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Topic: Law of excluded middle

	Law of excluded middle - Wikipedia, the free encyclopedia
		In logic, the law of excluded middle, or the principle of tertium non datur, is formulated in traditional logic as "A is B or A is not B ".
		The law of excluded middle can be misapplied, leading to the logical fallacy of the excluded middle, also known as a false dilemma.
		Take, for example, the law of excluded middle, in the form 'all propositions are true or false.' If from this law we argue that, because the law of excluded middle is a proposition, therefore the law of excluded middle is true or false, we incur a vicious circle fallacy” (p.
	en.wikipedia.org /wiki/Law_of_excluded_middle (4266 words)

	Talk:Law of excluded middle - Wikipedia, the free encyclopedia
		Anyway, as I understand the law of excluded middle, it simply means that something has to be either true or false; it can't be both, or partially-true, or whatever.
		The law of the excluded middle implies that the square root of 2 cannot have the qualities of an integer and thus must be something other than a rational number.
		Part of the confusion is that I'm still trying to determine whether the Law of excluded middle is in fact a disjunction or an exclusive disjunction, so I know whether Radical Middle thought disagrees with it.
	en.wikipedia.org /wiki/Talk:Law_of_excluded_middle (1452 words)

	Gnostic Christianity.com. The outlawed logic/logos teachings of Jesus.
		Laws of logic are at work in our everyday lives on a scale that dwarfs the effects of even laws of mathematics.
		The third law that institutionalized the prevailing principle is the law of excluded middle.
		In the everyday world, the law of diversity would cleanse the heart and mind of prejudicial reasoning, because it teaches us that prejudice is the consequence of reasoning according to the law of identity, when it is appropriate to use the law of diversity.
	www.gnosticchristianity.com /ch7.htm (8269 words)

	Law of Excluded Middle
		A law of classical mathematics and logic which states that for any mathematical or logical truth statement, the result or conclusion is either true or false exclusively: there are no values in between or outside of true or false required for establishing the truth of a sentence or proposition.
		Some anti-realist movements in mathematics, such as intuitionism, however, have rejected the law of excluded middle as an abstract and artificial idea that does not represent the status quo in the real mathematical world.
		Nevertheless, the law of excluded middle has proven to be powerful and efficacious in many mathematical and logical endeavors, and is incorporated into all systems employing some form of classical logic, including Boolean algebra and binary logic.
	www.iscid.org /encyclopedia/Law_of_Excluded_Middle (152 words)

	Learn more about Law of excluded middle in the online encyclopedia. (Site not responding. Last check: 2007-11-07)
		It also differs from Law of non-contradiction, which states (P and not-P) is false.
		This leaves open the possibility that certain systems of logic may reject bivalence (by allowing more than 2 truth values) but accept the law of excluded middle, by accepting that (P or not-P) is always true, even when P itself is neither true nor false.
		Some nontraditional logics, most notably intuitionistic logic, are not bivalent, and in such logics the law of excluded middle does not necessarily hold.
	www.onlineencyclopedia.org /l/la/law_of_excluded_middle.html (313 words)

	[No title]
		Because constructive mathematics assumes less than classical mathematics, which assumes the law of excluded middle, any theorem in the former is a theorem in the latter---that is really the only sense in which I would assert that the classical universe is a model for constructive mathematics.
		Although the notion of positive mathematical content is tricky in the presence of the law of excluded middle, which confounds a statement with its double negation, I wouldn't say that a classical theorem is empty of positive mathematical content unless proven in a constructive manner.
		This is typical of generalizations: the notion of a normal subgroup is equivalent to that of a subgroup in the context of the commutative law, just as the notion of a detachable subset is equivalent that of a subset in the context of the law of excluded middle.
	www.math.fau.edu /richman/Docs/intrview.html (9565 words)

	Wikinfo \| Logic (Site not responding. Last check: 2007-11-07)
		Aristotle and his followers held that two of the most important principles of logic are the law of non-contradiction and the law of the excluded middle.
		The law of non-contradiction states that no proposition is both true and false and law of excluded middle states that a proposition must either be true or false.
		It does not follow that the law of the excluded middle is false, or indeed that any other proposition of classical logic which was true is now false.
	www.wikinfo.org /wiki.php?title=Formal_logic (1859 words)

	Philosophy \| University of Northern Colorado - The Laws of Logic
		These are the laws of noncontradiction, the excluded middle, and identity.
		the law of identity for truth values, and there are many formulations of predicate logic in which nothing like “(x)x=x” is either an axiom or a theorem—namely, systems of first order predicate logic without identity.
		The man from whom I first learned logic when I was myself in school, Frederic Brenton Fitch, favored systems in which it was impossible to derive the law of excluded middle, this being his preferred way of avoiding the implications of the famous Russell paradox.
	www.unco.edu /philosophy/current/forums/topic.asp?TOPIC_ID=151 (360 words)

