Results for 'Free Logic'

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  1. Free Logics Their Foundations, Character and Some Applications Thereof.Karel Lambert - 1997
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  2. Higher-order free logic and the Prior-Kaplan paradox.Andrew Bacon, John Hawthorne & Gabriel Uzquiano - 2016 - Canadian Journal of Philosophy 46 (4-5):493-541.
    The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order (...). Our assessment of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value. (shrink)
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  3.  54
    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 (...)
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  4. Existence and Free Logic.Dolf Rami - manuscript
    In this paper I aim to defend a first‐order non‐discriminating property view concerning existence. The version of this view that I prefer is based on negative (or a specific neutral) free logic that treats the existence predicate as first‐order logical predicate. I will provide reasons why such a view is more plausible than a second‐order discriminating property view concerning existence and I will also discuss four challenges for the proposed view and provide solutions to them.
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  5. Non‐Standard Neutral Free Logic, Empty Names and Negative Existentials.Dolf Rami - manuscript
    In this paper I am concerned with an analysis of negative existential sentences that contain proper names only by using negative or neutral free logic. I will compare different versions of neutral free logic with the standard system of negative free logic (Burge, Sainsbury) and aim to defend my version of neutral free logic that I have labeled non-standard neutral free logic.
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  6. 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 (...)
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  7. 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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  8. 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 (...)
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  9. A Binary Quantifier for Definite Descriptions for Cut Free Free Logics.Nils Kürbis - 2022 - Studia Logica 110 (1):219-239.
    This paper presents rules in sequent calculus for a binary quantifier I to formalise definite descriptions: Ix[F, G] means ‘The F is G’. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of I. There are also brief comparisons of the present approach to the more common one that formalises definite descriptions (...)
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  10. 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 (...)
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  11.  92
    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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  12.  74
    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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  13. Cut-free Calculi and Relational Semantics for Temporal STIT Logics.Tim Lyon & Kees van Berkel - 2019 - In Francesco Calimeri, Nicola Leone & Marco Manna (eds.), Logics in Artificial Intelligence. Springer International Publishing. pp. 803 - 819.
    We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC frames.
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  14. Logical Problems of Evil and Free Will Defences.Graham Oppy - 2017 - In Chad Meister & Paul Moser (eds.), The Cambridge Companion to the Problem of Evil. Cambridge, UK: pp. 45-64.
    In this paper, I offer a novel analysis of logical arguments from evil. I claim that logical arguments from evil have three parts: (1) characterisation (attribution of specified attributes to God); (2) datum (a claim about evil); and (3) link (connection between attributes and evil). I argue that, while familiar logical arguments from evil are known to be unsuccessful, it remains an open question whether there are successful logical arguments from evil.
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  15. 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 (...)
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  16. On philosophical motivations for paraconsistency: an ontology-free interpretation of the logics of formal inconsistency.Walter Carnielli & Abilio Rodrigues - manuscript
    In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non- contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically (...)
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  17. For Free Speech, “Religious Offense,” and “Undermining Self-Respect”: A Reply to Bonotti and Seglow.Uwe Steinhoff - manuscript
    Recent arguments trying to justify further free speech restrictions by appealing to harms that are allegedly serious enough to warrant such restrictions regularly fail to provide sufficient empirical evidence and normative argument. This is also true for the attempt made by Bonotti and Seglow. They offer no valid argument for their claim that it is wrong to direct “religiously offensive speech” at “unjustly disadvantaged” minorities (thereby allegedly undermining their “self-respect”), nor for their further claim that this is not the (...)
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  18. Stoic logic and multiple generality.Susanne Bobzien & Simon Shogry - 2020 - Philosophers' Imprint 20 (31):1-36.
    We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply (...)
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  19. Agentive Free Choice.Melissa Fusco - forthcoming - Journal of Philosophical Logic:1-31.
    The Free Choice effect---whereby <>(p or q) seems to entail both <>p and <>q---has traditionally been characterized as a phenomenon affecting the deontic modal "may". This paper presents an extension of the semantic account of free choice defended in Fusco (2015) to the agentive modal "can", the "can" which, intuitively, describes an agent's powers. -/- I begin by sketching a model of inexact ability, which grounds a modal approach to agency (Belnap & Perloff 1998; Belnap, Perloff, and Xu (...)
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  20. The Free Choice Permission as a Default Rule.Daniela Glavaničová - 2018 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 25 (4):495-516.
    It is quite plausible to say that you may read or write implies that you may read and you may write (though possibly not both at once). This so-called free choice principle is well-known in deontic logic. Sadly, despite being so intuitive and seemingly innocent, this principle causes a lot of worries. The paper briefly but critically examines leading accounts of free choice permission present in the literature. Subsequently, the paper suggests to accept the free choice (...)
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  21.  63
    Weakly Free Multialgebras.Marcelo E. Coniglio & Guilherme V. Toledo - 2022 - Bulletin of the Section of Logic 51 (1):109-141.
    In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest (...)
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  22. Free will as a gift from God: A new compatibilism.Jim Stone - 1998 - Philosophical Studies 92 (3):257-281.
    I argue that God could give us the robust power to do other than we do in a deterministic universe.
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  23. Ancient Logic and its Modern Interpretations.John Corcoran (ed.) - 1974 - Boston: Reidel.
    This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient (...) texts. A renaissance in ancient logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)
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  24. Presuppositions, Logic, and Dynamics of Belief.Slavko Brkic - 2004 - Prolegomena 3 (2):151-177.
    In researching presuppositions dealing with logic and dynamic of belief we distinguish two related parts. The first part refers to presuppositions and logic, which is not necessarily involved with intentional operators. We are primarily concerned with classical, free and presuppositonal logic. Here, we practice a well known Strawson’s approach to the problem of presupposition in relation to classical logic. Further on in this work, free logic is used, especially Van Fraassen’s research of the (...)
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  25. The logical problem of evil: Mackie and Plantinga.Daniel Howard-Snyder - 2013 - In Justin McBrayer & Daniel Howard-Snyder (eds.), The Blackwell Companion to the Problem of Evil. Wiley-Blackwell. pp. 19-33.
    J.L. Mackie’s version of the logical problem of evil is a failure, as even he came to recognize. Contrary to current mythology, however, its failure was not established by Alvin Plantinga’s Free Will Defense. That’s because a defense is successful only if it is not reasonable to refrain from believing any of the claims that constitute it, but it is reasonable to refrain from believing the central claim of Plantinga’s Free Will Defense, namely the claim that, possibly, every (...)
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  26. Logicism, Possibilism, and the Logic of Kantian Actualism.Andrew Stephenson - 2017 - Critique.
    In this extended critical discussion of 'Kant's Modal Metaphysics' by Nicholas Stang (OUP 2016), I focus on one central issue from the first chapter of the book: Stang’s account of Kant’s doctrine that existence is not a real predicate. In §2 I outline some background. In §§3-4 I present and then elaborate on Stang’s interpretation of Kant’s view that existence is not a real predicate. For Stang, the question of whether existence is a real predicate amounts to the question: ‘could (...)
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  27. A Logical Approach to Reasoning by Analogy.Todd R. Davies & Stuart J. Russell - 1987 - In John P. McDermott (ed.), Proceedings of the 10th International Joint Conference on Artificial Intelligence (IJCAI'87). Morgan Kaufmann Publishers. pp. 264-270.
    We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization of the different types of dependency relations defined in database theory. Specifically, we define determination as a relation between schemata of first (...)
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  28. A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences.Jared Millson - 2019 - Studia Logica (6):1-34.
    In recent years, the e ffort to formalize erotetic inferences (i.e., inferences to and from questions) has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and regular erotetic implication. While an attempt has been (...)
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  29. Why is There Something Rather Than Nothing? A Logical Investigation.Jan Heylen - 2017 - Erkenntnis 82 (3):531-559.
    From Leibniz to Krauss philosophers and scientists have raised the question as to why there is something rather than nothing. Why-questions request a type of explanation and this is often thought to include a deductive component. With classical logic in the background only trivial answers are forthcoming. With free logics in the background, be they of the negative, positive or neutral variety, only question-begging answers are to be expected. The same conclusion is reached for the modal version of (...)
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  30. Judaic Logic: A Formal Analysis of Biblical, Talmudic and Rabbinic Logic.Avi Sion - 1995 - Geneva, Switzerland: Slatkine; CreateSpace & Kindle; Lulu..
    Judaic Logic is an original inquiry into the forms of thought determining Jewish law and belief, from the impartial perspective of a logician. Judaic Logic attempts to honestly estimate the extent to which the logic employed within Judaism fits into the general norms, and whether it has any contributions to make to them. The author ranges far and wide in Jewish lore, finding clear evidence of both inductive and deductive reasoning in the Torah and other books of (...)
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  31.  31
    Free Will Is No Defense.Simon Cushing - manuscript
    Why Plantinga's updated (2009) version of the Free Will Defense does not work, and consequently the Logical Argument From Evil against the God of Theism is undefeated.
