Mike's Reviews > Foundations Without Foundationalism: A Case for Second-Order Logic

Foundations Without Foundationalism by Stewart Shapiro
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's review
Dec 01, 11

Read from November 23 to December 01, 2011

A powerful, pithy, and well-reasoned book. Disturbingly to me, more and more students and young scholars of supposed "philosophy" I meet have little grounding in math nor in neuroscience, which seems to exclude a vast amount of what philosophy as a field must consider. This book reconsiders the very structure of mathematics in terms of greater applications of logic and how study of math as a discipline has come to exclude some of the most crucial underpinnings of ontological epistemology.

There will be other scholars who argue with some of Shapiro's finer points, but that's expected: his understanding of semantics and his application of such to mathematics is astoundingly sure and resounding. This book should be read by anyone working in maths, philosophy, or linguistics.
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