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Topic: Logical necessity

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	Modal logic - Wikipedia, the free encyclopedia
		Logics for handling a number of other ideas, such as eventually, formerly, can, could, might, may, must are by extension also called modal logics, since it turns out that these can be treated in similar ways.
		Logical possibility is a form of alethic possibility; (4) makes a claim about whether it is possible for a mathematical truth to have been false, but (3) only makes a claim about whether it is possible that the mathematical claim turns out false, for all Jones knows, and so again Jones does not contradict himself.
		Significantly, modal logics can be developed to accommodate most of these idioms; it is the fact of their common logical structure (the use of "intensional" or non-truth-functional sentential operators) that make them all varieties of the same thing.
	en.wikipedia.org /wiki/Modal_logic (2657 words)

	Blogger: Email Post to a Friend
		Logical necessity is a familiar concept, and it needs no introduction (let “2+2 = 4” and “no proposition is both true and false” stand as our paradigmatic logically necessary propositions); accidental necessity will require some exposition, however.
		Its fixity is not as strong as that of logical necessity, however—while a logically necessary proposition is necessary for any time t in all possible worlds, facts about the facts acquire their necessity or fixity over time.
		Logical necessity “transfers over” entailment to the consequent; indeed, that logical necessity is closed under entailment is not a controversial thesis.
	www.blogger.com /email-post.g?blogID=7995981&postID=111336902316828834 (2008 words)

	[No title]
		The main criticism of the PM approach to logical truth is that it generates a notion of logical necessity that is too weak.
		However, Swinburne's conflation of logical possibility with coherence results in psychologizing logic by making the logical necessity of a sentence p consist of the fact that p must be thought of as true.
		In other words: a sentence is logically necessary at a world w only if it remains true at w on all possible uses to its non-logical terms (whether this is both necessary and sufficient for logical truth at a world, as is maintained by the PM approach, is a point of contention).
	www.sorites.org /Issue_04/item4.htm (5613 words)

	[No title]
		In discussing the nature and foundation of logical necessity Georg Henrik von Wright fights against a tendency to mystify necessity which Wittgenstein was fighting in criticizing the prejudice of the "crystalline purity of logic" and the idea of the "hardness of the logical must".
		The necessity attributed to the principles or laws of logic is not founded on any preformed logical structure of the world but stems, von Wright argues, from an attitude we take to some propositions.
		Logical truth is defined in terms of logical form (without mentioningthis notion) without employing sets of models and the concept of truth in a model.
	fas-philosophy.rutgers.edu /~sider/teaching/modality_bib.htm (13258 words)

	Accidental Necessity and Logical Determinism
		It is clearly not logically, i.e., metaphysically, necessary that Socrates drank hemlock.
		And since it seems logically possible for a proposition to be a law of nature at one time and not at some later time, this feature of accidental necessity distinguishes it from both physical and causal necessity.
		But if this is so, then, given (B), the necessity of the past-tense proposition that it was the case that Katie will wash her car at T entails our inability to affect the present truth-value of the proposition that when T is present, Katie is washing her car.
	www.nd.edu /~afreddos/papers/anld.htm (8522 words)

	[No title]
		Logical modality examines the possible truth or necessity of a proposition according to logic.
		Logical necessity evaluates the truth of a proposition for all possible circumstances.
		The logical expression asserts that the proposition is compatible with the laws of logic, and is not necessarily false, regardless of whether or not the proposition is in fact true.
	www.ku.edu /~pyersqr/Ling331/Kearns3.htm (3845 words)

	Fatalism
		It may be argued for in various ways: by appeal to logical laws and metaphysical necessities; by appeal to the existence and nature of God; by appeal to causal determinism.
		If any state of affairs is sufficient for, though logically unrelated to, the occurrence of some further condition at the same time or any other time, then the former cannot occur without the latter occurring also.
		So, if it is logically impossible for someone to have infallible knowledge that Jones will mow the lawn and for Jones to have the power to refrain, it is no imperfection in God if he lacks such knowledge.
	plato.stanford.edu /entries/fatalism (8228 words)

