Aristotle on Mathematical Truth
نویسندگان
چکیده
منابع مشابه
Aristotle on Mathematical Truth
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We define constructive truth for arithmetic and for intuitionistic analysis, and investigate its properties. We also prove that the set of constructively true (first order) arithmetical statements is Π 2 and Σ 2 hard, and we conjecture it to be complete for second order arithmetic. A statement is constructively true iff it is realized by a constructive function under continuous function realiza...
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(c) H' is not Riemann integrable on any closed interval [a, b], for assume that it is. Then H' is continuous a.e. on [a, b]. But it is clear that H'(t) = 0 if H' is continuous at t ,and so H' = 0 a.e. on [a, b]. It follows from (b) that H is a constant on [a, b]-a palpable contradiction. (d) H ' is of Baire class one, being the pointwise limit of the continuous functions H,(x) = n[H(x + lln)-H(...
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P. Crivelli (PC) presents the first monograph to systematically reconstruct Aristotle's views on truth scattered over several writings. He approaches Aristotle from the perspective of analytic philosophy. This approach involves asking Aristotlèquestions he never dreamt of, perhaps even questions he lacked the conceptual apparatus to understand or to answer' (p. 40). However, the result is an ac...
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The mathematical structure of the continuum, in the guise of the domain of continuous, differentiable functions, has proved immensely useful in the study of nature. However, we have learned to be sceptical of any claim to the effect that our current favourite mathematical theory necessarily describes the actual structure of the physical universe. The continuous manifold of space-time may be no ...
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ژورنال
عنوان ژورنال: British Journal for the History of Philosophy
سال: 2012
ISSN: 0960-8788,1469-3526
DOI: 10.1080/09608788.2012.731230