 Appetizers and Lessons for Math and Reason  Alan Selby
Logic Appetizers to test or or improve reading, writing and thinking skills, with definitions, concepts and proofs in many subjects (Chains of Reason; One or TwoWay Implications; Islands & Divisions of Knowledge; Deception); Advice (How to Study
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 Archimedes  Chris Rorres, Drexel University
A collection of information on Archimedes' life and achievements, complete with historical quotes, illustrations, and animations. The site covers Archimedes' inventions and accomplishments: Archimedes' Claw, Burning Mirrors, the Golden Crown, the Archimedes
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 Archives Henri Poincaré  PierreEdouard Bour and Manuel Rebuschi
La laboratoire de Philosophie et d'Histoire des Sciences (LPHS) réunit des scientifiques intéressés à l'histoire et à l'épistémologie de leur disciplines et des philosophes et historiens prêts à
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 Arché: Philosophical Research Centre for Logic, Language, Metaphysics, and Epistemology  Crispin Wright, Director; University of St. Andrews, U.K.
Arché is a new research centre within the School of Philosophical and Anthropological Studies, St Andrews. Its goal is the promotion and publication of research of the highest quality in metaphysics, formal and philosophical logic, philosophy of
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 The Bertrand Russell Editorial Project  McMaster University
These archives, at McMaster University, house the complete papers of Bertrand Russell (18721970), British Philosopher, logician, essayist and renowned peace advocate. His Collected Papers include logical and philosophical works, Toward the "Principles
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 Canadian Society for the History and Philosophy of Mathematics (CSHPM)  Glen Van Brummelen, SecretaryTreasurer
Promotes research and teaching in the history and philosophy of mathematics. A History and Pedagogy of Mathematics Newsletter is free to members; back issues of the HPM Newsletter are available in WordPerfect format. The CSHPM Bulletin, with announcements,
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 Category Theory  JeanPierre Marquis
An entry in the Stanford Encyclopedia of Philosophy covers category theory's definitions, history, and philosophical significance. Also includes a bibliography.
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 Constructivism and Mathematical Concepts  Pathways to School Improvement
A discussion of constructivism as it relates to teaching mathematics. A list of reflective questions for teachers and references is included.
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 A Constructivist View of Science Education  University of Massachusetts Physics Education Research Group (UMPERG)
Four premises of constructivism: knowledge is constructed, not transmitted; prior knowledge impacts the learning process; initial understanding is local, not global; and building useful knowledge structures requires effortful and purposeful activity;
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 A Crash Course in the Mathematics of Infinite Sets  Peter Suber; Philosophy Department, Earlham College
An introductory guide for philosophers, explaining the use of infinitary set theory.
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 Cybernetics and Systems Theory  F. Heylighen; Principia Cybernetica Web
General background material on the field of Cybernetics and Systems Science (also: (General) Systems Theory or Systems Research), an academic domain that touches virtually all traditional disciplines, from mathematics, technology, and biology to philosophy
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 Dave's Mathematics, Education, Philosophy and Chreods Server  Dave Wilson
Searchable math and mathematics education resources: an archive of preservice teachers' essays, the Teaching and Learning Enquiry Group, Chreods, a journal covering math education, and other writings.
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 Ethics in Science  Dept. of Chemistry, Virginia Polytechnic Institute
A bibliography of publications that pertain to ethics and misconduct in science; Internetbased resources related to ethics and misconduct in science, including hyperlinks to online professional codes of conduct; Selected Essays on Ethics in Science (the
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 Famous Paradoxes  Isaac Reed
Zeno's Paradox and Cantor's Infinities.
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 Gödel's Incompleteness Theorem  William Denton
Excerpts/quotes explaining Gödel's Incompleteness Theorem: any logical system contains a true statement that cannot be proven using that system's rules.
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 Gödel's Theorem and Information  Gregory J. Chaitin
Gödel's theorem may be demonstrated using arguments having an informationtheoretic flavor arguing that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast
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 Gödel's Theorem  Microsoft Encarta Online
Gödel's Theorem, also known as the Incompleteness Theorem, two theorems proposed by Austrianborn American logician Kurt Gödel. These theorems state that some parts of mathematics are based on ideas that cannot be proven within the system of
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 Institute for Logic, Language and Computation (ILLC)  University of Amsterdam, The Netherlands
An institute founded to further the scientific study of the structure, modification, and transmission of information. Currently, the groups participating in ILLC are based at the Faculty of Mathematics, Computer Science, Physics, and Astronomy, the Faculty
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 Islands & Divisions of Knowledge (Pattern Based Reason)  Alan Selby
Not seeing the difference between one and twoway implications is a common source of confusion in reading, writing and mathematics. Oneway implication rules can sometimes be put together to get further implication rules. One and twoway implications
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 James Franklin
Research activities, books, articles, opinions, and more from the author of What Science Knows and The Science of Conjecture: Evidence and Probability Before Pascal. Franklin researches and teaches about the philosophy of mathematics in the School of
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 John Allen Paulos
John Allen Paulos is a mathematician and author of the books Mathematics and Humor, I Think, Therefore I Laugh, Innumeracy  Mathematical Illiteracy and Its
Consequences, Beyond Numeracy  Ruminations of a Numbers Man, A Mathematician Reads the Newspaper,and
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 John Dewey: Democracy and Education  Institute for Learning Technologies (ILTweb)
Text of the 1916 book about the philosophy and practice of education. 26 chapters on the Web.
