
	Where results make sense

Topic: Intuitionism philosophy of mathematics

Related Topics

Bacolod City

In the News (Mon 16 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Philosophy of mathematics - Wikipedia, the free encyclopedia
		Philosophy of mathematics is that branch of philosophy which attempts to answer questions such as: "why is mathematics useful in describing nature?", "in which sense(s), if any, do mathematical entities such as numbers exist?" and "why and how are mathematical statements true?".
		This is a prime concern of the philosophy of mathematics.
		Three schools, intuitionism, logicism and formalism, emerged around the start of the 20th century in response to the increasingly widespread realisation that mathematics (as it stood), and analysis in particular, did not live up to the standards of certainty and rigour with which it was over-credited.
	en.wikipedia.org /wiki/Philosophy_of_mathematics (3622 words)

	Intuitionism - Wikipedia, the free encyclopedia
		In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach to mathematics as the constructive mental activity of humans.
		Any mathematical object is considered to be a product of a construction of a mind, and therefore, the existence of an object is equivalent to the possibility of its construction.
		Intuitionism also rejects the abstraction of actual infinity; i.e., it does not consider as given objects infinite entities such as the set of all natural numbers or an arbitrary sequence of rational numbers.
	en.wikipedia.org /wiki/Intuitionism_(philosophy_of_mathematics) (313 words)

	Philosophy of mathematics - Open Encyclopedia (Site not responding. Last check: 2007-11-07)
		Mathematical logicians study formal systems but are just as often platonists as they are formalists.
		But this permanence is in fact grounded by much uncertainty: as mathematical practice evolves, the status of previous finished mathematics is cast into doubt, and is re-examined and corrected only to the degree it is required or desired by the needs of current applications and groups.
		Finished mathematics is often accorded too much status, and folk mathematics not enough, due to an over-belief in axiomatic proof and peer review as practices.
	open-encyclopedia.com /Philosophy_of_mathematics (3541 words)

	What is Mathematics
		Inventionism is a wonderful philosophy for the arts and humanities where we see the fruits of imaginative subjectivity; their nature and practice contrast so drastically with that of mathematics that the objective element seems to have failed to be adequately incorporated into this view of mathematics.
		Barrow's chapter on Intuitionism is probably the most interesting in the entire book, despite the fact that intuitionism is probably the weakest of all the mathematical philosophies.
		It is a philosophy of mathematics that is popular amongst physicists, but less so among mathematicians, and is almost universally regarded as an irrelevance by consumers of mathematics like computer scientists, psychologists, or economists.
	members.cox.net /mathmistakes/what_is_mathematics1.htm (4060 words)

	Foundations Study Guide: Philosophy of Mathematics -- Objectivist Center -- Reason, Individualism, Achievement, and ...
		The philosophy of mathematics is the philosophical study of the concepts and methods of mathematics.
		Mathematics is the substance of thought writ large, as the West has been told from Pythagoras to Bertrand Russell; it does provide a unique window into human nature.
		Thus, an area that an Objectivist philosophy of mathematics must address is the meaning and structure of measurement in the measurement omission theory; this subfield of the philosophy of mathematics might be called the mathematics of philosophy.
	ios.org /articles/foundations_phil-of-mathematics.asp (1796 words)

	Stewart Shapiro (ed.) - The Oxford Handbook of Philosophy of Mathematics and Logic - Reviewed by JC Beall, University ...
		The philosophy of mathematics and logic, perhaps contrary to popular impression, is driven by core philosophical topics -- matters of metaphysics, epistemology, language, and, to some extent, even mind.
		Mathematics, on the other hand, might not be as conspicuously central to philosophy as logic (maybe), but, if nothing else, it is a wonderful phenomenon for cutting one's philosophical teeth -- or wearing them out, if one wishes.
		The Oxford Handbook of the Philosophy of Mathematics and Logic is a very accessible, wide ranging work that serves not only to indicate the 'state of the art' in the given area, but, remarkably, also serves as a very fine introduction to the field.
	ndpr.nd.edu /review.cfm?id=3781 (1363 words)

	Philosophy of Mathematics
		Intuitionism clashed with classical mathematics in so far as Brouwer held that there are no truths beyond experience, and hence that the law of the excluded middle could not be applied to all mathematical statements (in particular infinitary parts of mathematics are indeterminate with respect to some properties).
		Mathematical logic is the formal study of mathematical structures and systems; its subparts include proof theory and model theory.
		Structuralists argue that mathematics is not about some particular collection of abstract objects but rather mathematics is the science of patterns of structures, and particular objects are relevant to mathematics only in so far as they instantiate some pattern or structure.
	www.bris.ac.uk /Depts/Philosophy/UG/Studyguide/maths.html (1925 words)

