Titlebook: Labyrinth of Thought; A History of Set The José Ferreirós Book 2007Latest edition Birkh?user Basel 2007 Ferreiros.Foundations of mathematic

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The Transfinite Ordinals and Cantor’s Mature Theorye study of point-sets through their derived sets for the purposes of the theory of trigonometric series. The second stretched from 1873 to 1878 and focused above all on the study of infinite cardinalities (chap. VI). The third period, 1879 to 1884, was guided by the core objective of proving the Con

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Logic and Type Theory in the Interwar Periodymbolic, formal system that might provide a framework for all of mathematics. It had to be possible to reconstruct mathematics on a completely secure basis, to find a system maximally immune to rational doubt.. But, in carrying out that project, caution was the keyword. Reminders were the by-then le

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Consolidation of Axiomatic Set Theorypted Zermelo’s axiom system explicitly.. As we saw in the preceding chapter, many favored the theory of types because it seemed to offer a safer framework, and at the same time it was sufficient for the limited amount of set theory that is necessary in so-called classical mathematics. As late as 193

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Sets and Maps as a Foundation for Mathematicsonal work, Was sind und was sollen die Zahlen? [1888], bears the motto: ?εì ó ???νθρωπο? ?ριθμητí?ει, ‘man always arithmetizes.’ It seems that, in Dedekind’s view, numbers are not made by God, but by men;. mathematics has nothing to do with a world of essences or a Platonic heaven, it is a free creation of the human mind [Dedekind 1888, 335, 360].