Results for 'weak law of the excluded middle'

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  1.  39
    Generalizations of the Weak Law of the Excluded Middle.Andrea Sorbi & Sebastiaan A. Terwijn - 2015 - Notre Dame Journal of Formal Logic 56 (2):321-331.
    We study a class of formulas generalizing the weak law of the excluded middle and provide a characterization of these formulas in terms of Kripke frames and Brouwer algebras. We use these formulas to separate logics corresponding to factors of the Medvedev lattice.
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  2.  28
    A cut-free gentzen-type system for the logic of the weak law of excluded middle.Branislav R. Boričić - 1986 - Studia Logica 45 (1):39-53.
    The logic of the weak law of excluded middleKC p is obtained by adding the formula A A as an axiom scheme to Heyting's intuitionistic logicH p . A cut-free sequent calculus for this logic is given. As the consequences of the cut-elimination theorem, we get the decidability of the propositional part of this calculus, its separability, equality of the negationless fragments ofKC p andH p , interpolation theorems and so on. From the proof-theoretical point of view, the (...)
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  3. The axiom of choice and the law of excluded middle in weak set theories.John L. Bell - 2008 - Mathematical Logic Quarterly 54 (2):194-201.
    A weak form of intuitionistic set theory WST lacking the axiom of extensionality is introduced. While WST is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up WST with moderate extensionality principles or quotient sets enables the derivation to go through.
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  4.  9
    Review: V. A. Jankov, Constructing a Sequence of Strongly Independent Superintuitionistic Propositional Calculi; V. A. Jankov, The Calculus of the weak "law of excluded Middle.". [REVIEW]Alfred Horn - 1972 - Journal of Symbolic Logic 37 (1):186-186.
  5.  22
    Jankov V. A.. Constructing a sequence of strongly independent superintuitionistic propositional calculi. English translation of XXXVII 206 by Yablonsky A.. Soviet mathematics, vol. 9 no. 4 , pp. 806–807.Jankov V. A.. The calculus of the weak “law of excluded middle.” English translation of XXXVII 206. Mathematics of the USSR—Izvestija , vol. 2 no. 5 , pp. 997–1004. [REVIEW]Alfred Horn - 1972 - Journal of Symbolic Logic 37 (1):186-186.
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  6.  14
    The algebraic significance of weak excluded middle laws.Tomáš Lávička, Tommaso Moraschini & James G. Raftery - 2022 - Mathematical Logic Quarterly 68 (1):79-94.
    For (finitary) deductive systems, we formulate a signature‐independent abstraction of the weak excluded middle law (WEML), which strengthens the existing general notion of an inconsistency lemma (IL). Of special interest is the case where a quasivariety algebraizes a deductive system ⊢. We prove that, in this case, if ⊢ has a WEML (in the general sense) then every relatively subdirectly irreducible member of has a greatest proper ‐congruence; the converse holds if ⊢ has an inconsistency lemma. The (...)
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  7.  19
    Wittgenstein on Weyl: the law of the excluded middle and the natural numbers.Jann Paul Engler - 2023 - Synthese 201 (6):1-23.
    In one of his meetings with members of the Vienna Circle, Wittgenstein discusses Hermann Weyl’s brief conversion to intuitionism and criticizes his arguments against applying the law of the excluded middle to generalizations over the natural numbers. Like Weyl, however, Wittgenstein rejects the classical model theoretic conception of generality when it comes to infinite domains. Nonetheless, he disagrees with him about the reasons for doing so. This paper provides an account of Wittgenstein’s criticism of Weyl that is based (...)
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  8. Laws of Non-Contradiction, Laws of the Excluded Middle, and Logics.Greg Restall - 2004 - In Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.), The law of non-contradiction : new philosophical essays. New York: Oxford University Press.
  9.  20
    On the law of the excluded middle.Alonzo Church - 1928 - Bulletin of the American Mathematical Society 34:75-78.
  10. Laws of Non-Contradiction, Laws of the Excluded Middle, and Logics.Greg Restall - 2004 - In Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.), The law of non-contradiction : new philosophical essays. New York: Oxford University Press.
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  11.  91
    Third possibilities and the law of the excluded middle.Roger Woolhouse - 1967 - Mind 76 (302):283-285.
  12.  60
    Intuitionistic modal logics incompatible with the law of the excluded middle.Dimiter Vakarelov - 1981 - Studia Logica 40 (2):103 - 111.
    In this paper, intuitionistic modal logics which do not admit the law of the excluded middle are studied. The main result is that there exista a continuum of such logics.
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  13. Wittgenstein and the Law of the Excluded Middle.Richard McDonough - 1975 - Dissertation, Cornell University
     
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  14.  8
    Navigating the Excluded Middle: The Jaina Logic of Relativity.Jeffery D. Long - 2023 - Studia Humana 12 (1-2):88-100.
