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  1. States of Affairs as Structured Extensions in Free Logic.Hans-Peter Leeb - forthcoming - Logic and Logical Philosophy:1.
    The search for the extensions of sentences can be guided by Frege’s “principle of compositionality of extension”, according to which the extension of a composed expression depends only on its logical form and the extensions of its parts capable of having extensions. By means of this principle, a strict criterion for the admissibility of objects as extensions of sentences can be derived: every object is admissible as the extension of a sentence that is preserved under the substitution of co-extensional expressions. (...)
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  2. McKinsey's "Consequences of Reference Failure". [REVIEW]Ulf Hlobil - 2020 - Notre Dame Philosophical Reviews 2020:N/A.
  3. Definite Descriptions in Intuitionist Positive Free Logic.Nils Kürbis - 2020 - Logic and Logical Philosophy 30:1.
    This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite descriptions recommended (...)
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  4. A State-of-Affairs-Semantic Solution to the Problem of Extensionality in Free Logic.Hans-Peter Leeb - 2020 - Journal of Philosophical Logic 49 (6):1091-1109.
    If one takes seriously the idea that a scientific language must be extensional, and accepts Quine’s notion of truth-value-related extensionality, and also recognizes that a scientific language must allow for singular terms that do not refer to existing objects, then there is a problem, since this combination of assumptions must be inconsistent. I will argue for a particular solution to the problem, namely, changing what is meant by the word ‘extensionality’, so that it would not be the truth-value that had (...)
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  5. A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation.Nils Kürbis - 2019 - Bulletin of the Section of Logic 48 (2):81-97.
    This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.
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  6. Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic.Nils Kürbis - 2019 - Bulletin of the Section of Logic 48 (4):299-317.
    Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as ‘The F is G’. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INFι of intuitionist negative free logic extended by such a quantifier, which was presented in (...)
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  7. Logic: The Basics (2nd Edition).Jc Beall & Shay A. Logan - 2017 - Routledge.
    Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader an idea of how they can take their knowledge further and the (...)
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  8. Anselm's God in Isabelle/HOL.Ben Blumson - 2017 - Archive of Formal Proofs:9.
    Paul Oppenheimer and Edward Zalta's formalisation of Anselm's ontological argument for the existence of God is automated by embedding a free logic for definite descriptions within Isabelle/HOL.
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  9. Russell's Revenge: A Problem for Bivalent Fregean Theories of Descriptions.Jan Heylen - 2017 - Pacific Philosophical Quarterly 98 (4):636-652.
    Fregean theories of descriptions as terms have to deal with improper descriptions. To save bivalence various proposals have been made that involve assigning referents to improper descriptions. While bivalence is indeed saved, there is a price to be paid. Instantiations of the same general scheme, viz. the one and only individual that is F and G is G, are not only allowed but even required to have different truth values.
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  10. Truth and Existence.Jan Heylen & Leon Horsten - 2017 - Thought: A Journal of Philosophy 6 (1):106-114.
    Halbach has argued that Tarski biconditionals are not ontologically conservative over classical logic, but his argument is undermined by the fact that he cannot include a theory of arithmetic, which functions as a theory of syntax. This article is an improvement on Halbach's argument. By adding the Tarski biconditionals to inclusive negative free logic and the universal closure of minimal arithmetic, which is by itself an ontologically neutral combination, one can prove that at least one thing exists. The result can (...)
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  11. Second-Order Modal Logic.Andrew Parisi - 2017 - Dissertation, University of Connecticut
    This dissertation develops an inferentialist theory of meaning. It takes as a starting point that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. From this starting point the dissertation develops a theory of quantification as marking (...)
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  12. Existence Hedges and Neutral Free Logic.Daniel Yeakel - 2016 - Proceedings of the Aristotelian Society 116 (3):379-386.
    I argue that neutral free logic and existence hedging are incompatible. Primarily, I respond to proposals by James Pryor intended to reconcile the two. Consideration of those proposals will reveal that on any neutral free logic either some existence hedges will entail some undesired existence claims, or they will not entail some desired existence claims.
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  13. Gödel's "Slingshot" Argument and His Onto-Theological System.Srećko Kovač & Kordula Świętorzecka - 2015 - In Kordula Świętorzecka (ed.), Gödel's Ontological Argument: History, Modifications, and Controversies. Semper. pp. 123-162.
  14. Quantificational Logic and Empty Names.Andrew Bacon - 2013 - Philosophers' Imprint 13.
    The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in order (...)
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  15. Fregean Free Logics.Siu-Fan Lee - 2009 - Philosophical Researches (Dec):123-129.
    This paper asks which free logic a Fregean should adopt. It examines options within the tradition including Carnap’s (1956) chosen object theory, Lehmann’s (1994, 2002) strict Fregean free logic, Woodruff’s (1970) strong table about Boolean operators and Bencivenga’s (1986, 1991) supervaluational semantics. It argues for a neutral free logic in view of its proximity towards explaining natural languages. However, disagreeing with Lehmann, it claims a Fregean should adopt the strong table based on Frege’s discussion on generality. Supervaluation uses strong table (...)
