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Topic: Intuitionism

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Mathematical intuitionism

Constructivist logic

Constructive proof

Intuitionistic type theory

Axiomatic set theory

Set theory

Set of uniqueness

Heyting algebra

Arend Heyting

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Continuum hypothesis

Cardinal number

Real number

Cantor set

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	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.
		As such, intuitionism is a variety of mathematical constructivism; but it is not the only kind.
		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 (546 words)

	Ethical intuitionism - Wikipedia, the free encyclopedia
		Sometimes the term "ethical intuitionism" is associated with a pluralistic, deontological position in normative ethics, a position defended by W.D. Ross.
		Some intuitionists characterize "intuitions" as a species of beliefs, beliefs which are self-evident in the sense that they are justified simply by virtue of one's understanding of the proposition believed.
		Ethical intuitionism suffered a dramatic fall from favor by the middle of the century, probably due in part to the influence of logical positivism, in part to the rising popularity of naturalism in philosophy, and in part to philosophical objections based on the phenomenon of widespread moral disagreement.
	en.wikipedia.org /wiki/Ethical_intuitionism (1336 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		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 takes the validity of a mathematical statement to be equivalent to its having been proved; what other criteria can there be for truth (an intuitionist would argue) if mathematical objects are merely mental constructions?
		In particular, the law of excluded middle, A or not A, is disallowed since one cannot assume that it is always possible to either prove the statement A or its negation.
	wikiwhat.com /encyclopedia/i/in/intuitionism.html (278 words)

	A PHILOSOPHY 111A PAGE ON THE WORLD WIDE WEB
		We are therefore left with the metaethical theories of intuitionism, coherentism, and constructivism as theories that all meet the skeptical argument of the infinite regress and are all equally successful (or unsuccessful) at meeting the skeptical argument from error.
		Intuitionism is not unreasonable in spite of its small justificatory circle precisely because intuitionism makes a claim to perception of objective truth, and this claim stands up to the skeptical arguments as well as any other truth claims.
		The self-justification in intuitionism is that the intuitionist believes something is true because her special faculty tells her it is true, and the special faculty determines truth because it is the nature of the special faculty to do so.
	people.brandeis.edu /~teuber/rawls6.html (17233 words)

	Intuitionism (Site not responding. Last check: 2007-11-06)
		Obviously Brouwer is responsible for the philosophy of intuitionism.
		Later he reconstructed portions of set theory, topology, and analysis in terms of intuitionism.
		Weyl also suggested that a defeat of intuitionism may be considered a defeat of phenomonology.
	www.andrew.cmu.edu /~cebrown/notes/intuitionism.html (179 words)

	Intuitionism (Site not responding. Last check: 2007-11-06)
		Intuitionism is a view of the origin of ideas which claims we know directly without any "mediation"--that is, without any processes between the knowledge and the knower.
		Intuitionism is the least understood source of ideas since we cannot identify the source by which we gain intuitive knowledge.
		While intuitionism is often criticized because there are no objective standards by which to judge its accuracy, the intuitionist would say that the experience is so powerful, it is self-authenticating.
	www.whitworth.edu /Academic/Department/Core/Classes/Co250/Intro/d_intui.htm (193 words)

	Henry Sidgwick's The Methods of Ethics
		Ethical Intuitionism, according to Sidgwick, asserts that proper conduct conforms to rules or principles which are known intuitively.
		Ethical Intuitionism may also assert that the rightness or wrongness of some actions may be known intuitively, even when the consequences of these actions are undetermined.
		Intuitionism may assert that some actions may be judged as right or wrong because of their own intrinsic qualities, without comparing them to ethical standards or to actions which are required by moral duty.
	www.angelfire.com /md2/timewarp/sidgwick.html (1701 words)

	mill (Site not responding. Last check: 2007-11-06)
		Modern intuitionism is a reaction to Thomas Hobbes’ belief that human beings are materialistic, deterministic and egoistic, driven by self-interest even if self-interest appears to be altruism, and that morality is relative to what an individual or a society finds good or pleasurable, and bad or painful (7).
		Intuition will lead our actions to be in conformity with the "eternal and immutable rule of right", or the "law of nature", or the "fitness of things" (10, 178).
		Intuitionism's belief in the innateness of human character is according to Mill "one of the chief hindrances to the rational treatment of great social questions, an upholder of conservative doctrines, and one of the greatest stumbling blocks to human improvement" (17, 465).
	www-rohan.sdsu.edu /~frantz/Mill.html (5171 words)

