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| A '''free logic''' is a [[logic]] with fewer [[existential clause|existential]] presuppositions than classical logic. Free logics may allow for [[Term (first-order logic)|terms]] that do not denote any object. Free logics may also allow [[structure (mathematical logic)|models]] that have an [[empty domain]]. A free logic with the latter property is an '''inclusive logic'''.
| | == month after month == |
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| == Explanation ==
| | In the slightly squat, it seems poised to take off. And in this 'golden beast god' statue back, Luo Feng was lying on the scales, eyes narrowed, the air in front of him is a myriad of complex Arcanum golden thread constantly flowing.<br><br>seemingly laid-back millions of years and no two years of penance,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_25.htm オークリー レディース サングラス], in fact Luo Feng is caught in a particular state.<br><br>a million years have been years of fellowship of God's beast Arcanum eight maps,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_69.htm オークリーサングラス カスタム], each piece Arcanum figure represents a 'golden beast God' on the one hand, eight Arcanum figure ...... Luo Feng seems to be in order to watch every day God's golden on each side of the beast,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_56.htm オークリーサングラス画像], day after day,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_68.htm オークリー サングラス イチロー], month after month,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_27.htm オークリー サングラス 店舗], year after year ......<br><br>years continued to tick away.<br><br>Luo Feng has been studying Arcanum figure eight,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_22.htm オークリー サングラス 種類], long years of the beast as if God always and gold together.<br><br>in the moment ,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_36.htm オークリー サングラス 登山]......<br><br>experienced 180 million years of Arcanum Figure practice, he suddenly forget his own,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_35.htm オークリー野球サングラス], if he is at this moment ...... beast God! |
| | | 相关的主题文章： |
| In [[classical logic]] there are theorems that clearly presuppose that there is something in the [[domain of discourse]]. Consider the following classically valid theorems. | | <ul> |
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| :1. <math> \forall xA \rightarrow \exists xA</math>
| | <li>[http://www.gkybi.com.cn/plus/feedback.php?aid=398 http://www.gkybi.com.cn/plus/feedback.php?aid=398]</li> |
| :2. <math> \forall xA \rightarrow A(r/x)</math> (where r does not occur free for x in A and A(r/x) is the result of substituting r for all free occurrences of x in A) | | |
| :3. <math> Ar \rightarrow \exists xAx</math> (where r does not occur free for x in A)
| | <li>[http://hanjun123.com/forum.php?mod=viewthread&tid=376596&fromuid=50247 http://hanjun123.com/forum.php?mod=viewthread&tid=376596&fromuid=50247]</li> |
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| A valid scheme in the theory of [[First-order_logic#Equality_and_its_axioms|equality]] which exhibits the same feature is
| | <li>[http://www.adsrack.com/article/56274/minnesota-state-remains/index.cgi http://www.adsrack.com/article/56274/minnesota-state-remains/index.cgi]</li> |
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| :4. <math> \forall x(Fx \rightarrow Gx) \land \exists xFx \rightarrow \exists x(Fx \land Gx)</math> | | </ul> |
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| Informally, if F is '=y', G is 'is Pegasus', and we substitute 'Pegasus' for y, then (4) appears to allow us to infer from 'everything identical with Pegasus is Pegasus' that something is identical with Pegasus. The problem comes from substituting nondesignating constants for variables: in fact, we cannot do this in standard formulations of [[first-order logic]], since there are no nondesignating constants. Classically, ∃x(x=y) is deducible from the open equality axiom y=y by particularization (i.e. (3) above).
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| In free logic, (1) is replaced with
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| :1b. <math> \forall xA \land E!t \rightarrow \exists xA</math>, where E! is an existence predicate (in some but not all formulations of free logic, E!t can be defined as ∃y(y=t)) | |
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| Similar modifications are made to other theorems with existential import (e.g. the Rule of Particularization becomes (Ar → (E!r → ∃xAx)).
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| [[Axiom]]atizations of free-logic are given in [[Jaakko Hintikka|Hintikka]] (1959),<ref>Jaako Hintikka (1959). Existential Presuppositions and Existential Commitments. Journal of Philosophy 56 (3):125-137.</ref> [[Karel Lambert|Lambert]] (1967), [[Theodore Hailperin|Hailperin]] (1957), and [[Richard L. Mendelsohn|Mendelsohn]] (1989).
