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Kurt Gödel: Unpublished Philosophical Essays

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Godel has shown that truth is not identical to provability, and reality is not identical to consistency as imagined by logical positivists who tend to be rather easy-going about metaphysics. That is the view he challenged, or let us say instead, eliminated. He in fact worked on philosophy for a very long time, trying to construct a world view consistent with his mathematical results. Even before he obtained the celebrated incompleteness theorems, he says that he had a philosophical motivation and that he never looked at the Vienna Circle with much sympathy. In view of his mathematical results, he considered the realist implications of his work most likely among others. Rodriquez argues in the book that although many philosophers "borrowed" their most important ideas from Godel, Godel's realist philosophy does not seem to follow directly from his mathematical theorems. He could have argued against realism starting from the same logical premises. In particular, Godel believed in a deity and the existence of mathematical objects resolutely. It was hard to give up on these ideas no matter what he found in metamathematics.

He did, however, show that conventionalism had fatal flaws. Not simply minor flaws that could be patched later, but flaws which erased the unsatisfying metaphysics of conventionalism. He argued against Carnap and others but was hesitant to publish his papers, because he found his philosophical work incomplete, being a perfectionist he wanted to be absolutely sure he had the final answer. That is one of the reasons his philosophy remained in obscurity. The other is that no other Godel came.

In these essays he argues for a metaphysics in which mathematical objects exist in a realm of their own, and their perception can be achieved only through indirect means, by mathematical intuition which operates on a kind of data that is not the same as sense data. He also offered a disjunctive proposition which claimed that either the mind is infinitely more powerful than a computer, or there are such propositions that are absolutely unsolvable by a computer. He contends that both possibilities will frustrate the materialists, for either the human mind is not mechanical, or there is a realm of abstract objects. Throughout the essays, the most persistent idea is that mathematics cannot be reduced to syntax, and that mathematical truth is not our creation: it exists independently.

These ideas should be taken seriously because they originate from the same person who has shaken the world of 20th century mathematics with his foundational results.

Rodriquez exposes this dramatic turn of events in the first half of 20th century in a vibrant and rigorous fashion including Godel's completeness theorem and incompleteness theorems. The first half of the book is dedicated to laying out the background for Godel's two unpublished philosophical essays. In this part, Rodriquez summarizes the history of developments which have led to Godel's philosophical work and the philosophical views of Godel and his contemporaries. A very detailed and scholarly analysis of Godel's philosophy, including a lucid description of his ontology and epistemology are being presented. One wonders how much work must have gone into deciphering Godel's work and establishing the relationships which Rodriquez uncovered. The second part of the book contains the essays, edited from Godel's unpublished manuscripts. The essays are most striking, and they are written in an almost mathematically precise language and they are dense with argument in every sentence. The first essay is the script of his famous Gibbs lecture, which he read to an audience only once. The second essay is a response to Carnap's "The Logical Syntax of Language". Both essays have been revised significantly by Godel over the years, and Rodriquez does his best to provide a complete account of Godel's work.

I read this book in Japanese translation. Godel mentioned �gvitalism�h only once in it. But I think this word is what he wanted to say most about the incompleteness theorem. Mathematicians learned the form of the theorem, but ignored the meaning of it. This book is a precious clue to answer the question: What is mathematics?�@I am now trying to depicting mathematics from the start of thinking to the end. This book is a reliable navigator for me.