Foundations without Foundationalism is popular PDF and ePub book, written by Stewart Shapiro in 1991-09-19, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Foundations without Foundationalism can be Read Online from any device for your convenience.
Foundations without Foundationalism Book PDF Summary
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 development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows how first-order languages are insufficient to codify many concepts in contemporary mathematics, and thus that higher-order logic is needed to fully reflect current mathematics. Throughout, the emphasis is on discussing the philosophical and historical issues associated with this subject, and the implications that they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic as might be gained from 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 this subject.
Detail Book of Foundations without Foundationalism PDF
- Author : Stewart Shapiro
- Release : 19 September 1991
- Publisher : Clarendon Press
- ISBN : 9780191524011
- Genre : Mathematics
- Total Page : 302 pages
- Language : English
- PDF File Size : 9,6 Mb
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