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The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify many concepts in contemporary mathematics, and thus that both first-and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today.
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Stewart Shapiro is Professor of Philosophy at Ohio State University.
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Foundations without Foundationalism
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Foundations without Foundationalism: A Case for Second-order Logic (Oxford Logic Guides)
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Foundations without Foundationalism: A Case for Second-Order Logic
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Oxford University Press, 2000
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Foundations without Foundationalism
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Condizione: New. Stewart Shapiro presents a distinctive original view of the foundations of mathematics, arguing that second-order logic has a central role to play in laying these foundations. He gives an accessible account of second-order and higher-order logic, paying spe. Codice articolo 446842118
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Foundations Without Foundationalism : A Case for Second-Order Logic
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Foundations Without Foundationalism : A Case for Second-Order Logic
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Oxford University Press, 2000
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Foundations without Foundationalism (Paperback)
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Paperback. Condizione: new. Paperback. Stewart Shapiro presents a distinctive and persuasive view of the foundations of mathematics, arguing controversially that second-order logic has a central role to play in laying these foundations. To support this contention, he first gives a detailed development of second-order and higher-order logic, in a way that will be accessible to graduate students. He then demonstrates that second-order notions are prevalent in mathematics as practised, and that higher-orderlogic is needed to codify many contemporary mathematical concepts. Throughout, he emphasizes philosophical and historical issues that the subject raises. Foundations without Foundationalism is a keycontribution both to philosophy of mathematics and to mathematical logic. 'In this excellent treatise Shapiro defends the use of second-order languages and logic as framework for mathematics. His coverage of the wide range of logical and philosophical topics required for understanding the controversy over second-order logic is thorough, clear, and persuasive. . . . Shapiro recognizes that it is unlikely that he has had the last word on these controversial philosophicalsubjects. Nevertheless, his book is certainly an excellent place to start work on them.' Michael D. Resnik, History and Philosophy of Logic This view of the foundations of mathematics argues that second-order logic has a central role. After a detailed development of second-order and higher-order logic the text demonstrates that second-order notions are prevalent in mathematics and that higher-order logic is needed to codify concepts. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9780198250296
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