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	Vacuous truth - Wikipedia, the free encyclopedia
		Informally, a logical statement is vacuously true if it is true but doesn't say anything; examples are statements of the form "everything with property A also has property B", where there is nothing with property A. It is tempting to dismiss this concept as vacuous or silly.
		Vacuous truth is usually applied in classical logic, which in particular is two-valued, and most of the arguments in the next section will be based on this assumption.
		There are however vacuous truths that even most mathematicians will outright dismiss as "nonsense" and would never publish in a mathematical journal (even if grudgingly admitting that they are true).
	en.wikipedia.org /wiki/Vacuous_truth (2168 words)

	Vacuous truth -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		Vacuous truth should be compared to ((logic) a statement that is necessarily true) tautology, with which it is sometimes conflated.
		Vacuous truth is usually applied in (Click link for more info and facts about classical logic) classical logic, which in particular is two-valued, and most of the arguments in the next section will be based on this assumption.
		Vacuous truths occur commonly in (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics.
	www.absoluteastronomy.com /encyclopedia/v/va/vacuous_truth.htm (1865 words)

	Stanford Semantics and Pragmatics Workshop
		The data suggest that while classical logic is only concerned with the preservation of truth (from premises to a conclusion,) more is required for an inference pattern to be plausible in natural-language reasoning.
		The main part of the talk is concerned with the question of how to define the semantic values of conditionals in the familiar possible-worlds semantics in such a way as to exploit the merits of the probabilistic approach.
		An alternative reaction is to abandon the notion that conditionals ever have truth values, claiming instead that they are used solely as statements about beliefs (Adams, 1975 and elsewhere.) Both of those approaches are plagued by a number of shortcomings.
	www-linguistics.stanford.edu /semgroup/archive/2000/kaufmann.html (785 words)

	vacuous truth (Site not responding. Last check: 2007-11-06)
		Informally, a logical statement is vacuously true if it is true but doesn't say anything; examples are statements of the form "everything with property A also has property B", where there is nothing with property A. Table of contents
		Vacuous truth should be compared to tautology, with which it is sometimes conflated.
		First, if we were to make the general declaration that statements like S are always false, then, using a truth table, we could show that P ⇒ Q is logically equivalent to not(P and not(Q)).
	www.yourencyclopedia.net /vacuous_truth.html (1574 words)

	The Correspondence Theory of Truth
		Although the truth that the cat is on the mat does not resemble the cat or the mat (the truth doesn't smell, etc.), it does resemble the fact that the cat is on the mat.
		Molecular truths are not assigned any matching facts: strictly speaking, they do not correspond to facts at all; but their truth-values are explained in terms of logical structure and correspondence of atomic constituents.
		Truth for singular sentences, consisting of a name and an arbitrarily complex predicate, is defined thus: A singular sentence is true iff the object denoted by the name satisfies the predicate.
	plato.stanford.edu /entries/truth-correspondence (7677 words)

	When is truth vacuous? Is infinity a bunch of nothing?
		Clearly, Dan's definition of vacuous truth--which is implied in his clever "(p and (p-->q is vacuously true) requires that q is true)--is the same as the definition I suggest.
		That is, in a vacuously true statement of this form it is irrelevant whether q is true or not.
		Vacuous truth in the sense that John mentions can be seen from tautologies such as all x e X(x e X) and E!x e X(x' e X) [where E is the existential quantifier and x' means a unique element].
	www.geocities.com /n_fold/vactruth.html (4095 words)

	Vacuous truth (Site not responding. Last check: 2007-11-06)
		is vacuously true since there are no inside a loaf of bread; here property is "being an elephant inside a loaf bread" and property B is "being pink".
		Vacuous truth is usually applied in classical logic which in particular is two-valued and of the arguments in the next section be based on this assumption.
		Avoidance of such paradox is the impetus the development of non-classical systems of logic relevant logic and paraconsistent logic which refuse to admit the validity one or two of the axioms of classical logic.
	www.freeglossary.com /Vacuously_true (1656 words)

	The Identity Theory of Truth
		The simplest and most general statement of the identity theory of truth is that when a truth-bearer (e.g., a proposition) is true, there is a truth-maker (e.g., a fact) with which it is identical and the truth of the former consists in its identity with the latter.
		But since both true and false judgments are equally composed of real constituents, truth would not be distinguished from falsehood by being identical with reality; an identity theory of truth is thus unavailable on this view of judgment because it would be rendered vacuous by being inevitably accompanied by an identity theory of falsehood.
		This allows his identity theory of truth to be accompanied by a non-identity theory of falsehood, since he can account for falsehood as a falling short of this vast judgment and hence as an abstraction of part of reality from the whole.
	plato.stanford.edu /entries/truth-identity (2033 words)

