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Defending the Axioms

2011-01-27 Mathematics
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Release : 2011-01-27
Genre : Mathematics
Kind : eBook
Book Rating : 182/5 ( reviews)

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Book Synopsis Defending the Axioms by : Penelope Maddy

Download or read book Defending the Axioms written by Penelope Maddy. This book was released on 2011-01-27. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. The axioms of set theory have long played this role, so the question of how they are properly judged is of central importance. Maddy discusses the appropriate methods for such evaluations and the philosophical backdrop that makes them appropriate.

Defending the Axioms

2011 Axiomatic set theory
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Release : 2011
Genre : Axiomatic set theory
Kind : eBook
Book Rating : 395/5 ( reviews)

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Book Synopsis Defending the Axioms by :

Download or read book Defending the Axioms written by . This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt:

Defending the Axioms

2011-01-27 Philosophy
Download Defending the Axioms PDF Online Free

Author :
Release : 2011-01-27
Genre : Philosophy
Kind : eBook
Book Rating : 532/5 ( reviews)

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Book Synopsis Defending the Axioms by : Penelope Maddy

Download or read book Defending the Axioms written by Penelope Maddy. This book was released on 2011-01-27. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments.

Naturalism in Mathematics

1997-11-13 Philosophy
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Release : 1997-11-13
Genre : Philosophy
Kind : eBook
Book Rating : 972/5 ( reviews)

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Book Synopsis Naturalism in Mathematics by : Penelope Maddy

Download or read book Naturalism in Mathematics written by Penelope Maddy. This book was released on 1997-11-13. Available in PDF, EPUB and Kindle. Book excerpt: Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view—realism—is assessed and finally rejected in favour of another—naturalism—which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Second Philosophy

2007-04-19 Mathematics
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Release : 2007-04-19
Genre : Mathematics
Kind : eBook
Book Rating : 669/5 ( reviews)

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Book Synopsis Second Philosophy by : Penelope Maddy

Download or read book Second Philosophy written by Penelope Maddy. This book was released on 2007-04-19. Available in PDF, EPUB and Kindle. Book excerpt: Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In this book, Penelope Maddy describes and practises a particularly austere form of naturalism called 'Second Philosophy'. Without a definitive criterion for what counts as 'science' and what doesn't, Second Philosophy can't be specified directly - 'trust only the methods of science!' or some such thing - so Maddy proceeds instead by illustratingthe behaviours of an idealized inquirer she calls the 'Second Philosopher'. This Second Philosopher begins from perceptual common sense and progresses from there to systematic observation, active experimentation, theory formation and testing, working all the while to assess, correct and improve hermethods as she goes. Second Philosophy is then the result of the Second Philosopher's investigations.Maddy delineates the Second Philosopher's approach by tracing her reactions to various familiar skeptical and transcendental views (Descartes, Kant, Carnap, late Putnam, van Fraassen), comparing her methods to those of other self-described naturalists (especially Quine), and examining a prominent contemporary debate (between disquotationalists and correspondence theorists in the theory of truth) to extract a properly second-philosophical line of thought. She then undertakes to practise SecondPhilosophy in her reflections on the ground of logical truth, the methodology, ontology and epistemology of mathematics, and the general prospects for metaphysics naturalized.

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