81. Untitled Philosophy of Mathematics Dr. Carl Posy Greg J. Badros Table of Contents Part I General Survey of Philosophy of Mathematics 1 I.1 Prehistory of numbers 1 I.2 Greek Development of Math 2 2.1 Flowering of the Pythagoreans 3 http://www.nku.edu/~longa/classes/philmath/philmath.htm

Philosophy of Mathematics Class Notes PHL-113 Dr. Carl Posy Duke University Fall 1992 Prepared by Greg J. Badros From this website Table of Contents Part I: General Survey of Philosophy of Mathematics 1 I.1 Prehistory of numbers 1 I.2 Greek Development of Math 2 2.1 Flowering of the Pythagoreans 3 2.2 Downfall of the Pythagoreans 3 2.3 Greek Reaction to the Downfall 4 I.3 Road to Non-Euclidean Geometry 12 3.1 Hilbert's axiomatization of Geometry 12 3.2 The Evaluation of non-Euclidean Geometry 13 I.4 History of the concept of a number 16 I.5 Conceptual Foundations of Mathematics 22 5.0 General Overview of Reactions to Berkeley 23 5.0.1 Kant's Philosophy of Mathematics 24 5.1.1 Introduction of the Notion of a Limit 25 5.1.2 Arithmetization of Mathematics 26 5.2 Cantor 29 5.3.1 Peano 33 5.3.2 Frege 34 I.6 Two of the Three Reactions to the Third Crisis 37 6.1 Platonistic Reaction 37 6.2 Hilbert's Program 40 Part II: Intuitionism, A Third Direction 46 II.1 General Introduction to Intuitionism 46 II.2 Intuitionist's Construction of the Natural Numbers 47 II.3 Intuitionist's Construction of the Real Numbers 47

82. ANNOTATED BIBLIOGRAPHY OF MIND-RELATED TOPICS Gupta Anil Belnap Nuel THE REVISION THEORY OF TRUTH (MIT Press, 1993) HeytingArend INTUITIONISM (North Holland, 1956) Lukaszewicz Witold NONMONOTONIC http://www.thymos.com/mind/topic.html

Accessing the Bibliography By Topic This file provides an index organized by topic to the bibliography. Find the topic you're interested in, then scan the titles, then go back to the appropriate file of the bibliography to consult the corresponding entry. Many more books are available than are listed here. If you know the book (or the author) that you are looking for, go directly to the main bibliography This index is only meant as an "entry point", a way to access the bibliography when you don't really know what you are looking for. The bibliography has been growing since 1995 and it has now reached the point where it is virtually impossible to read all the titles to find what one needs. Therefore this index. Send your suggestions to piero@scaruffi.com Other resources that may help you locate a title according to its subject. Categories Listed in this index: Artificial Intelligence/ Turing Test Artificial Life Categorization Cognitive Models of Memory Cognitive Science ... Common Sense/ Qualitative Reasoning/ Knowledge Representation Connectionism/ Neural Networks Consciousness Cybernetics/ Information Theory Dreaming Ecological Realism Emotion Language / Semantics Life / Evolution/ Growth/ Genetics Mental Imagery Metaphor Models of Cognition Natural Language Processing ... Probabilistic, Plausible and Fuzzy Reasoning

83. Mathematical Constructivism - Wikipedia Main Page Recent changes Edit this page Older versions Specialpages. http://www.wikipedia.org/wiki/Mathematical_constructivism

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Mathematical constructivism From Wikipedia, the free encyclopedia. In the philosophy of mathematics mathematical constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists. When you assume that an object does not exist, and derive a contradiction from that assumption, you still have not found it, and therefore not proved its existence, according to constructivists. Constructivism is often confused with mathematical intuitionism , but in fact, intuitionism is only one kind of constructivism. Intuitionism maintains that the foundations of mathematics lie in the individual mathematician's intuition, thereby making mathematics into an intrinsically subjective activity. Constructivism does not, and is entirely consonant with an objective view of mathematics. Mathematicians that have contributed to constructivism Leopold Kronecker L.E.J. Brouwer

84. Mathematical Constructivism - Acapedia - Free Knowledge, For All Friends of Acapedia Mathematical constructivism. From Wikipedia, thefree encyclopedia. In the philosophy of mathematics, mathematical http://acapedia.org/aca/Mathematical_constructivism

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