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Mathematical Intuition
"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or hol...
After Gödel
Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Gödel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Gödel's texts on foundations with materials from Gödel's Nachlass and from Hao Wang's discussions with Gödel. As well as providing discussions of Gödel's views on the philosophical significance of his technical results on completeness, incompleteness, undecidability, consistency proofs, speed-up theorems, and independence proofs, Tieszen furnish...
Phenomenology, Logic, and the Philosophy of Mathematics
In this 2005 book, logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences.
Simply Gödel
Simply Gödel examines the life and principal ideas of Kurt Gödel (1906-1978), widely regarded as one of the greatest logicians of all time.
Encyclopedia of Phenomenology
This encyclopedia presents phenomenological thought and the phenomenological movement within philosophy and within more than a score of other disciplines on a level accessible to professional colleagues of other orientations as well as to advanced undergraduate and graduate students. Entries average 3,000 words. In practically all cases, they include lists of works "For Further Study." The Introduction briefly chronicles the changing phenomenological agenda and compares phenomenology with other 20th Century movements. The 166 entries are a baut matters of seven sorts: ( 1) the faur broad tendencies and periods within the phenomenological movement; (2) twenty-three national traditions ofpheno...
A Logical Journey
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 intima...
After Gödel
Richard Tieszen analyzes, develops, and defends the writings of Kurt Gödel (1906-1978) on the philosophy and foundations of mathematics and logic. Gödel's relation to the work of Plato, Leibniz, Husserl, and Kant is examined, and a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is proposed.
Simply Gödel
"Tieszen’s Simply Gödel is a remarkable achievement—a handy guide with the impact of a philosophical tome. It’s all here: elegantly lucid discussions of Kurt Gödel’s epochal discoveries, a sympathetic account of the eccentric genius’s life, focused discussions of his encounters with his astonished peers, and a visionary peek into the future of mathematics, philosophy, and the on-rushing specter of robots with minds. A compact masterpiece, brimming with fresh revelations." —Rudy Rucker, author of Infinity and the Mind Kurt Gödel (1906–1978) was born in Austria-Hungary (now the Czech Republic) and grew up in an ethnic German family. As a student, he excelled in languages and m...
Continental Philosophy of Science
Continental Philosophy of Science provides an expert guideto the major twentieth-century French and German philosophicalthinking on science. A comprehensive introduction by the editor provides a unifiedinterpretative survey of continental work on philosophy ofscience. Interpretative essays are complemented by key primary-sourceselections. Includes previously untranslated texts by Bergson, Bachelard,and Canguilhem and new translations of texts by Hegel andCassirer. Contributors include Terry Pinkard, Jean Gayon, RichardTieszen, Michael Friedman, Joseph Rouse, Mary Tiles,Hans-Jöerg Rheinberger, Linda Alcoff, Todd May, Axel Honneth,and Penelope Deutscher.
The Cambridge Companion to Husserl
Exploring the full range of Husserl's work, these essays reveal just how systematic his philosophy is. An underlying theme is resistance to the idea, current in much intellectual history, of a radical break between "modern" and "postmodern" philosophy, with Husserl as the last of the great Cartesians.
