David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Oxford University Press (1991)
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.
|Keywords||Logic, Symbolic and mathematical|
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|Buy the book||$38.24 used (28% off) $44.46 new (17% off) $45.05 direct from Amazon (15% off) Amazon page|
|Call number||QA9.S48 1991|
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Roman Frigg & Ioannis Votsis (2011). Everything You Always Wanted to Know About Structural Realism but Were Afraid to Ask. European Journal for Philosophy of Science 1 (2):227-276.
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Bradley Armour-Garb & James A. Woodbridge (2012). The Story About Propositions. Noûs 46 (4):635-674.
Gila Sher (2011). Is Logic in the Mind or in the World? Synthese 181 (2):353 - 365.
Stewart Shapiro (2007). The Objectivity of Mathematics. Synthese 156 (2):337 - 381.
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