	Trespassing limits
		The Law of the Excluded Middle, that currently proclaims that a statement can only be true or false, is to a large extent responsible for the categorical way western people conceive of reality.
		This law establishes that in a closed system the amount of energy available for work is always decreasing: the Law of Entropy puts a physical end to the happy Newtonian-categorical belief in a clockwise Universe where limits and boundaries are clearly fixed and obey neat universal laws.
		Excluded middles "were bad shit, to be avoided." Oedipa--or is it the narrator?--concludes by the end of her inverted quest.
	tarlton.law.utexas.edu /lpop/etext/okla/collado24.htm (10460 words)

	Andrews, Excluded Middle
		a science a priori of the necessary laws of thinking, not, however, in respect of particular objects but all objects in general: it is a science, therefore, of the right use of the understanding and of reason as such, not subjectively, i.e.
		Far from "expressly rejecting the breakdown of our Law", he is not accepting a Principle of Excluded Middle in any of its guises when it purports to determine the indeterminate.
		There are other assertions of some apparent form of Excluded Middle, at 19a30 for example: "I mean, for example, it is necessary for there to be or not to be a sea-battle tomorrow; but it is not necessary for the sea battle to take place tomorrow, nor for one not to take place..." Ackrill, 53.
	www.mun.ca /animus/1996vol1/andrews.htm (5202 words)

	Fuzzy Sets (Site not responding. Last check: 2007-11-07)
		The law of identity which states that A is A (what is, is); the law of contradiction (A is not non-A); and the law of excluded middle (A cannot be A and non-A).
		Their dogmatic thinking was the first to challenge the law of excluded middle.
		Or, with satanic systems which keep the law of excluded middle but do not accept the law of identity, because, only when A is non-A, the angel of darkness becomes an angel of light.
	www.newfalcon.com /excerpts/fuzzy_sets_e.htm (977 words)

	Thought, laws of -- Britannica Student Encyclopedia (Site not responding. Last check: 2007-11-07)
		fundamental principles of logic: (1) law of contradiction—something cannot exist and not exist at the same time; (2) law of excluded middle—something either exists or it does not, no middle condition is possible; (3) law of identity—something is always identical with itself; 20th-century philosophers have criticized, even rejected, the laws, which derive from ancient Greek…
		traditionally, the three fundamental laws of logic: (1) the law of contradiction, (2) the law of excluded middle (or third), and (3) the principle of identity.
		fundamental principles of logic: (1) law of contradiction—something cannot exist and not exist at the same time; (2) law of excluded middle—something either exists or it does not, no middle condition is possible; (3) law of identity—something is always identical with itself; 20th-century philosophers have criticized, even rejected, the laws, which derive from ancient...
	www.britannica.com /ebi/article-9338392?tocId=9338392 (917 words)

	Laws of Non-Contradiction, Laws of the Excluded Middle and Logics - RESTALL (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Laws of Non-Contradiction, Laws of the Excluded Middle and Logics - RESTALL (ResearchIndex)
		Laws of Non-Contradiction, Laws of the Excluded Middle and Logics (2000)
		Laws of Non-Contradiction, Laws of the Excluded Middle and Logics.
	citeseer.ist.psu.edu /290897.html (426 words)

	Chapter
		But it can be seen that rejection of this law of excluded middle would invalidate most of the theorems of classical analysis.
		Statement (iii), the law of double negation, statement (iv), the DeMorgan?s law, and statement (v), the law of contraposition, remain unchanged.
		Also, for non-self-referential statements, the law of noncontradiction and the law of excluded middle would come up as special cases in tautology and hence the classical analysis would not be violated.
	www.rpi.edu /~sivars/Interlude.htm (2509 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		The relevance of all this to the principles of excluded middle and contradiction is as follows.
		If we take Peirce to have meant LEM and LNC, then it appears that he wanted to deny the principle of bivalence (according to which all propositions are true or else false) with regard to universally quantified propositions, and that he meant to claim that existentially quantified propositions are both true and false.
		Once we see what Peirce meant by "principles of excluded middle and contradiction," we see that this is not what he was claiming.
	www.digitalpeirce.fee.unicamp.br /lane/p-prilan.htm (1788 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		In fact, the answers to a whole class of related questions has to be asserted to exist, even though we don't in general have a way to get at them.
		The way that it's proven, in the ordinary development of mathematics, is by implicit application of the law of excluded middle: that every proposition P is either true or false.
		It's been said that we have compelling reasons for using the law of excluded middle in mathematics, but I don't know of any compelling reasons to do so, certainly not all of the time and while not paying any particular attention to it.
	www.math.niu.edu /~rusin/known-math/99/LEM (354 words)