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 Laws of Form  Richard Shoup
Inspired by the book Laws of Form by George SpencerBrown, in which the author built a "calculus of distinctions." Read an interpretation of his laws of calling and crossing as a logical arithmetic; see a simple analysis of SpencerBrown's Counter; learn
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 Laws of Thought  Keith Devlin (Devlin's Angle)
"What Zeno of Citium actually did was found the Stoic school of logic. Though modern mathematical logic is popularly credited as having its beginnings in the syllogistic logic of Aristotle, most of the fundamental notions of contemporary propositional
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 Math by Proof: What is it, and why should we?  Roger Jones
Formalised mathematics is distinguished from informal mathematics by three features: machine processable languages with precisely defined semantics in which mathematical propositions are expressed; machine checkable reliable criteria for demonstrating
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 Mathematical Connections  Whittle, Luoma; Dept. of Learning Support, Augusta State University
"Exploring the Interplay Between Mathematics and the Humanities." A forum for exploring the interplay between mathematics and the humanities, including, but not limited to, the relationship between mathematics and the arts, anthropology, history, literature,
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 Mathematicians and Philosophers: Chalk and Cheese?  Keith Devlin (Devlin's Angle)
...mathematicians and philosophers go about their business in very different ways, and on the whole they don't mix. Mathematicians who arguably would benefit from reading works in philosophy rarely do so  books by Daniel Dennett and John Searle excepted
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 MSMS World of Logic  Claudia Carter; Mississippi School for Mathematics and Science (MSMS)
MSMS Logic and Game Theory is a study of logic, symbolic notation, truth tables, simple game theory, and problemsolving strategies. Links to significant figures in the world of logic: Lewis Carroll, George Boole, Giuseppe Peano, Von Neuman, Willard Van
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 Museum of the History of Science  Oxford University, U.K.
The Museum houses a collection of historic scientific instruments in the Old Ashmolean on Broad Street, Oxford, covering almost all aspects of the history of science, from antiquity to the early twentieth century. Particular strengths include the collections
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 The nCategory Café  John Baez, David Corfield, and Urs Schreiber
A blog devoted to "that heady interface between physics, mathematics and philosophy." Read posts, many with MathML, that date back to August, 2006.
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 Observer Mechanics: a Formal Theory of Perception  Bennett, Hoffman, Prakash
Full book online in pdf format. An inquiry into the subject of perception, the book suggests an approach to the study of perception that attempts to be both rigorous and general. The authors also attempt to introduce a new formalism, including mathematical
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 Of What Does Mathematical Knowledge Consist?  Annie and John Selden; Mathematical Association of America
Answers to epistemological questions such as "Does mathematical knowledge consist of competencies, or in seeing connections between mathematical concepts and results, or between various representations of a single concept?" Sections include Kinds of Mathematical
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 On Constructivism  Susan Hanley
"The constructivist approach opens new avenues for learning as well as challenges for the teacher trying to implement it." Hanley outlines problems in traditional teaching methods, describes constructivism as a possible solution, and reviews research
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 Principia Mathematica  A.D.Irvine; Stanford Encyclopedia of Philosophy
The philosophy encyclopedia's entry on Principia Mathematica, the landmark work on mathematical logic and the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell. Next to Aristotle's Organon, it is the most influential book
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 Radical Constructivism  Alex Riegler, Ed.
People, organizations, and online papers that deal with radical, epistemological, psychological and educational constructivism and second order cybernetics. Includes general introductions, online books and papers, links, conferences, and a URL submission
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 Sacred Science: Essays on Mathematics, Physics and Spiritual Philosophy  Thomas J. McFarlane
Essays in philosophy and religion intended to reveal the harmony in mathematical, physical and spiritual knowledge: Quantum Mechanics and Reality; Symmetry in Science and Religion; Science: Physical and Spiritual; Kant and Mathematical Knowledge; The
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 Spinozistic Calculus  Joseph B. Yesselman
Spinoza's Insights expressed in a Calculus format.
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 Strategy and Conflict: An Introductory Sketch of Game Theory  Roger A. McCain
Game theory is an interdisciplinary approach to studying human behavior that touches on computer science, social sciences, and behavioral sciences. Designed as a supplement to existing texts as a means of making the basic ideas a bit more accessible,
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 Teaching Logic and Reasoning in an Illogical World  DIMACS Symposium
A July 1996 symposium: Participants, schedule, list of papers, and the papers themselves in html, ascii, or postscript. Sample papers: S. Maurer: Teaching reasoning, broadly and narrowly; C. Nelan: Student's attitude toward the relationship between language
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 What is Mathematics: Goedel's Theorem and Around  Karlis Podnieks
An extended translation of Podnieks' book, published in 1992 in Russian. Contents include: Platonism, intuition and the nature of mathematics; Axiomatic set theory; First order arithmetic; Hilbert's Tenth problem; Incompleteness theorems; Around Goedel's
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 What is Mathematics?  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about what mathematics is, such as "Is math a science, an art, or some other anomaly?" and "Is there a difference between arithmetic and mathematics, and what is it?" and "Is math a science or an art?"
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 Wireless Philosophy
Free videos on the practice of philosophy — teaching viewers how to develop critical thinking skills and do philosophy, rather than simply learn what philosophers have thought. See, in particular, Wi Phi's categories of videos on the philosophy
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 Wordplay  John Langdon
On the application of ambigrams (words as art) in various fields of study. Most ambigrams are based on one form of symmetry or another; most of Langdon's ambigrams exemplify rotational symmetry.
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