منابع مشابه
Is Mathematical Truth Time-Dependent?
(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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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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This paper argues that truth is by nature context-dependent – that no truth can be applied regardless of context. I call this “strong contextualism”. Some objections to this are considered and rejected, principally: that there are universal truths given to us by physics, logic and mathematics; and that claiming “no truths are universal” is self-defeating. Two “models” of truth are suggested to ...
متن کاملMathematical Knowledge Is Context Dependent
We argue that mathematical knowledge is context dependent. Our main argument is that on pain of distorting mathematical practice, one must analyse the notion of having available a proof, which supplies justifi cation in mathematics, in a context dependent way. 'But a proof is sometimes a fuzzy concept, subject to whim and personality.
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 1974
ISSN: 0002-9890
DOI: 10.2307/2318997