	Glossary of Terms: Ex (Site not responding. Last check: 2007-11-07)
		The Law of the Excluded Middle is that “if a given proposition is not true then its denial must be true”.
		Whereas formal logic places an absolute ban on Contradiction, Intuitionism is a branch of Logic which holds that the Law of Excluded Middle is not valid.
		For dialecitcs, this law has only relative truth; due to the inherently mobile and interconnected nature of all concepts, it is frequently the case that neither a proposition nor its denial may be accepted as absolutely true.
	www.marxists.org /glossary/terms/e/x.htm (1699 words)

	The Problem of Logical Fatalism (Site not responding. Last check: 2007-11-07)
		One of them is the law of excluded middle, which states for every proposition P, either P is true or Not P is true.
		Another logical principle is called the law of noncontradiction, which says that something cannot simultaneously be and not be of a specified kind or quantity.
		[2] In terms of proposition P, the Law says that it is impossible for both P and Not P to be true.
	www.angelfire.com /mn2/tisthammerw/polf.html (540 words)

	Russell's Paradox and the Law of Excluded Middle
		Russell’s Paradox and the Law of Excluded Middle
		So, by insisting that the Law of Excluded Middle ranges over everything without restrictions, you end up being able to prove “squounds are blue and squounds are not blue”!
		None of this means, of course, that you can’t have bivalence and Excluded Middle relative to a domain.
	personal.bgsu.edu /~roberth/russell.html (1125 words)

	nomiddle (Site not responding. Last check: 2007-11-07)
		Rumors suggest that the Bank of Japan may actually be considering adopting some form of inflation targeting, with a positive upper bound.
		I know that all of this is painful to think about; policymakers are certainly not used to dealing with such paradoxical-sounding problems, and their instinct is always to go for some sort of middle ground.
		But the law of the excluded middle here is not some abstract professorial quibble.
	web.mit.edu /krugman/www/nomiddle.html (382 words)

	Math Notes - Set Membership
		The Law of the Excluded Middle is a simple idea.
		Some statements do not fit easily into the law of the excluded middle and seem more appropriate to explanation using multi-value logical systems.
		It seems that the law of the Excluded Middle is very useful in finding programming solutions.
	home.att.net /~p.konieczko/excluded.html (602 words)

	Archived Article -- Believing a Lie (Site not responding. Last check: 2007-11-07)
		Among these are the Law of Excluded Middle and the Law of Non-Contradiction.
		The Law of Excluded Middle basically states that a proposition (in other words, a meaningful sentence) is either true or false.
		The Law of Non-Contradiction is just a fancy way of saying that something cannot be true and false simultaneously.
	free.hostdepartment.com /l/lordofall/bal.html (473 words)

	excluded middle - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "excluded middle" is defined.
		EXCLUDED MIDDLE : Irivng Hexham's Concise Dictionary of Religion [home, info]
		Phrases that include excluded middle: law of excluded middle, excluded middle law of
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=excluded+middle (114 words)

	Why abandon logic? -- Ben's Message Board (Site not responding. Last check: 2007-11-07)
		No, it is not a fallacy any more than the law of noncontradiction is a fallacy.
		Either the universe begins to >>>exist or it does not (law of excluded middle).
		>> >>The law of excluded middle also happens to be an >>either or fallacy > >No, it is not a fallacy any more than the law of >noncontradiction is a fallacy.
	www.voy.com /22190/4864.html (1509 words)

	Loving God with all your mind: logic and creation
		The Law of Non-Contradiction prevents both premises being true, while the Law of Excluded Middle points out that a pair of contradictory premises exhausts all possibilities.
		An example of the fallacy of affirming the consequent is using verified predictions as ‘proof’ of a scientific law.
		This can be shown by the Law of Excluded Middle: either things were made (creation) or they weren’t (evolution).
	www.answersingenesis.org /tj/v12/i2/logic.asp (6980 words)

	[The Law of Excluded Middle] (Site not responding. Last check: 2007-11-07)
		You lean into his touch, stretch out on the couch and turn your face downward, feel rough denim against your lips that are somehow already tender and swollen long before you actually push yourself up and press your mouth into JC's smile.
		Sometimes you wake up in the middle of the night.
		Sometimes you get scared because you can't hear JC at all and you're not sure if he's alive.
	www.illuminations.nu /justsopretty/nfic/middle.html (5469 words)

	The Subjunctive Conditional Law of Excluded Middle
		I will write “p·®q” for the subjunctive conditional “were p true, then q would be true.” The subjunctive conditional law of excluded middle (SCLEM) is then:
		Note that SCLEM does not follow in any obvious way from the ordinary law of excluded middle (LEM) which only gives us the tautologous claims that (p·®q) or ~(p·®q) and that p·®(q or ~q). I will assume throughout this article that the ordinary LEM is true.
		,… all be ~q and observe that from the ordinary LEM it follows that p·®(q
	www.georgetown.edu /faculty/ap85/papers/SCLEM.html (1100 words)

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