	A Kripkean Account of Vacuous Names
		Vacuous names do not have an actual existing object for a referent, and therefore, seemingly could not be named through ostension or through description.
		In order to account for vacuous names, all one has to do is trace the name down to its initial baptism: the naming of something need not have an actual existing object for a referent to be treated as a rigid designator or to be used and understood in a historical context.
		Vacuous names are those groups of word which are names and yet have no actual existing referent in the world.
	artsweb.uwaterloo.ca /~pthurley/index/kripke.html (2388 words)

	Vacuous truth (Site not responding. Last check: 2007-11-06)
		The statement "0 mathematicians can change a is not vacuously true (or indeed true at the lightbulb joke "in a group of 0 mathematicians one of them can change a lightbulb" is vacuously true.
		Second picking "true" as the truth value many mathematical propositions that people tend to are true come out as true.
		There are however vacuous truths that even mathematicians will outright dismiss as " nonsense " and would never publish in a journal (even if grudgingly admitting that they true).
	www.freeglossary.com /Vacuous_truth (1656 words)

	Vacuous truth : Vacuously true (Site not responding. Last check: 2007-11-06)
		Informally, a logical statement is vacuously true if it is true but doesn't really say anything.
		is vacuously true; it is true, but there is really no consequence of it being true, since there are no elephants inside any loaves of bread.
		Such logics have been studied, such as relevant logic, but there are a number of advantages to the classical approach, such as represententing logical statements with a boolean algebra.
	www.wordlookup.net /va/vacuously-true.html (971 words)

	Search for Vacuous Truth - WordIQ.com (Site not responding. Last check: 2007-11-06)
		Vacuous truth is usually applied in classical logic, which in particular is two-valued, and most of the...
		Vacuous truth is usually applied in classical logic, which in particular is two-valued, and most of the arguments in the...
		Vacuous truth is usually applied in classical logic, which in particular is...
	www.wordiq.com /web/vacuous+truth.html (535 words)

	Tim Riffe (Site not responding. Last check: 2007-11-06)
		For those who think that language is the key to unlocking the truth about our minds and the rest of the world, creating a system whereby the meanings of linguistic expressions can be known with certainty is an activity worthy of investing much time and energy.
		Truth conditions, may be able to provide certain meanings for words and then derive certain meanings for sentences from these words.
		We might say that the meanings of sentences are dependant upon the meanings of words because without words and their meanings (or truths) there would be no sentences, and so sentences would be unable to have meanings because they would not exist.
	www-personal.umich.edu /~triffe/truthconditions.htm (1684 words)

	sciforums.com - A Rational Explanation of the Trinity
		"'The truth is the truth' is true" is a part of the set of truths, since it is true, but only in a tangencial way, as far as it doesn't need any other truth as a fundament and it exists necessarily.
		In an infinite succession of eternal truths (since the nature of the truth as not contradiction is immutable), the last truth, that at the same time is the first one, guarantees the coherence between all of them.
		If there were infinite truths and, nevertheless, we were lack of last truth, we could not affirm that “the truth is the truth”, since every truth links to another one, none that is not over all of them is capable of embrace them at the same level.
	www.sciforums.com /showthread.php?t=40880 (8799 words)

	"Intensional" Aspects of Names in Russell and Frege
		Concerning the latter, if the means by which a name indicates its object is irrelevant, then all vacuous names — expressions whose grammatical form makes it seem that they denote an object, yet in fact fail to do so — must be, in some sense, equivalent.
		[14] However, when such propositions involve indirect speech — the discussion of one proposition in another where it is “indifferent to the truth of the whole whether the subordinate clause is true or false” — this principle seems to break down.
		To create this basic level, Russell introduces the notion of acquaintance: we are acquainted with certain entities, and those entities with which we are not acquainted can, after a sufficient amount of analysis, be expressed in descriptions composed only of entities with which we are acquainted.
	www.stevesachs.com /papers/paper_frege.html (4339 words)

	Stand to Reason Commentary - Bashing Catholic Bashers
		It only happens when specific issues of truth are raised, articulated in a clear way and challenged based on our understanding of authority, sound reasoning and clear thinking.
		This kind of discourse is the traditional motif for clarifying truth and error.
		It's a sorry state of affairs when any attempt to separate truth from error in the public arena is labeled bashing.
	str.org /free/commentaries/theology/cathbash.htm (771 words)

	songsinthenight (Site not responding. Last check: 2007-11-06)
		Popper wants to establish truth as the goal of science, not because he thinks we can reach it, but because seeking truth provides boundaries, between which the scientific endeavor can function successfully.
		For it is only via the search for truth that we may become aware of and hope to learn from our mistakes.
		Scientists can be described as seeking truth, not because they believe they can find it, but because they hope that in the process of searching they would be able to lessen the sum of their errors.
	www.homestead.com /songsinthenight/popper.html (806 words)

	notes on "Truth by Convention"
		"a definition is not a premise to a theory", truths involving defined terms are abbreviations of truths not involving those terms.
		The notion of occuring vacuously and that of vacuous variant are defined (without being related to any antecedent tradition).
		A vacuous variant of a sentence is one in which some vacuously occurring term has been changed.
	www.rbjones.com /rbjpub/philos/bibliog/quine36.htm (686 words)