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  32.  59
    Free Will Fundamentals: Agency, Determinism, and (In)compatibility.Kristin Mickelson - 2012 - Dissertation, University of Colorado, Boulder
    NOTE TO READERS: My current research program is firmly grounded in the technical aspects of this dissertation. That said, my views have evolved significantly since writing this dissertation, e.g. I've flipped my views on the best working definition of 'determinism', and I no longer defend the viability of incompatibilist-impossibilism (I still grant the superficial logical consistency of the two views, but now contend that there is no way to defend one without rejecting the other). I have also given up on (...)
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  33. Future Logic: Categorical and Conditional Deduction and Induction of the Natural, Temporal, Extensional, and Logical Modalities.Avi Sion - 1996 - Geneva, Switzerland: CreateSpace & Kindle; Lulu..
    Future Logic is an original, and wide-ranging treatise of formal logic. It deals with deduction and induction, of categorical and conditional propositions, involving the natural, temporal, extensional, and logical modalities. Traditional and Modern logic have covered in detail only formal deduction from actual categoricals, or from logical conditionals (conjunctives, hypotheticals, and disjunctives). Deduction from modal categoricals has also been considered, though very vaguely and roughly; whereas deduction from natural, temporal and extensional forms of conditioning has been all (...)
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  34. JTB-Epistemology and the Gettier problem in the framework of topological epistemic logic.Thomas Mormann - manuscript
    Abstract. Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological models (...)
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  35. The Cut‐Free Approach and the Admissibility‐Curry.Ulf Hlobil - 2018 - Thought: A Journal of Philosophy 7 (1):40-48.
    The perhaps most important criticism of the nontransitive approach to semantic paradoxes is that it cannot truthfully express exactly which metarules preserve validity. I argue that this criticism overlooks that the admissibility of metarules cannot be expressed in any logic that allows us to formulate validity-Curry sentences and that is formulated in a classical metalanguage. Hence, the criticism applies to all approaches that do their metatheory in classical logic. If we do the metatheory of nontransitive logics in a (...)
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  36. Fine-Grained Type-Free Intensionality.George Bealer - 1989 - In Gennero Chierchia, Barbara H. Partee & Raymond Turner (eds.), Properties, Types, and Meaning, Volume 1. Kluwer Academic Publishers. pp. 177-230.
    Commonplace syntactic constructions in natural language seem to generate ontological commitments to a dazzling array of metaphysical categories - aggregations, sets, ordered n-tuples, possible worlds, intensional entities, ideal objects, species, intensive and extensive quantities, stuffs, situations, states, courses of events, nonexistent objects, intentional and discourse objects, general objects, plural objects, variable objects, arbitrary objects, vague kinds and concepts, fuzzy sets, and so forth. But just because a syntactic construction in some natural language appears to invoke a new category of entity, (...)
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  37. Gödel's incompleteness theorems, free will and mathematical thought.Solomon Feferman - 2011 - In Richard Swinburne (ed.), Free Will and Modern Science. Oup/British Academy.
    The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no matter (...)
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  38. Property theory: The Type-Free Approach v. the Church Approach.George Bealer - 1994 - Journal of Philosophical Logic 23 (2):139 - 171.
    In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The discussion focuses on: (...)
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  39.  61
    Book ReviewsRichard Tuck,. Free Riding.Cambridge, MA: Harvard University Press, 2008. Pp. 223. $35.00. [REVIEW]S. M. Amadae - 2008 - Ethics 119 (1):211-216.
    This review of Richard Tuck's Free Riding conveys Tuck's crucial distinction between the logic of collective action which fails due to the problem of causal negligibility, and free riding, which has been modeled as a Prisoner's Dilemma and involves casually impacting another actor in an adverse manner. Tuck also distinguishes the practice of voting which he argues neither fails due to the worry of causal negligibility or due to free riding; instead it represents a problem of (...)
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  40. The Logical Problem of the Trinity: A New Solution.Joshua Sijuwade - 2022 - Religions 13 (9):1-46.
    This article aims to introduce a new solution to the Logical Problem of the Trinity. This solution is provided by utilising a number of theses within the field of contemporary metaphysics in order to establish a conceptual basis for a novel account and model of the doctrine of the Trinity termed Monarchical Aspectivalism, which will provide the means for proposing an alternative reading of the Athanasian Creed that is free from any consistency problems.
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  41. The Concept of Sense in Gilles Deleuze's Logic of Sense.Daniel W. Smith - 2022 - Deleuze and Guattari Studies 16 (1):3-23.
    What is the concept of sense developed by Deleuze in his 1969 Logic of Sense? This paper attempts to answer this question analysing the three dimensions of language that Deleuze isolates: the primary order of noises and intensities ; the secondary order of sense ; and the tertiary organisation of propositions. What renders language possible is that which separates sounds from bodies and organises them into propositions, freeing them for the expressive function. Deleuze argues that it is the dimension (...)
