New Books
B. Gelbman, A. Heguy, T. O'Connor
Feb 1, 1957
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Environmental Health Perspectives
Full text
Semantic Scholar
Key Takeaway Key Takeaway: Gödel's life and work, as well as his views on metaphysics, mathematics, and religion, are well-documented in this book.
Abstract
This very valuable book is a continuation of the same author’s Reflections on Kurt Gödel and From Mathematics to Philosophy. Together they create a remarkable sense of being close to one of the greatest thinkers of the twentieth century. Like From Mathematics to Philosophy, this present book, a decade in preparation, is based on Wang’s extensive conversations with Gödel. A mathematician who himself made deep contributions to mathematical logic and to the philosophy of mathematics, Wang was (he died while this book was in preparation) peculiarly well-fitted to be the amanuensis who recorded, interpreted and communicated Gödel’s thought, and, of course, who also knew what questions needed to be asked, and where. In this volume, however, philosophy is centre-stage, Wang reporting his attempts, in long discussions with Gödel, to understand and evaluate the latter’s quest to do ‘for metaphysics just as much as Newton did for physics’ (p. 332). Wang discovered that, far from achieving this end, Gödel evaluated his pursuit of it just as he did his work in logic after 1940, as largely unsuccessful. It is all rather a sad story, of increasing frustration caused by the failure to prove the independence of the Continuum Hypothesis, of the turn to philosophy, and of the failure there to produce results of a similar magnitude to the proof of the completeness of first order logic, of the incompleteness theorems, and of the relative-consistency proofs of the Axiom of Choice and the Continuum Hypothesis. It will probably strike the reader as strange that someone could even have thought in the middle of the twentieth century that results of that sort of definitive character could be achieved in pure philosophy. But Gödel was an obstinate follower of Leibniz, and even more of Plato, and believed their unfashionable doctrine that a priori conceptual analysis could yield not just clarification but also and more importantly truth. Wang devotes a whole chapter of the present book to a discussion of this striking feature of Gödel’s philosophical outlook. Other chapters discuss Gödel’s views of the mind, of mathematical objectivism, of set theory, of religion, and of other philosophers. Introducing this assorted material are a couple of biographical chapters, one a valuable account of Gödel’s intellectual development, and the other including a fascinating and at times touching account of Gödel’s close relationship with Einstein at the Institute of Advanced Study at Princeton. In their work both Einstein and Gödel appear as heroic figures united in their desire to achieve fundamental goals, and to an unfortunately great extent united also in a heroic failure to do so. Temperamental opposites, each nevertheless sought out and confided in the other: Einstein remarked once towards the end of his life that he merely came into the Institute to have the privilege of walking home with Gödel (p.57). Nor were they simply temperamental opposites: