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?
An edition of The Provenance of Pure Reason
(2005)
The Provenance of Pure Reason
Essays in the Philosophy of Mathematics and Its History (Logic and Computation in Philosophy)
by William Tait
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"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 Godel." "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."--Jacket.
Previews available in: English
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The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History (Logic and Computation in Philosophy)
January 12, 2005, Oxford University Press, USA
in English
019514192X 9780195141924
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"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?"
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