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  42. Two Notions of Logical Form.Andrea Iacona - 2016 - Journal of Philosophy 113 (12):617-643.
    This paper claims that there is no such thing as the correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and semantics. The first part of the paper outlines the thesis that a unique notion of logical form fulfils both roles, and argues that the alleged best candidate for making it true is unsuited for one of the two (...)
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  43. Norm Performatives and Deontic Logic.Rosja Mastop - 2011 - European Journal of Analytic Philosophy 7 (2):83-105.
    Deontic logic is standardly conceived as the logic of true statements about the existence of obligations and permissions. In his last writings on the subject, G. H. von Wright criticized this view of deontic logic, stressing the rationality of norm imposition as the proper foundation of deontic logic. The present paper is an attempt to advance such an account of deontic logic using the formal apparatus of update semantics and dynamic logic. That is, we (...)
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  44.  38
    God’s Prime Directive: Non-Interference and Why There Is No (Viable) Free Will Defense.David Kyle Johnson - 2022 - Religions 13 (9).
    In a recent book and article, James Sterba has argued that there is no free will defense. It is the purpose of this article to show that, in the most technical sense, he is wrong. There is a version of the free will defense that can solve what Sterba (rightly) takes to be the most interesting and severe version of the logical problem of moral evil. However, I will also argue that, in effect (or, we might say, in (...)
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  45. A Note on Logical Truth.Corine Besson - 2014 - Logique Et Analyse 57 (227):309-331.
    Classical logic counts sentences such as ‘Alice is identical with Alice’ as logically true. A standard objection to classical logic is that Alice’s self-identity, for instance, is not a matter of logic because the identity of particular objects is not a matter of logic. For this reason, many philosophers argue that classical logic is not the right logic, and that it should be abandoned in favour of free logiclogic (...) of existential commitments with respect to singular terms. In most standard free logics, sentences such as ‘Alice is identical with Alice’ are not logically true. This paper argues that this objection from existential commitments is some- what superficial and that there is a deeper reason why ‘Alice is identical with Alice’ should not be considered a logical truth. Indeed, a key fundamental thought about the nature of logic is that a logical truth is true in virtue of its logical form. The fundamental problem I raise is that a sentence such as ‘Alice is identical with Alice’ appears to not even be true in virtue of its logical form. Thus this paper argues that given that such a sentence is not true in virtue of its logical form, it should not be counted as logically true. It moreover argues, on the same grounds, that even the sentences which free logicians regard as logically true shouldn’t be regarded as logically true. So in this sense free logic is no repair to classical logic. (shrink)
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  46. Completeness of an ancient logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.
    In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the (...)
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  47.  86
    Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents.Tim Lyon, Alwen Tiu, Rajeev Gore & Ranald Clouston - 2020 - In Maribel Fernandez & Anca Muscholl (eds.), 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Dagstuhl, Germany: pp. 1-16.
    We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without (...)
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  48. Plantinga's Free Will Defence: Critical Note.Leslie Allan - manuscript
    Some atheistic philosophers have argued that God could have created a world with free moral agents and yet absent of moral evil. Using possible world semantics, Alvin Plantinga sought to defuse this logical form of the problem of evil. In this critical note, Leslie Allan examines the adequacy of Plantinga's argument that the existence of God is logically compatible with the existence of moral evil. The veracity of Plantinga's argument turns on whether his essential use of counterfactual conditionals preserves (...)
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  49. Binding On the Fly: Cross-Sentential Anaphora in Variable— Free Semantics.Anna Szabolcsi - 2003 - In R. Oehrle & J. Kruijff (eds.), Resource Sensitivity, Binding, and Anaphora. Kluwer Academic Publishers. pp. 215--227.
    Combinatory logic (Curry and Feys 1958) is a “variable-free” alternative to the lambda calculus. The two have the same expressive power but build their expressions differently. “Variable-free” semantics is, more precisely, “free of variable binding”: it has no operation like abstraction that turns a free variable into a bound one; it uses combinators—operations on functions—instead. For the general linguistic motivation of this approach, see the works of Steedman, Szabolcsi, and Jacobson, among others. The standard view (...)
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  50. Mill on logic.David Godden - 2017 - In Dale E. Miller & Christopher Macleod (eds.), A companion to Mill. Hoboken, NJ: John Wiley & Sons. pp. 175-191.
    Working within the broad lines of general consensus that mark out the core features of John Stuart Mill’s (1806–1873) logic, as set forth in his A System of Logic (1843–1872), this chapter provides an introduction to Mill’s logical theory by reviewing his position on the relationship between induction and deduction, and the role of general premises and principles in reasoning. Locating induction, understood as a kind of analogical reasoning from particulars to particulars, as the basic form of inference (...)
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