Read Philosophy of Mathematics: Structure and Ontology

Philosophy of Mathematics: Structure and Ontology

Stewart Shapiro

4.9/5 (21891 ratings)

Description:Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic.As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences.Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Philosophy of Mathematics: Structure and Ontology. To get started finding Philosophy of Mathematics: Structure and Ontology, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Pages: —

Format: PDF, EPUB & Kindle Edition

Publisher: —

Release: —

ISBN: 0198025459

Description: Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic.As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences.Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Philosophy of Mathematics: Structure and Ontology. To get started finding Philosophy of Mathematics: Structure and Ontology, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Special Offer | $0.00

Special Offer! | $0.00

Philosophy of Mathematics: Structure and Ontology

Philosophy of Mathematics: Structure and Ontology

More Books

Thinking about Mathematics: The Philosophy of Mathematics

Thinking about Mathematics: The Philosophy of Mathematics

The Oxford Handbook of Philosophy of Mathematics and Logic

The Oxford Handbook of Philosophy of Mathematics and Logic

Foundations without Foundationalism: A Case for Second-order Logic (Oxford Logic Guides)

Foundations without Foundationalism: A Case for Second-order Logic (Oxford Logic Guides)

Vagueness in Context

Vagueness in Context

Varieties of Logic

Varieties of Logic

Philosophy of Mathematics: Structure and Ontology by Stewart Shapiro (1997-11-30)

Philosophy of Mathematics: Structure and Ontology by Stewart Shapiro (1997-11-30)

By Stewart Shapiro Varieties of Logic [Hardcover]

By Stewart Shapiro Varieties of Logic [Hardcover]

Thinking about Mathematics: The Philosophy of Mathematics 1st (first) Edition by Shapiro, Stewart [2000]

Thinking about Mathematics: The Philosophy of Mathematics 1st (first) Edition by Shapiro, Stewart [2000]

[Varieties of Logic] [Author: Shapiro, Stewart] [September, 2014]

[Varieties of Logic] [Author: Shapiro, Stewart] [September, 2014]