	Final Exam Theory Quiz: Answers
		If you thought (c) was vacuously true, it was probably because you know that in a Tarski world, no two blocks can be in the same column and same row simultaneously, because that would put them in the same square, which is impossible.
		It is a logical truth that objects are the same size if one of them is neither larger nor smaller than the other, but this depends on the meanings of the predicates Larger, Smaller, and SameSize, and not just on the connectives and quantifiers.
		But it is not a logical truth, since outside of Tarski worlds there are more gradations of size, and so one can have 3 objects that differ in size but all of which are small.
	faculty.washington.edu /smcohen/120/TheoryQuizFinalAnswers.htm (3684 words)

	[Phil-logic] 'Tautologous' and' Vacuous' (Site not responding. Last check: 2007-11-06)
		But redundancy is also a tractable issue when there are 2^2^n F's as the truth table resultant.
		As it is impossible to pack an infinitely wide bandwidth into the measurable limitations of our five senses, so they have had to take mind of a sixth sense, which they have named 'intuition'.] It is so bad that apparently we have not even got an English word to do the job.
		I now propose; Vacuous: A formula which, given the truth-table definitions of the connectives, is False under every interpretation of its constituent formulas.
	philo.at /pipermail/phil-logic/2004-October/005110.html (343 words)

	[No title]
		Foot note 3_1 the ontology necessary for Lewis' theory is qualitatively unparsimonious: It «is committed to the unicorns, to the gods, to the ghosts and to the qualia which occur in other possible worlds.» That is to say, it is committed to that which in the actual world would be regarded as impossible.
		Foot note 3_3 and equally clear that there are many timelines that could satisfy the antecedent of (2) and (3).
		The real task we face, of course, is explicating the middle case -- subjunctive conditionals such as (2) and (3) which have non-vacuous truth values -- and to this the remainder of this paper is devoted.
	www.sorites.org /Issue_05/item4.htm (938 words)

	Plato and Cantor vs. Wittgenstein and Brouwer
		Many mathematicians would assert that if a truth value is unknowable, the issue of a priori truth value is irrelevant.
		In the case of the continuum hypothesis, we see a case where a logico-mathematical statement has a 0 truth value, validating the warning against unrestricted use of the principle of the excluded middle.
		Though the truth value remains forever undecidable, it is presumed to have an a priori truth value.
	www.angelfire.com /az3/nfold/plato.html (4945 words)

	vacuous - OneLook Dictionary Search
		Vacuous : Online Plain Text English Dictionary [home, info]
		Phrases that include vacuous: vacuous quantification, no vacuous application principle, vacuous movement hypothesis, vacuous truth
		Words similar to vacuous: empty, inane, asinine, fatuous, hollow, mindless, vacuously, vacuousness, more...
	www.onelook.com /?w=vacuous&ls=all (188 words)

	September 2000 Columns Magazine - Letters to the Editor
		In discussing the hiring of the new football coach, McCormick repeats that in hiring "a chemist or a football coach...
		In other words, all the rhetoric about the "equal opportunities" in the search for truth and beauty and ethics is largely vacuous.
		The truth is that the university, like society in general, is governed by the law of supply and demand.
	www.washington.edu /alumni/columns/sept00/letters0900.html (684 words)

	vacuous - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "vacuous" is defined.
		vacuous : Compact Oxford English Dictionary [home, info]
		vacuous : The American Heritage® Dictionary of the English Language [home, info]
	www.onelook.com /?w=vacuous&ls=all (188 words)

	Shark Blog: John Kerry: The man and the myths
		Kerry was asked what he would want people to remember about his presidency.
		Speaking of truth, as a mathematician I would say that the last statement is a vacuous truth.
		Let me guess...you're saying the statement is vacuous because "it" (the Kerry administration) did not exist and will not exist?
	www.usefulwork.com /shark/archives/002922.html (2351 words)

	[No title]
		Necessary truth is vacuous truth reflecting linguistic conventions (e.g., "either it will rain or it won't").
		But conventional, vacuous truths don't make a "real difference" in life.
		It is possible that we could learn them through divine illumination (Plato, Augustine).
	www.andrew.cmu.edu /user/kk3n/religionclass/ontological.html (976 words)

Vacuous truth : Vacuously true (Site not responding. Last check: 2007-11-06)

Vacuous truth : Vacuously true

Vacuous truth : Vacuously true
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