    The Jaina tradition is known for its distinctive approach to prima facie incompatible claims about the nature of reality. The Jaina approach to conflicting views is to seek an integration or synthesis, in which apparently contrary views are resolved into a vantage point from which each view can be seen as expressing part of a larger, more complex truth. Viewed by some contemporary Jaina thinkers as an extension of the principle of ahiṃsā into the realm of intellectual discourse, Jaina logic (...)
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  15.  30
    Natural factors of the Medvedev lattice capturing IPC.Rutger Kuyper - 2014 - Archive for Mathematical Logic 53 (7):865-879.
    Skvortsova showed that there is a factor of the Medvedev lattice which captures intuitionistic propositional logic (IPC). However, her factor is unnatural in the sense that it is constructed in an ad hoc manner. We present a more natural example of such a factor. We also show that the theory of every non-trivial factor of the Medvedev lattice is contained in Jankov’s logic, the deductive closure of IPC plus the weak law of the excluded middle $${\neg p (...)
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  16.  27
    Undecidability of First-Order Modal and Intuitionistic Logics with Two Variables and One Monadic Predicate Letter.Mikhail Rybakov & Dmitry Shkatov - 2018 - Studia Logica 107 (4):695-717.
    We prove that the positive fragment of first-order intuitionistic logic in the language with two individual variables and a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals \ and \, where QKC is the logic of the weak law of the excluded middle and QBL and QFL are first-order counterparts of Visser’s basic (...)
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  17.  42
    Constructive Logic and the Medvedev Lattice.Sebastiaan A. Terwijn - 2006 - Notre Dame Journal of Formal Logic 47 (1):73-82.
    We study the connection between factors of the Medvedev lattice and constructive logic. The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov, logic). We discuss the relation between the weak law of the excluded middle and the algebraic notion of join-reducibility. Finally we discuss autoreducible degrees.
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  18.  26
    Excluded Middle versus Choice in a topos.Bernhard Banaschewski - 2005 - Mathematical Logic Quarterly 51 (3):282.
    It is shown for an arbitrary topos that the Law of the Excluded Middle holds in its propositional logic iff it satisfies the limited choice principle that every epimorphism from 2 = 1 ⊕ 1 splits.
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  19.  49
    The Law of Excluded Middle and the Problem of Idealism.Marian Przełecki - 1982 - Grazer Philosophische Studien 18 (1):1-16.
    The law of excluded middle is usually considered as intrinsically connected with the realistic standpoint and incompatible with the idealistic position. This is just what Ajdukiewicz claims in his critique of transcendental idealism. The analysis of Ajdukiewicz's argumentation raises the problem of validity of the law of excluded middle for vague (or incomplete) languages. The problem is being solved by differentiating between the logical (or ontological) and the metalogical (or semantical) law of excluded middle: (...)
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  20. The law of excluded middle and intuitionistic logic.Piotr Ukowski - 1998 - Logica Trianguli 2:73-86.
    This paper is a proposal of continuation of the work of C. Rauszer. The logic of falsehood created by her may constitute the starting point for construction of logic formalising reductive reasonings. The extension of Heyting-Brouwer logic to its deductive-reductive form sheds new light upon those classical tautologies which are rejected in intuitionism. It turns out that among HBtautologies there can be found all the classical ones. Some of them are characteristic for deductive reasoning and they are accepted by intuitionism. (...)
     
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  21.  19
    The Law of Excluded Middle and the Problem of Idealism.Marian Przełecki - 1982 - Grazer Philosophische Studien 18 (1):1-16.
    The law of excluded middle is usually considered as intrinsically connected with the realistic standpoint and incompatible with the idealistic position. This is just what Ajdukiewicz claims in his critique of transcendental idealism. The analysis of Ajdukiewicz's argumentation raises the problem of validity of the law of excluded middle for vague (or incomplete) languages. The problem is being solved by differentiating between the logical (or ontological) and the metalogical (or semantical) law of excluded middle: (...)
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  22. Frontiers of Conditional Logic.Yale Weiss - 2019 - Dissertation, The Graduate Center, City University of New York
    Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional (...)
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  23.  69
    The Law of Excluded Middle Is Synthetic A Priori, If Valid.Neil Tennant - 1996 - Philosophical Topics 24 (1):205-229.
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  24.  74
    The law of excluded middle and the axiom of choice.W. W. Tait - 1994 - In Alexander George (ed.), Mathematics and mind. New York: Oxford University Press. pp. 45--70.
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  25. Does the law of excluded middle require bivalence?Charles Sayward - 1989 - Erkenntnis 31 (1):129 - 137.