	John Dewey [Internet Encyclopedia of Philosophy]
		The basis of Dewey's discussion in the Logic is the continuity of intelligent inquiry with the adaptive responses of prehuman organisms to their environments in circumstances that check efficient activity in the fulfillment of organic needs.
		Logical form, the specialized subject matter of traditional logic, owes its genesis not to rational intuition, as had often been assumed by logicians, but due to its functional value in (1) managing factual evidence pertaining to the problematic situation that elicits inquiry, and (2) controlling the procedures involved in the conceptualized entertainment of hypothetical solutions.
		Traditional views in logic had held that the logical import of propositions is defined wholly by their syntactical form (e.g., "All As are Bs," "Some Bs are Cs").
	www.utm.edu /research/iep/d/dewey.htm (5925 words)

	[No title]
		Logical possibility is the property of not contradicting the laws of logic.
		Boundary conditions are logically possible in which photons are set in motion without having been emitted from anything, and which converge in shrinking spheres on an anti-emitter.
		Indeed, all of the conclusions of logic are binding on all possible minds, as logic is in fact the study of valid inference.
	humanknowledge.net /HumanKnowledge.txt (17891 words)

	The Possibility of Necessity
		The things that are logically necessary (LN) are excluded from this discussion because they constitute a meta-level: they result from the true theorems in the logical systems within which LP, PP and PA reside.
		A metaphysical necessity is an objective one and is stronger than a logical necessity.
		A logical necessity, therefore, would be a logical proposition which is true in all the logically possible worlds.
	samvak.tripod.com /necessity.html (1267 words)

	Brainstorms: Necessity and Design
		Of course we should also remember the analytic truths that are based on logical (tautological) necessity, like: "It will rain or it won't rain tomorrow." In this context it occurred to me that it might as well be possible to classify designs according to what kind of necessity they employ.
		Charles Peirce subdivided Kant's category of Necessity into the laws of logical necessity, physical necessity, and intentional or subjective necessity.
		As forms of necessity they represent the rules and guideposts that constraint possibility (we might call them the definitory rules of design).
	www.iscid.org /boards/ubb-get_topic-f-6-t-000044.html (470 words)

	Jan Dejnozka Second Book - Bertrand Russell on Modality and Logical Relevance. Ashgate, 1999. Avebury Series in ...
		This is in the same sense in which his logic functions as arithmetic, explicitly using classes of classes as logical substitutes for numbers.
		Last, Dejnozka argues that John Maynard Keynes inspired the 1912 Russell to adopt a theory of probability as degrees of logical relevance, and that Keynes was inspired in turn by the 1903 Russell and by the legal concept of logical relevance, and ultimately by Aristotle's theory of induction.
		Thus, the notions of (logical) necessity and possibility are not 'fundamental notions'....On this basis, Dejnozka develops a higher level of modality, where the quantification scope extends to the predicates yielding what Russell calls 'fully general propositions'....
	www.members.tripod.com /~Jan_Dejnozka/book2.html (1684 words)

	20th WCP: Translation, Quotation and Truth
		Term recurrence is essential to logical truth, because it's the sole strictly syntactic device enforcing necessary coextension of terms, thereby securing necessary truth in a sentence appropriately structured by logical constants.
		Synomic intercepting of logical sentences embedded in extralogical sentences (Jess said "A lawyer is a lawyer"; RW believes it's a logical truth that a lawyer is a lawyer) can convert a contingent truth into a falsehood.
		Synomic interceptions of (object level) logical sentences are simply untranslatable (except by importing the terms) since their factual content is only an artifact of internotational contingencies.
	www.bu.edu /wcp/Papers/Math/MathWert.htm (3089 words)

	Theology Today - Vol 20, No. 2 - July 1963 - CRITICSCORNER - Rationale of the Ontological Proof
		It is that I overlook the distinction between two kinds of necessity, logical and real (he says, "factual").
		Nor does the logical necessity of "divinity exists" entail reversion to the first form of argument (which I have admitted is unsound).
		In other words, he supposes that the real necessity of the divine existence could be correctly asserted in a proposition which could have been false.
	theologytoday.ptsem.edu /jul1963/v20-2-criticscorner3.htm (1690 words)

