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The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History (Logic and Computation in Philosophy)
 
 
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The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History (Logic and Computation in Philosophy) [Hardcover]

William Tait (Author)

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Book Description

019514192X 978-0195141924 February 10, 2005 1st
William Tait is one of the most distinguished philosophers of mathematics of the last fifty years. This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics, including some on historical figures ranging from Plato to G�del.

Tait's main contributions were initially in proof theory and constructive mathematics, later moving on to more philosophical subjects including finitism and skepticism about mathematics. This collection, presented as a whole, reveals the underlying unity of Tait's work. The volume includes an introduction in which Tait reflects more generally on the evolution of his point of view, as well as an appendix and added endnotes in which he gives some interesting background to the original essays. This is an important collection of the work of one of the most eminent philosophers of mathematics in this generation.

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"Due to the range of topics discussed in the book, and the clarity of the exposition, anyone interested in the philosophy of mathematics will find at least a few of the chapters of this book (and certainly the introduction) well worth reading." --The Mathematical Association of America


About the Author

William Tait is at University of Chicago.

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Inside This Book (learn more)
First Sentence:
The crux to understanding Hilbert's conception of finitist mathematics (Hilbert, 1925, 1927) and (Hilbert and Bernays, 1934) is this question: In what sense can we prove general propositions, such as xy(x + y = y + x) about the natural numbers, without assuming the infinitude of numbers or some other infinite totality? Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
finitist functions, recursive number theory, transfinite objects, finitist reasoning, divided line simile, finitist mathematics, second number class, finitist proof, axiomatic conception, nested recursion, pure units, default sense, primitive recursive arithmetic, transient reality, transfinite numbers, primitive recursive definition, transfinite types, skeptical paradox, primitive recursion, large ordinals, simple infinity, free mathematics, ordinal notations, conceptual sphere, definitional equality
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Howard Stein, The Provenance of Pure Reason, Philosophical Investigations, Euclid's Elements, General Reflection Principle, Intermediate Value Theorem, University of Chicago, Zorn's Lemma, Form Triangle, Down Stage
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