    Determining whether the law of excluded middle requires bivalence depends upon whether we are talking about sentences or propositions. If we are talking about sentences, neither side has a decisive case. If we are talking of propositions, there is a strong argument on the side of those who say the excluded middle does require bivalence. I argue that all challenges to this argument can be met.
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  26. The Law of Excluded Middle.Peter Geach - 1956 - Aristotelian Society Supplementary Volume 30 (1):59-90.
  27.  41
    The law of excluded middle.Eric Toms - 1941 - Philosophy of Science 8 (1):33-38.
    It is my purpose to examine this law in those cases in which it is generally held to be untrue. I inquire what can be meant, in each case of a statement p considered, by denying the law, that is, by saying ‘Neither p nor —p‘. After separating the possible meanings of this declared indeterminacy, I go on to inquire, taking each possibility in turn, whether the law does in fact fail.
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  28. The law of excluded middle.Neil Cooper - 1978 - Mind 87 (346):161-180.
  29. The Law of Excluded Middle and intuitionistic logic PiotrLUKOWSKI.Logica Trianguli - 1998 - Logica Trianguli: Logic in Łódź, Nantes, Santiago de Compostela 2:73.
     
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  30.  59
    Evidence and the Law of Excluded Middle: Brentano on Truth.Maria van der Schaar - 1999 - In Timothy Childers (ed.), The Logica Yearbook 1998. Filosofia.
    The central question of my paper is whether there is a coherent logical theory in which truth is construed in epistemic terms and in which also some version of the law of excluded middle is defended. Brentano in his later writings has such a theory.2 My first question is whether his theory is consistent. I also make a comparison between Brentano’s view and that of an intuitionist at the present day, namely Per Martin-Löf. Such a comparison might provide (...)
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  31.  9
    Transduction of The Laws of Logomachy.Joel White - 2023 - Technophany 1 (2).
    This article is one in a series that develops the concept of logomachy. Logomachy is a philosophy of semantics or sense that takes into consideration the thermodynamic status of things in the world (their quamity). In particular, this article, looks at Gilbert Simondon’s claim that the laws of thought (Identity, Contradiction and the Excluded Middle) do not hold once certain thermodynamic states such as metastability (in between stability and instability) are taken into account. This article formulates, through a (...)
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  32.  18
    Investigations into intuitionistic and other negations.Satoru Niki - 2022 - Bulletin of Symbolic Logic 28 (4):532-532.
    Intuitionistic logic formalises the foundational ideas of L.E.J. Brouwer’s mathematical programme of intuitionism. It is one of the earliest non-classical logics, and the difference between classical and intuitionistic logic may be interpreted to lie in the law of the excluded middle, which asserts that either a proposition is true or its negation is true. This principle is deemed unacceptable from the constructive point of view, in whose understanding the law means that there is an effective procedure to determine (...)
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  33.  15
    $$\Delta ^0_1$$ variants of the law of excluded middle and related principles.Makoto Fujiwara - 2022 - Archive for Mathematical Logic 61 (7):1113-1127.
    We systematically study the interrelations between all possible variations of \(\Delta ^0_1\) variants of the law of excluded middle and related principles in the context of intuitionistic arithmetic and analysis.
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  34.  8
    Rules of Explosion and Excluded Middle: Constructing a Unified Single-Succedent Gentzen-Style Framework for Classical, Paradefinite, Paraconsistent, and Paracomplete Logics.Norihiro Kamide - forthcoming - Journal of Logic, Language and Information:1-36.
    A unified and modular falsification-aware single-succedent Gentzen-style framework is introduced for classical, paradefinite, paraconsistent, and paracomplete logics. This framework is composed of two special inference rules, referred to as the rules of explosion and excluded middle, which correspond to the principle of explosion and the law of excluded middle, respectively. Similar to the cut rule in Gentzen’s LK for classical logic, these rules are admissible in cut-free LK. A falsification-aware single-succedent Gentzen-style sequent calculus fsCL for classical (...)
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  35.  45
    Conditional Excluded Middle in Systems of Consequential Implication.Claudio Pizzi & Timothy Williamson - 2005 - Journal of Philosophical Logic 34 (4):333-362.
    It is natural to ask under what conditions negating a conditional is equivalent to negating its consequent. Given a bivalent background logic, this is equivalent to asking about the conjunction of Conditional Excluded Middle (CEM, opposite conditionals are not both false) and Weak Boethius' Thesis (WBT, opposite conditionals are not both true). In the system CI.0 of consequential implication, which is intertranslatable with the modal logic KT, WBT is a theorem, so it is natural to ask which (...)