	[No title]
		Nomic Necessity 3: P(Q is nomically necessary just in case it is true in the actual world and in every world that shares the same physical and psychophysical laws as the actual world.
		Laws, Natural Necessity and Empirical Generalization I wish now to examine the notion of “laws” needed for a notion of “nomic necessity”, and to consider whether what is required is stronger than counterfactual-supporting empirical generalizations.
		However, with the addition of such a metric, a model of counterfactuals shares with a model of necessity and possibility the feature that it should be determinate, in the sense that the resources of the model are adequate to determining the truth-value of modal statements.
	shorst.web.wesleyan.edu /mwn/Nov02/17_NaturalNecessity.doc (9017 words)

	CATHOLIC ENCYCLOPEDIA: Existence of God
		A self-existing world would exist of absolute necessity and would be infinite in every kind of perfection; but of nothing are we more certain than that the world as we know it, in its totality as well as in its parts, realizes only finite degrees of perfection.
		It is a mere contradiction in terms, however much one may try to cover up and conceal the contradiction by an ambiguous and confusing use of language, to predicate infinity of matter or of the human mind, and one or the other or both must be held by the Pantheist to be infinite.
		Rational theism is a necessary logical basis for revealed religion; and that the natural knowledge of God and natural religion, which Catholic teaching holds to be possible, are not necessarily the result of grace, i.e.
	www.newadvent.org /cathen/06608b.htm (4611 words)

	quine: terms explained (Site not responding. Last check: 2007-10-22)
		An example of logical necessity is the statement that "All bachelors are unmarried." This statement is necessarily true because that is how we define the word bachelors, as men who are unmarried.
		A proposition is logically necessary if it is not logically possible for it to be false.
		It is often thought that analytic statements must be logically necessary (see analytic statements).
	www.rit.edu /~quine/necessity.html (177 words)

	Ayer on Laws
		The chains which logic puts upon nature are purely formal: being formal they weigh nothing, but for the same reason they are indissoluble.” (Curd 1998 pg.
		O” is analytic, known via the rules of logic and the meaning of the terms.
		This is the crux of the reply to the conventionalist claim: we need empirical content for anything remotely resembling science, but the laws of logic have no empirical content and in part receive their necessity because of this lack of empirical content.
	ucsub.colorado.edu /~hafere/PHIL1400/Ayer.htm (1207 words)

	Causality and necessity in Islamic thought
		Discussions of causality and necessity in Islamic thought were the result of attempts to incorporate the wisdom of the Greeks into the legacy of the Qur''an, and specifically to find a philosophical way of expressing faith in the free creation of the universe by one God.
		Rather, the terms were those introduced by 'the philosophers', turning on the necessity of the connections between events in nature, specifically between those which we recognize as causes and their effects.
		Clearly these connections could not be akin to logical necessity, or there would be no room whatsoever for miracles like the 'descent' of the Qur'an; yet if the universe is the result of God's free action and not of necessity, the creator will continue to be free to act within creation.
	www.muslimphilosophy.com /ip/rep/H005.htm (1906 words)

	Accidental Necessity and Power over the Past
		By investigating accidental necessity in some detail, we will be able to come to a deeper understanding of the issues involved in the question of whether we have power over the past.
		Also, since it appears to be logically possible for a proposition to be physically necessary (or a law of nature) at one moment and not at some later moment, this feature of accidental necessity distinguishes it from both physical and causal necessity.
		Undergraduates, when first confronted with an argument for logical (or theological) determinism based on the necessity of the past, frequently respond that it is now true (or: God now knows) that David will be in Chicago at T because it will be the case at T that David is in Chicago.
	www.nd.edu /~afreddos/papers/anpp.htm (7252 words)