	Philosophy of Mathematics - Phil 567/667 - Winter 05 - Richard Zach - University of Calgary
		The philosophy of mathematics deals with, as its name suggests, philosophical issues that are raised by mathematics.
		This includes the debate about the metaphysics of mathematical objects, in particular, whether there are any (realism) or not (nominalism), and the status of mathematical truths; structuralism in mathematics; mathematical explanation; and empiricist and naturalist approaches to mathematics.
		Two previous courses in Philosophy, one of which must be PHIL 367 or 467, and one of which must be a 400 or higher level course; or consent of the Department.
	www.ucalgary.ca /~rzach/567 (2071 words)

	Wittgenstein, Education and the Philosophy of Mathematics
		Ernest (1999) argues that the traditional absolutist (read “objectivist”) account of mathematics should be replaced by a “conceptual change” philosophy of mathematics built upon principles of radical constructivism that, nevertheless, does not deny the existence of the physical and social worlds.
		Mathematical truths arise from the definitional truths of natural language, acquired by social interaction .The truths of mathematics are defined by implicit social agreement - shared patterns of behaviour - on what constitute acceptable mathematical concepts, relationships between them, and methods of deriving new truths from old.
		To the traditional aims -- to reproduce mathematical skill and knowledge based capability, and to develop creative capabilities in mathematics - he suggests adding: to develop empowering mathematical capabilities and a critical appreciation of the social applications and uses of mathematics, and to develop an inner appreciation of mathematics: its big ideas and nature.
	theoryandscience.icaap.org /content/vol003.002/peters.html (3423 words)

	Inconsistent Mathematics
		Inconsistent mathematics is the study of the mathematical theories that result when classical mathematical axioms are asserted within the framework of a (non-classical) logic which can tolerate the presence of a contradiction without turning every sentence into a theorem.
		Gödel's contribution to the philosophy of mathematics was to show that the first three of these can be rigorously expressed in arithmetical theories, albeit in theories which are either inconsistent or incomplete.
		Projective geometry is a mathematical theory which is interesting because we are creatures with an eye, since it explains why it is that things look the way they do in perspective.
	plato.stanford.edu /entries/mathematics-inconsistent (2006 words)

	Constructive Mathematics
		Mathematics arises when the subject of two-ness, which results from the passage of time, is abstracted from all special occurrences.
		However, the comparison with classical mathematics should not be made superficially: in order to understand that there is no real contradiction here, we must appreciate that the meaning of such terms as “function” and even “real number” in intuitionistic mathematics is quite different from that in the classical setting.
		What was needed to raise the profile of constructivism in mathematics was a top-ranking classical mathematician to show that a thoroughgoing constructive development of mathematics was possible without a commitment to Brouwer's non-classical principles or to the machinery of recursive function theory.
	plato.stanford.edu /entries/mathematics-constructive (6375 words)

	Guilford College - Philosophy of Mathematics
		The portals to Plato's academy contained the message (paraphrased): "Let no one enter here who does not know mathematics." As this quotation suggests, there is a rich history to the connections between mathematics and philosophy.
		Philosophy of Mathematics is a cross-disciplinary and cross-divisional concentration that investigates the connections between philosophy and mathematics.
		It is particularly designed as a companion to either a philosophy or mathematics major.
	www.guilford.edu /academics/index.cfm?ID=100003890 (148 words)

	Philosophy of Mathematics
		We mention philosophy because in a sense Nuprl embodies a philosophy of mathematics.
		This is a contribution to an analysis of the foundations of mathematics, which is a philosophical matter.
		A simplistic view of the philosophy of mathematics says that there are four schools of thought: Platonism; Logicism; Formalism; and Intuitionism.
	www.cs.cornell.edu /Info/Projects/NuPrl/Intro/Philosophy/philosophy.html (635 words)

	University of Bristol / Department of Philosophy / Philosophy of Mathematics
		Mathematics is very important in Kant's thought, and his ideas about the nature of mathematical knowledge have had an influence in epistemology that is hard to overestimate.
		No particular mathematical knowledge is required for this course, but we shall at times need to use simple mathematical proofs as examples or make use of elementary arithmetic and geometry.
		The doctrine of ‘mathematicals’ or ‘intermediates’ in Plato and Aristotle
	www.bris.ac.uk /depts/Philosophy/UG/ugunits0001/maths.html (1952 words)

	Philosophy of Mathematics Syllabus
		PL 3074 - Philosophy of Mathematics - Spring 2003
		Mathematics is sometimes referred to as the science of the infinite.
		These papers should conform to the guidelines for writing philosophy papers that will be handed out in class.
	ls.poly.edu /~jbain/philmath/philmathsyl.htm (299 words)

	On Gödel's Philosophy of Mathematics, Notes
		Gödel, "Russell's Mathematical Logic," in P. Benacerraf and H. Putnam, eds., Philosophy of Mathematics (Englewood Cliffs, 1964), pp.
		Brouwer, "Intuitionism and Formalism," in P. Benacerraf and H. Putnam, eds., Philosophy of Mathematics, pp.
		Mathematical knowledge is not generally divided into categories, especially where a classical existence proof is considered sufficient without further comment.
	www.friesian.com /goedel/notes.htm (2210 words)

