Philosophy of Mathematics: Structure and Ontology

* Read * Philosophy of Mathematics: Structure and Ontology by Stewart Shapiro ↠ eBook or Kindle ePUB. Philosophy of Mathematics: Structure and Ontology As Benacerraf first noted, we are confronted with the following powerful dilemma. 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. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, b

Philosophy of Mathematics: Structure and Ontology

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Rating : 4.13 (951 Votes)
Asin : 0195094522
Format Type : paperback
Number of Pages : 296 Pages
Publish Date : 2016-12-13
Language : English

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As Benacerraf first noted, we are confronted with the following powerful dilemma. 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. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. 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. As a way out of this dilemma, Shapiro articulates a structuralist approach. 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 re

Palabras Mayores "Philosophy of Mathematics: Structure and Ontology", es una de las obras fundamentales de uno de los más importantes filósofos de las matemáticas del siglo XXI. Shapiro con una prosa soberbia, por ratos árida, nos presenta y fundamenta, desde el estructuralismo al que pertenece, una visión de las matemáticas. Su libro comienza repasando aspectos generales sobre la filosofía de las matemáticas para que, posteriormente, en el capítulo segundo, nos muestre su propuesta entrando a analizar en detalle su aspecto ontológico y epistemológico. Shapiro finaliza su tratado

Stewart Shapiro, Professor of Philosophy, Ohio State University at Newark.

"This book is an important contributionpresenting an original, structuralist philosophy and axiomatic framework in comprehensive detail, placing it in broad philosophical and historical perspective, and comparing it systematically with other approaches seen as leading structuralist alternatives to the one set forth by Shapiro himselfis is an interesting, important, and thought-provoking book."--Journal of Symbolic Logic

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