08-21 |
ISBN-10 |
: 9781107002661 |
ISBN-13 |
: 1107002664 |
Rating |
: 4/5 (61 Downloads) |
Synopsis Interpreting Godel by : Juliette Kennedy
In this groundbreaking volume, leading philosophers and mathematicians explore Kurt Gödel's work on the foundations and philosophy of mathematics.
Author |
: Stephen Pollard |
Publisher |
: Courier Dover Publications |
Total Pages |
: 196 |
Release |
: 2015-07-15 |
ISBN-10 |
: 9780486797144 |
ISBN-13 |
: 0486797147 |
Rating |
: 4/5 (44 Downloads) |
Synopsis Philosophical Introduction to Set Theory by : Stephen Pollard
This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
Author |
: Jens Allwood |
Publisher |
: Cambridge University Press |
Total Pages |
: 200 |
Release |
: 1977-09-15 |
ISBN-10 |
: 0521291747 |
ISBN-13 |
: 9780521291743 |
Rating |
: 4/5 (47 Downloads) |
Synopsis Logic in Linguistics by : Jens Allwood
The authors offer a clear, succinct and basic introduction to set theory and formal logic for linguists.
Author |
: Neil Barton |
Publisher |
: Cambridge University Press |
Total Pages |
: 0 |
Release |
: 2024-06-30 |
ISBN-10 |
: 1009227262 |
ISBN-13 |
: 9781009227261 |
Rating |
: 4/5 (62 Downloads) |
Synopsis Iterative Conceptions of Set by : Neil Barton
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.