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  16. State-of-Affairs Semantics for Positive Free Logic.Hans-Peter Leeb - 2006 - Journal of Philosophical Logic 35 (2):183-208.
    In the following the details of a state-of-affairs semantics for positive free logic are worked out, based on the models of common inner domain - outer domain semantics. Lambert's PFL system is proven to be weakly adequate (i.e., sound and complete) with respect to that semantics by demonstrating that the concept of logical truth definable therein coincides with that one of common truth-value semantics for PFL. Furthermore, this state-of-affairs semantics resists the challenges stemming from the slingshot argument since logically equivalent (...)
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  17. Sachverhalte und Extensionalität in der freien Logik.Hans-Peter Leeb - 2006 - Sankt Augustin: Academia Verlag.
    Empty individual expressions are needed to reconstruct the actual use of scientific language as well as to make logic free from existence assumptions. According to Quine, a language must be extensional to be adequate for the purposes of science. By means of Lambert's non-extensionality argument it can be demonstrated that a language containing empty individual expressions cannot be extensional as long as truth-values are the extensions of sentences. This book investigates the soundness of Lambert's argument and examines the question of (...)
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  18. Free Logic: Selected Essays. [REVIEW]Ken Akiba - 2004 - International Philosophical Quarterly 44 (2):281-283.
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  19. Free Logics.Ermanno Bencivenga - 2002 - In D. M. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd Edition. Kluwer Academic Publishers. pp. 147--196.
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  20. Handbook of Philosophical Logic, 2nd Edition.D. M. Gabbay & F. Guenthner (eds.) - 2002 - Kluwer Academic Publishers.
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  21. More Free Logic.Scott Lehmann - 2002 - In Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic, vol. 5. New York: Springer. pp. 197-259.
    By a free logic is generally meant a variant of classical first-order logic in which constant terms may, under interpretation, fail to refer to individuals in the domain D over which the bound variables range, either because they do not refer at all or because they refer to individuals outside D. If D is identified with what is assumed by the given interpretation to exist, in accord with Quine’s dictum that “to be is to be the value of a [bound] (...)
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  22. Karel Lambert, Free Logics: Their Foundations, Character, and Some Applications Thereof (Prophil Projekte Zur Philosophie Bd. 1. Eine Schriftenreihe des Forschungsinstituts Philosophie/Technik/Wirtschaft an der Universität Salzburg). Sankt Augustin: Academia-Verlag, 1997. 156 Pp. Asch. 239. ISBN 3-89665-000-9. [REVIEW]Hans-Peter Leeb - 2001 - History and Philosophy of Logic 22:233-236.
    Free logics aim at freeing logic from existence assumptions by making them explicit, e.g., by adding an existence premisse to the antecedence of the classical axiom-schema of Universal Instantiation. Their historical development was motivated by the problem of empty singular terms, and that one of simple statements containing at least one such singular term: what is the referential status of such singular terms and what truth-value, if any, do such statemants have? Free logics can be classified with regard to their (...)
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  23. `No Input, No Output' Logic.Scott Lehmann - 2001 - In Karel Lambert, Edgar Morscher & Alexander Hieke (eds.), New Essays in Free Logic: In Honour of Karel Lambert. Norwell, Mass: Kluwer. pp. 147-155.
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  24. Quasi-Truth, Supervaluations and Free Logic.Newton C. A. da Costa & Otavio Bueno - 1999 - History and Philosophy of Logic 20 (3-4):215-226.
    The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free logic and supervaluations), and apply the (...)
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  25. Subject-Predicate Calculus Free From Existential Import.V. A. Bocharov - 1983 - Studia Logica 42 (2-3):209 - 221.
    Two subject-predicate calculi with equality,SP = and its extensionUSP =, are presented as systems of natural deduction. Both the calculi are systems of free logic. Their presentation is preceded by an intuitive motivation.It is shown that Aristotle's syllogistics without the laws of identitySaP andSiP is definable withinSP =, and that the first-order predicate logic is definable withinUSP =.
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  26. First-Order Logic Based on Inclusion and Abstraction.John Bacon - 1982 - Journal of Symbolic Logic 47 (4):793-808.
  27. A Free IPC is a Natural Logic: Strong Completeness for Some Intuitionistic Free Logics.Carl J. Posy - 1982 - Topoi 1 (1-2):30-43.
    IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(A c /x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).
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  28. Slightly Non-Standard Logic.Scott Lehmann - 1980 - Logique Et Analyse 23 (92):379-92.
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  29. Possibility Pre-Supposition Free Logics.Roderic A. Girle - 1974 - Notre Dame Journal of Formal Logic 15 (1):45-62.
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  30. Axiomatizing Category Theory in Free Logic.Christoph Benzmüller & Dana Scott - manuscript
    Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL interactive proof assistant, and this formalization utilizes a semantically correct embedding of free logic in classical higher-order logic. The modeling and formal analysis of our axiom sets has been significantly supported by series of experiments with automated reasoning tools integrated with Isabelle/HOL. We also address the (...)
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