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Axiomatic Method and Category Theory

2013-10-14 Philosophy
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Release : 2013-10-14
Genre : Philosophy
Kind : eBook
Book Rating : 042/5 ( reviews)

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Book Synopsis Axiomatic Method and Category Theory by : Andrei Rodin

Download or read book Axiomatic Method and Category Theory written by Andrei Rodin. This book was released on 2013-10-14. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.

Axiomatic Philosophy

1996 Metaphysics
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Release : 1996
Genre : Metaphysics
Kind : eBook
Book Rating : 119/5 ( reviews)

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Book Synopsis Axiomatic Philosophy by : Pritam Sen

Download or read book Axiomatic Philosophy written by Pritam Sen. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: # Scientific Method In Philosophy : Scientific Method, Summary Of Axiomatic Philosophies# Western Philosophies : Plato, Aristotle, Kant, Russell# Eastern Philosophies : Samkara, Bhagavadgita, Confucius, Lao Tzu# New Axioms: New Aristotelian Philosophy, A Rational Religious Philosophy# References# Index.

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.

Axiomatic Theories of Truth

2014-02-27 Philosophy
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Release : 2014-02-27
Genre : Philosophy
Kind : eBook
Book Rating : 232/5 ( reviews)

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Book Synopsis Axiomatic Theories of Truth by : Volker Halbach

Download or read book Axiomatic Theories of Truth written by Volker Halbach. This book was released on 2014-02-27. Available in PDF, EPUB and Kindle. Book excerpt: At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth.

Set Theory and its Philosophy

2004-01-15 Philosophy
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Release : 2004-01-15
Genre : Philosophy
Kind : eBook
Book Rating : 432/5 ( reviews)

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Book Synopsis Set Theory and its Philosophy by : Michael Potter

Download or read book Set Theory and its Philosophy written by Michael Potter. This book was released on 2004-01-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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