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  36.  51
    Concerning the laws of contradiction and excluded middle.V. J. McGill - 1939 - Philosophy of Science 6 (2):196-211.
    Tradition usually assigns greater importance to the so-called laws of thought than to other logical principles. Since these laws could apparently not be deduced from the other principles without circularity and all deductions appeared to make use of them, their priority was considered well established. Generally, it was held that the laws of thought have no proof and need none, that as universal constitutive or transcendental principles they are self-evident.
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  37. Supervaluationism and the law of excluded middle.Michael Tye - 1989 - Analysis 49 (3):141-143.
  38.  26
    On Weakening the Law of Excluded Middle.Douglas Odegard - 1966 - Dialogue 5 (2):232-236.
    Let us use ‘false’ and ‘not true’ in such a way that the latter expression covers the broader territory of the two; in other words, a statement's falsity implies its non-truth but not vice versa. For example, ‘John is ill’ cannot be false without being nontrue; but it can be non-true without being false, since it may not be true when ‘John is not ill’ is also not true, a situation we could describe by saying ‘It is neither the case (...)
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  39.  45
    Galvin’s “Racing Pawns” Game, Internal Hyperarithmetic Comprehension, and the Law of Excluded Middle.Chris Conidis, Noam Greenberg & Daniel Turetsky - 2013 - Notre Dame Journal of Formal Logic 54 (2):233-252.
    We show that the fact that the first player wins every instance of Galvin’s “racing pawns” game is equivalent to arithmetic transfinite recursion. Along the way we analyze the satisfaction relation for infinitary formulas, of “internal” hyperarithmetic comprehension, and of the law of excluded middle for such formulas.
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  40. The subjunctive conditional law of excluded middle.Alexander Pruss - manuscript
    p and q, one of “were p true, q would be true” and “were p true, not- q would be true” is true. Therefore, even if Curley is not offered the bribe, either he would take it were he offered it or he would not take it were he offered it.
     
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  41.  81
    The principle of excluded middle in quantum logic.P. Mittelstaedt & E. -W. Stachow - 1978 - Journal of Philosophical Logic 7 (1):181 - 208.
    The principle of excluded middle is the logical interpretation of the law V ≤ A v ヿA in an orthocomplemented lattice and, hence, in the lattice of the subspaces of a Hilbert space which correspond to quantum mechanical propositions. We use the dialogic approach to logic in order to show that, in addition to the already established laws of effective quantum logic, the principle of excluded middle can also be founded. The dialogic approach is based on (...)
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  42.  21
    Symposium: The Law of Excluded Middle.P. T. Geach & W. F. Bednarowski - 1956 - Aristotelian Society Supplementary Volume 30 (1):59 - 90.
  43.  6
    Symposium: The Law of Excluded Middle.P. T. Geach - 1956 - Aristotelian Society Supplementary Volume 30 (1):59-90.
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  44.  34
    Does Choice Really Imply Excluded Middle? Part I: Regimentation of the Goodman–Myhill Result, and Its Immediate Reception†.Neil Tennant - 2020 - Philosophia Mathematica 28 (2):139-171.
    The one-page 1978 informal proof of Goodman and Myhill is regimented in a weak constructive set theory in free logic. The decidability of identities in general (⁠|$a\!=\!b\vee\neg a\!=\!b$|⁠) is derived; then, of sentences in general (⁠|$\psi\vee\neg\psi$|⁠). Martin-Löf’s and Bell’s receptions of the latter result are discussed. Regimentation reveals the form of Choice used in deriving Excluded Middle. It also reveals an abstraction principle that the proof employs. It will be argued that the Goodman–Myhill result does not provide (...)
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  45.  43
    Logical truth and the law of excluded middle.Henry H. Jack - 1959 - Mind 68 (269):93-97.
  46.  4
    Concerning the Laws of Contradiction and Excluded Middle.V. J. Mcgill - 1939 - Journal of Symbolic Logic 4 (2):101-101.
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  47.  15
    Toms Eric. The law of excluded middle. Philosophy of science, vol. 8 , pp. 33–38.Alonzo Church - 1941 - Journal of Symbolic Logic 6 (1):35-35.
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  48. Excluded middle.Hugh S. Chandler - 1967 - Journal of Philosophy 64 (24):807-814.
    This is a paper on borderline cases and the law of Excluded Middle. In it I try to make use of some long forgotten, but perhaps valuable, work on the topic – a bit of Hegel for instance.
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  49.  17
    Review: Eric Toms, The Law of Excluded Middle[REVIEW]Alonzo Church - 1941 - Journal of Symbolic Logic 6 (1):35-35.
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  50. Future contingents, non-contradiction, and the law of excluded middle muddle.Craig Bourne - 2004 - Analysis 64 (2):122–128.
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