A Logical Journey: From Gödel to Philosophy by Hao Wang PDF

By Hao Wang

ISBN-10: 0262231891

ISBN-13: 9780262231893

Hao Wang (1921-1995) used to be one of many few confidants of the good mathematician and philosopher Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and in addition elaborates on discussions contained in From arithmetic to Philosophy. A decade in instruction, it comprises vital and unusual insights into Gödel's perspectives on quite a lot of matters, from Platonism and the character of common sense, to minds and machines, the lifestyles of God, and positivism and phenomenology.

The influence of Gödel's theorem on twentieth-century idea is on par with that of Einstein's conception of relativity, Heisenberg's uncertainty precept, or Keynesian economics. those formerly unpublished intimate and casual conversations, even though, convey to gentle and magnify Gödel's different significant contributions to common sense and philosophy. They show that there's even more in Gödel's philosophy of arithmetic than is usually believed, and extra in his philosophy than his philosophy of mathematics.

Wang writes that "it is even attainable that his rather casual and loosely based conversations with me, which i'm freely utilizing during this publication, will turn into the fullest current expression of the varied elements of his inadequately articulated basic philosophy."

The first chapters are dedicated to Gödel's existence and psychological improvement. within the chapters that persist with, Wang illustrates the search for overarching ideas and grand unifications of data and motion in Gödel's written speculations on God and an afterlife. He provides the heritage and a chronological precis of the conversations, considers Gödel's reviews on philosophies and philosophers (his help of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his try and show the prevalence of the mind's strength over brains and machines. 3 chapters are tied jointly through what Wang perceives to be Gödel's governing excellent of philosophy: a precise conception during which arithmetic and Newtonian physics function a version for philosophy or metaphysics. eventually, in an epilog Wang sketches his personal method of philosophy unlike his interpretation of Gödel's outlook.

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Example text

I rememberthat we discussed ' whether Turing was married. On Turing s suicide and that Godel asked " he said that he was not , Perhaps he wanted to get married , being told " This observation indicated to me the importance Godel could not. but ' ' attributed to marriage for a man s, and perhaps also for a woman s, life and death. ' Two days after Godel s death on 14 January1978 I went to seeAdele, having learned the news from Hassler Whitney that morning. On this occasionAdele told me that Godel, although he did not go to church, was religious and read the Bible in bed every Sunday morning.

The completenesstheorem (1) may be seenas the successfulconclusion of our quest for a satisfactory formulation of what Godel calls " the logic for the finite mind: ' This theorem also supplementsthe incompleteness theorems (2) and (3) so as to demonstrateboth the powers and the limitations of mechanizationand concrete intuition . The implications of (2), (7), and (9) provide us with instructive examplesof our capacity to find new axioms and new concepts. In particular, the proof of (2) gives us a general way of seeing new axioms, by exhibiting, for each substantive consistent formal system, certain new axioms not provable within it.

In physics, according to Godel, the present " two -level" " " " " theory (with its quantization of a classicalsystem, and its divergent series) was admittedly very unsatisfactory( Wang1974:13). In the letters to his mother, Gooel often explains Einstein's attitude with sympathy. In 1950 he commented on an article calling Einstein's " " theory the key to the universe, and declared that such sensational " ' " " reports were very much against Einsteins own will . on the basisof his ideasmight justify them.

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A Logical Journey: From Gödel to Philosophy by Hao Wang

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