A Logical Journey: From Gödel to Philosophy

Voorkant
MIT Press, 3 feb. 1997 - 408 pagina's

Hao Wang (1921-1995) was one of the few confidants of the great mathematician and logician Kurt Gödel. A Logical Journey is a continuation of Wang's Reflections on Gödel and also elaborates on discussions contained in From Mathematics to Philosophy. A decade in preparation, it contains important and unfamiliar insights into Gödel's views on a wide range of issues, from Platonism and the nature of logic, to minds and machines, the existence of God, and positivism and phenomenology.

The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics.

Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy."

The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.

 

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Populaire passages

Pagina 330 - Philosophy may in no way interfere with the actual use of language; it can in the end only describe it— It leaves everything as it is. It also leaves mathematics as it is, and no mathematical discovery can advance it
Pagina 226 - But despite their remoteness from sense experience, we do have something like a perception also of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don't see any reason why we should have less confidence in this kind of perception,
Pagina 101 - to Action The philosophers have only interpreted the world, in various ways; the point, however, is to change it. Marx, Theses on
Pagina 175 - the facts of experience do not permit him to let himself be too much restricted in the construction of his conceptual world by the adherence to an epistemological system. He therefore must appear to the systematic epistemologist as a type of unscrupulous opportunist
Pagina 231 - and there is quite as much reason to believe in their existence. They are in the same sense necessary to obtain a satisfactory system of mathematics as physical objects are necessary for a satisfactory theory of our sense perceptions,
Pagina 334 - And we may not advance any kind of theory. There must not be anything hypothetical in our considerations. We must do away with all explanations, and description alone must take its place (Wittgenstein
Pagina 154 - philosophy,' this title, on the one hand, seems appropriate, on the other hand it certainly has misled people. (One might say that the subject we are dealing with is one of the heirs of the subject which used to be called 'philosophy.')
Pagina 300 - they resemble; not of the figures they draw, but of the absolute square and the absolute diameter, and so on?—The forms which they draw or make, and which have shadows and reflections in water of their own, are converted by them into images, but they are really seeking to behold the things themselves, which can only be seen with the eye of the mind.
Pagina 224 - To him who is a discoverer in this field, the products of his imagination appear so necessary and natural that he regards them, and would like to have them regarded by others, not as creations of thought but as given realities
Pagina 19 - The reciprocal relationship of epistemology and science is of noteworthy kind. They are dependent upon each other. Epistemology without contact with science becomes an empty scheme. Science without epistemology is—insofar as it is thinkable at all—primitive and muddled

Over de auteur (1997)

Hao Wang is Professor of Logic at The Rockefeller University and author of scores of articles and several books on logic, computers, and philosophy, including From Mathematics to Philosophy (extensively discussed with Gödel and containing contributions by him) and Beyond Analytic Philosophy: Doing Justice to What We Know (MIT Press Bradford Books). He is currently preparing a companion volume, Conversations with Kurt Gödel which will concentrate on Gödel's unpublished ideas.

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