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| ==Interpretation==
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| [[Karel Lambert]] wrote in 1967:<ref>''Free Logic and the Concept of Existence'' by Karel Lambert, Notre Dame Journal of Formal Logic, V.III, numbers 1 and 2, April 1967</ref>
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| "In fact, one may regard free logic... literally as a theory about singular existence, in the sense that it lays down certain minimum conditions for that concept." The question that concerned the rest of his paper was then a description of the theory, and to inquire whether it gives a necessary and sufficient condition for existence statements.
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| Lambert notes the irony in that [[Willard Van Orman Quine]] so vigorously defended a form of logic that only accommodates his famous dictum, "To be is to be the value of a variable," when the logic is supplemented with [[Bertrand Russell|Russellian]] assumptions of [[Theory of Descriptions|description theory]]. He criticizes this approach because it puts too much ideology into a logic, which is supposed to be philosophically neutral. Rather, he points out, not only does free logic provide for Quine's criterion—it even proves it! This is done by brute force, though, since he takes as axioms <math> \exists xFx \rightarrow (\exists x(E!Fx))</math> and <math>Fy \rightarrow (E!y \rightarrow \exists xFx)</math>, which neatly formalizes Quine's dictum. So, Lambert argues, to reject his construction of free logic requires you to reject Quine's philosophy, which requires some argument and also means that whatever logic you develop is always accompanied by the stipulation that you must reject Quine to accept the logic. Likewise, if you reject Quine then you must reject free logic. This amounts to the contribution that free logic makes to ontology.
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| The point of free logic, though, is to have a formalism that implies no particular ontology, but that merely makes an interpretation of Quine both formally possible and simple. An advantage of this is that formalizing theories of singular existence in free logic brings out their implications for easy analysis. Lambert takes the example of the theory proposed by [[Wesley C. Salmon]] and [[George Nahknikian]],<ref>George Nahknikian and Wesley C. Salmon, "'Exists' as a Predicate" ''Philosophical Review'' Vol. 66: 1957 pp. 535-542</ref> which is that to exist is to be self-identical.
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| ==See also== | |
| * [[Square of opposition]]
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| * [[Table of logic symbols]]
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| ==References==
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| {{reflist}}
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| * Lambert, Karel, 2003. ''Free logic: Selected essays.'' Cambridge Univ. Press.
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| *-------, 2001, "Free Logics," in Goble, Lou, ed., ''The Blackwell Guide to Philosophical Logic''. Blackwell.
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| * ------, 1997. ''Free logics: Their foundations, character, and some applications thereof.'' Sankt Augustin: Academia.
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| * ------, ed. 1991. ''Philosophical applications of free logic.'' Oxford Univ. Press.
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| * Morscher, Edgar, and Hieke, Alexander, 2001. ''New essays in free logic.'' Dordrecht: Kluwer.
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| == External links ==
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| *{{sep entry|logic-free|Free logic|John Nolt}}
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| {{DEFAULTSORT:Free Logic}}
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| [[Category:Non-classical logic]]
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month after month
In the slightly squat, it seems poised to take off. And in this 'golden beast god' statue back, Luo Feng was lying on the scales, eyes narrowed, the air in front of him is a myriad of complex Arcanum golden thread constantly flowing.
seemingly laid-back millions of years and no two years of penance,オークリー レディース サングラス, in fact Luo Feng is caught in a particular state.
a million years have been years of fellowship of God's beast Arcanum eight maps,オークリーサングラス カスタム, each piece Arcanum figure represents a 'golden beast God' on the one hand, eight Arcanum figure ...... Luo Feng seems to be in order to watch every day God's golden on each side of the beast,オークリーサングラス画像, day after day,オークリー サングラス イチロー, month after month,オークリー サングラス 店舗, year after year ......
years continued to tick away.
Luo Feng has been studying Arcanum figure eight,オークリー サングラス 種類, long years of the beast as if God always and gold together.
in the moment ,オークリー サングラス 登山......
experienced 180 million years of Arcanum Figure practice, he suddenly forget his own,オークリー野球サングラス, if he is at this moment ...... beast God!
相关的主题文章：