Philosophy of Mathematics: Structure and Ontology by Stewart Shapiro (PDF)

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.

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Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Allow me to start off by saying that this review does not reflect the material on the book. This review is unfortunately due to the condition the book came to me in. Upon opening the book it was soaked in what smelled like Windex cleaner. The whole bottom right part of my book is now water damaged. Of course, this doesn’t affect the material, but its a huge bummer considering most of us like to keep our books in good condition, especially if bought brand new.

⭐”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 proponiendo extender el estructuralismo a otras ramas de las matemáticas, la ciencia y el lenguaje natural. Como acertadamente afirma: ” Es un trabajo de interés tanto para filósofos como matemáticos”

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