	MainFrame: Possible Worlds
		This parallels the connection between necessity (which is defined in terms of the former) and analyticity (or validity), which can be defined in terms of the latter.
		The semantics of the logical constants is fixed by the semantics of first order logic, but not that of other symbols, which are regarded as completely uninterpreted.
		More generally the notion of necessity flowing from this definition of possible world will fail to encompass sentences whose truth can be seen to follow from the definitions of the terms which they contain.
	www.rbjones.com /rbjpub/philos/metap/metap004.htm (1798 words)

	A selection of papers on Ontology and the Theory of
		Remarkable in its analytic power for both ontology and logic is the here developed Particularized Predicate Logic (PPL), the logic inherent in the realist version of the doctrine of unit or individuated predicates.
		Leaving logical concepts and material ontology aside, the resulting 32 categories in 13 families range from the obvious (identity/difference, existence/nonexistence) through the fairly obvious (part/whole, one/many, sequential order) and the surprisingly familiar (illocutionary modes, mass/count, indexical/descriptive) to the controversial (moment/fundament, transparent/opaque) and the arcane (modes of class delimitation, taxonomic rank, aspects of designators).
		The article provides an interpretation of Husserl's claim that there are metaphysical necessities which are necessarily recognized by the human mind on the basis of Husserl's well-known distinction between the meanings of mental acts and their objective correlates.
	www.formalontology.it /onto_papers.htm (5312 words)

	Wittgenstein on Logical Necessity (Site not responding. Last check: 2007-10-22)
		Such necessity is also attributed by philosophers to logical inferences.
		logical necessity — but the trouble is that it is nothing more than a
		"logical" necessity, that the coercion or inexorability attributed to logic
	faculty.frostburg.edu /phil/forum/WittgMath.htm (4097 words)

	Times & Seasons » Benevolent Theodicy: the Logical Necessity of Eternal Progression
		From that kind of logic, it simply wouldn’t be proper for (former) mortals to attain that kind of stature.
		Matt, it is not that your argument doesn’t work, it is just that it is based on a lot of assumptions that aren’t logically necessary.
		God is perfect in knowledge and power, and if he is omnibenevolent and omnipotent, he will necessarily help those he loves increase in knowledge and power.
	www.timesandseasons.org /?p=913 (2535 words)

	(3) Necessity = Broadly logical necessity (Site not responding. Last check: 2007-10-22)
		If the necessity operator is interpreted 'it is logically necessary that' or 'in all logically possible worlds it is true that' then the second premiss of the argument is false.
		For there are many possible worlds in which, say, Marilyn remains on the straight and narrow, with the upshot that God foreknows that she will remain on the straight and narrow, and God does not know (because it is not true) that she will consent to do evil.
		In general, as our argument itself shows, it is logically necessary that God know that p only if it is logically necessary that p.
	www.angelfire.com /oh4/webjourney/node46.html (134 words)

	Logical Necessity and the Foundations of Mathematics
		This paper presents at greater length ideas on Logic and the foundations of Mathematics first approached in my paper "Logical foundations and formal verifications".
		It was not my intention in that paper to seriously address any philosophical issues, but the formal system which formed the main subject of the paper could not be justified as a foundation system without an appeal to philosophical ideas which had guided me to it.
		This induces a desire to economise by bringing together programming language type system and logical type systems, and in turn this unification makes demains upon the type theory which cannot be met in classical systems.
	www.rbjones.com /rbjpub/rbjcv/papers/wp51.htm (1400 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		To determine if a sentence is a logical truth, it must be true in all circumstances.
		A logical possibility is always a tautological possibility but not vice versa.ó´`¨Exercise¡ þ¨ÝCreate sentences that are logically possible but are not TW-possible tautologically possible but are not logically possible not tautologically possible.
		If two sentences are logically equivalent, then they are TW-equivalent but not vice versa.ó·d¨Exercise¡ þ¨ÙCreate pairs of sentences that are TW-equivalent but are not logically equivalent, logically equivalent but are not TT-equivalent, not TT-equivalent.
	www.cs.pitt.edu /~utp/cs1502/notes/s06-logic-of-boolean-connectives.ppt (1214 words)

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