	H.A. Prichard, W.D. Ross - Moral Writings and The Right and the Good - Reviewed by Mark Timmons, University of Memphis ...
		Intuitionismâs progress was interrupted in the mid-1930s with the publication of A. Ayerâs Language, Truth, and Logic in which Ayer, in opposition to intuitionism, defended a version of emotivism, signaling noncognitivismâs initial volley that was followed by wide-spread rejection of intuitionism.
		Both apprehensions are immediate in the sense that in both insight into the nature of the subject directly leads us to recognize its possession of the predicate; and it is only stating this fact from the other side to say that in both cases the fact apprehended is self-evident.
		Whereas much of Prichardâs writing in ethics is polemical and his favored version of intuitionism tends to be in the background of his writings, in Ross we find a clear statement, elaboration, and defense of intuitionism.
	ndpr.nd.edu /review.cfm?id=1317 (2412 words)

	There are at least five effects of using intuition: (Site not responding. Last check: 2007-11-06)
		Intuition and Science (3) states that intuition is what we call "all the intellectual mechanisms which we do not know how to analyze or even name with precision, or which we are not interested in analyzing or naming" (3, p.
		Intuitionism maintains that there are self-evident truths or moral principles which are the basis for ethical behavior and known through intuition.
		Intuitionism sees intuition as a unique form of intelligence, a unique source of knowledge independent of sense experience, and that intuition is essential to knowledge.
	www-rohan.sdsu.edu /~frantz/KeynesOutline.htm (7914 words)

	Brouwer's Cambridge Lectures on Intuitionism (Site not responding. Last check: 2007-11-06)
		Meanwhile, under the pressure of well-founded criticism exerted upon old formalism, Hilbert founded the New Formalist School, which postulated existence and exactness independent of language not for proper mathematics but for meta-mathematics, which is the scientific consideration of the symbols occurring in perfected mathematical language, and of the rules of manipulation of these symbols.
		In this situation intuitionism intervened with two acts, of which the first seems to lead to destructive and sterilising consequences, but then the second yields ample possibilities for new developments.
		Completely separating mathematics from mathematical language and hence from the phenomena of language described by theoretical logic, recognising that intuitionistic mathematics is an essentially languageless activity of the mind having its origin in the perception of a move of time.
	www.marxists.org /reference/subject/philosophy/works/ne/brouwer.htm (2524 words)

	intuition from FOLDOC
		In moral philosophy, intuitionism is the metaethical theory that moral judgments are made by reference to a direct, non-inferential awareness of moral value.
		Even though intuitionism is a form of intrinsicism, it ends up being a kind of subjectivism, in which the justification for ethical values is the fact that a certain person or philosopher thinks they are true.
		Historically, intuitionism has tended to be a kind of deontologism, although the cause may have been simply the beliefs of the intuitionists themselves and not anything about intuitionism in general.
	lgxserver.uniba.it /lei/foldop/foldoc.cgi?intuition (395 words)

	Sample Chapter for Audi, R.: The Good in the Right: A Theory of Intuition and Intrinsic Value.
		Intuitionism has been a force in the history of ethics since at least the eighteenth century, but there are a number of reasons for its growing prominence.
		Chapter 1 introduces ethical intuitionism, beginning with Sidgwick's account of the position and proceeding, through Moore, Prichard, and Broad, to the position of Ross, which was the most prominent intuitionist view throughout most of the twentieth century.
		From the vantage point of the integration between Rossian intuitionism and the framework of the Kantian categorical imperative, Chapter 4 pursues the connection between intuitionism as a deontological (duty-based) position and the theory of value, and thus between the right and the good.
	pup.princeton.edu /chapters/i7750.html (1331 words)

	Ethics 04 - Intuitionism (Site not responding. Last check: 2007-11-06)
		Intuitionism says that "good" is an indefinable notion.
		Intuitionism makes three claims: (1) "Good" is indefinable, (2) there are objective moral truths, and (3) the basic moral truths are self-evident to a mature mind.
		And appealing to intuitions can lead to an early stalemate on moral issues -- as when we argue with someone who has racist intuitions.
	www.jcu.edu /philosophy/gensler/et/et-04-00.htm (351 words)

	Investigating Moral Claims: Intuitionism, Emotivism, and Naturalism
		Philosophers in the 1900’s examined moral claims through the ethical theories of intuitionism, emotivism, and naturalism.
		Intuitionism and emotivism both differ and agree on philosophical views, yet both will argue against naturalistic claims.
		Digging deeper into the intuitionist claim, we must understand that their theory is solely based on inklings.
	www.truthawakens.com /intuitionismandemotivism.asp (978 words)

	[No title]
		Moral intuitionism, in its classic formulation, was held by many leading British moral theorists in the early twentieth century, including G.
		One of the obstacles to its wider acceptance, I suspect, is the sense that its truth is incompatible with a naturalistic worldview.
		In this paper, I defend intuitionism, in its more recent formulations, against the criticism that there is something objectionably non-natural about its conception of moral properties.
	www.wku.edu /~jan.garrett/kpa/tropman.htm (144 words)