	[No title]
		Philosophy of Mathematics involves the epistemology, ontology, and methodology of mathematics.
		Intuitionism was founded in 1907 in the Ph.D. dissertation of L. Brouwer at the University of Amsterdam.
		Frege was a professor of mathematics at Jena university.
	www.badros.com /greg/doc/philmath.htm (12971 words)

	Philosophy of Mathematics Syllabus
		Prerequisites: The stated prerequisite for this course is MAT303 Foundations of Geometry or MAT306/COM306 Discrete and Algorithmic Mathematics.
		Philosophy: For centuries, mathematics has enjoyed its reputation as a most indubitable area of human knowledge.
		Proceedings of the Canadian Society for the History and Philosophy of Mathematics 16: 103-109, 2003.
	www.thecoo.edu /~jadouma/WebDocs/390Philsyl.J05.htm (2006 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		The Philosophy of Mathematics Workshop traditionally meets most quarters on Mondays at 3:00 PM in the Philosophy Common Room (Dodd 399).
		And, it is features of applied mathematics that tend to drive discussions of the structure of continuous bodies within continuum physics.
		And since they lie at the intersection of philosophy of physics (since their source is a well-developed physical theory), metaphysics (since mereological axioms are involved), and philosophy of applied mathematics (since features of applied mathematics drive much of the discussion), these considerations have inherent interest in their own right.
	www.math.ucla.edu /~dam/291/mathworkshop.html (1192 words)

	On Gödel's Philosophy of Mathematics, Bibliography
		Bar-Hillel, Y. "On a neglected ontology-free philosophy of mathematics," Problems in the Philosophy of Mathematics, ed.
		Brouwer, L. "Intuitionism and Fomalism," Philosophy of Mathematics, ed.
		Infinitistic Methods: Proceedings of the Symposium on Foundations of Mathematics Warsaw 12-9 September 1959.
	www.friesian.com /goedel/biblio.htm (471 words)

	Sources on the Philosophy of Mathematics (Site not responding. Last check: 2007-11-07)
		For philosophical material relating to intuitionism Dummett must be mentioned (not withstanding his conspicuous absence from my bibliography).
		Introduction to the Foundations of Mathematics by Wilder is an informal text on the Foundations of Mathematics (though, according to [Tymoczko98] Wilder was not appreciated by philosophers until they began to question foundations).
		Many of them can't really be said to be about the foundations of mathematics, but are nevertheless thought by some to be at least relevant to the foundations of mathematics.
	www.rbjones.com /rbjpub/philos/maths/faq008.htm (374 words)

	Notre Dame Philosophy Faculty
		"Philosophy of Mathematics in the 20th Century," vol.
		IX, Philosophy of Science, Logic and Mathematics in the Twentieth Century, Routledge History of Philosophy (1996)
		Poincare vs. Russell on the Role of Logic in Mathematics Philosophia Mathematica 1 (1993): 24-49.
	www.nd.edu /~ndphilo/faculty/mdet.htm (216 words)

	Powell's Books - The Philosophy of Mathematics: An Introductory Essay by Stephan Korner
		Lucid and comprehensive essay surveys the views of Plato, Aristotle, Leibniz and Kant on the nature of mathematics; examines the propositions and theories of the schools these philosophers inspired; and concludes with a discussion on the relation between mathematical theories, empirical data and philosophical presuppositions.
		Lucid and comprehensive essay surveys the views of Plato, Aristotle, Leibniz and Kant concerning propositions and theories of applied and pure mathematics.
		Intuitionism and the logical status of applied mathematics
	www.powells.com /cgi-bin/biblio?inkey=4-0486250482-1 (153 words)

	intuitionism - OneLook Dictionary Search
		Intuitionism : The Ism Book A Field Guide to the Nomenclature of Philosophy [home, info]
		noun: (philosophy) the doctrine that knowledge is acquired primarily by intuition
		Phrases that include intuitionism: mathematical intuitionism, ultra intuitionism
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=intuitionism (207 words)

	Philosophy 146: Philosophy of Mathematics (Site not responding. Last check: 2007-11-07)
		This is an introduction to the classics of philosophy of mathematics with emphasis on the
		Week 3: Kant on pure intuition in arithmetic and geometry.
		Week 11: The emergence of Cantorian set theory and the mathematical theory of the infinite; Zermelo's axiom of choice and his axiomatization of set theory; semi-intuitionism.
	philosophy.berkeley.edu /mancosu/philmath146 (231 words)

	EpistemeLinks: Electronic Texts for Philosophy of Mathematics
		Just one of dozens of designs including philosophy quotes, philosophy humor, and more...
		An Excerpt and Fragments from his Cambridge Lectures on Intuitionism (1951)
		The modern development of the foundations of mathematics in the light of philosophy
	www.epistemelinks.com /Main/TextName.aspx?TopiCode=Math (219 words)

Try your search on: Qwika (all wikis)