	Search Results for "Intuitionism"
		...The movement as a whole was profoundly influenced by the pragmatism of William James, the intuitionism of Henri Bergson, and the philosophy of action of Maurice Blondel....
		According to mathematical intuitionism, mathematical knowledge rests on mathematical concepts that...
		His own utilitarianism is based upon a new synthesis of intuitionism and empiricism.
	www.bartleby.com /cgi-bin/texis/webinator/sitesearch?FILTER=&query=Intuitionism (243 words)

	Moral Non-Naturalism
		However, this view is more often referred to as ‘intuitionism’ and I shall henceforth also refer to it as intuitionism.
		The non-naturalist's standard move here is to defend some form of "intuitionism." In its most straightforward form, intuitionism holds that we come to know about moral properties through direct observation of those properties.
		Non-naturalism's opponents, by contrast, put a great deal of weight on explaining our moral practices in a way that fits well with a properly scientific view of the world and are happy to reject the presuppositions of common sense if they conflict with that conception.
	plato.stanford.edu /entries/moral-non-naturalism (8990 words)

	Mathematics is Analytic
		Intuitionism is often represented as the only one of these schools to have escaped lethal criticism.
		The serious debilitation which intuitionism promised for mathematics was so horrifying to most mathematicians that they looked no further for flaws in the system or its justification.
		As time passed by the scope of intuitionistic mathematics has been shown to be much greater than it had been feared, and intuitionism as apostle of constructive mathematics has presented itself as the natural and most appropriate approach for computer science and information systems engineering.
	www.rbjones.com /rbjpub/philos/maths/inter007.htm (954 words)

	intuitionism - yourDictionary.com - American Heritage Dictionary (Site not responding. Last check: 2007-11-06)
		The theory that truth or certain truths are known by intuition rather than reason.
		The theory that ethical principles are known to be valid through intuition.
		The view that the subject matter of mathematics consists of the mental or symbolic constructions of mathematicians rather than independent and timeless abstractions, as is held in Platonism.
	www.yourdictionary.com /ahd/i/i0210200.html (80 words)

	Intuitionism
		Intuitionism was simply another sense that allowed one to detect that property.
		In both cases they are likely to say the same things in much the same way, but you can pick up on the slight nuances that belie their real feelings.
		Anyway, I find the concept of intuitionism and the subject of intuition very interesting and have been intrigued recently by some mentions and new connections.
	www.arrod.co.uk /archive/blog_20031004_intuitionism.php (645 words)

	[No title]
		By intuitionism I mean the approach to mathematics based on intuitionistic logic, a well-defined body of axioms and rules of inference [6] [3].
		By comparing mathematical realism with intuitionism from an informal axiomatic point of view, we can steer clear of most of the metaphysical problems involved in analyzing these notions from the ground up, and concentrate on what may be termed the purely mathematical aspects.
		Any analysis of realism versus intuitionism in mathematics, that desires to say something relevant to mathematical practice, should be informed by this corpus of applied intuitionism.
	www.math.fau.edu /Richman/Docs/philmath.html (1926 words)

	Robert Audi - The Good in the Right: A Theory of Intuition and Intrinsic Value - Reviewed by Bart Streumer, Fitzwilliam ...
		Audi begins the book by discussing the historical development of intuitionism, and by formulating what he takes to be the most plausible version of this view.
		Audi calls the resulting view 'Kantian intuitionism', and he claims that, by showing that the principles of prima facie duty can be inferred from the categorical imperative, Kantian intuitionism systematizes these principles.
		In chapter 4, Audi shows how his Kantian intuitionism can be grounded in considerations about value, by arguing that acting on Kantian intuitionism contributes to human flourishing, and thereby to the realization of value.
	ndpr.nd.edu /review.cfm?id=3041 (1930 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Short Notes on Intuitionism Michael Misamore, Dec 25, 2002, edited Dec 08, 2004 Intuitionism denies Platonism, so instead objects must be constructed.
		Intuitionism is concerned primarily with "mental constructions." Constructions need not be physically possible.
		Common examples in Intuitionism deal with numbers whose definitions depend on whether things such as a string of consecutive digits 0123456789 appears in the decimal expansion of pi.
	userpages.umbc.edu /~mmisam1/doc.intuit.txt (1693 words)

	Chapter 6e
		The name "Intuitionism" seems to suggest an epistemic principle of classification, and the opposite of it would seem to be "Empiricism".
		On the other hand, the opposition of Egoistic and Universalistic Hedonism to Intuitionism rests on a quite different basis, viz., on whether some types of action are intrinsically right or wrong or whether the rightness or wrongness of actions always depends on their conduciveness to certain ends.
		Teleological theories hold that the rightness or wrongness of an action is always determined by its [207] tendency to produce certain consequences which are intrinsically good or bad.
	www.ditext.com /broad/ftet/ftet6e.html (692 words)

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