Results for 'Nonclassical Logic'

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  1. Probability and Nonclassical Logic.Robert Williams - 2016 - In Alan Hajek & Christopher Hitchcock (eds.), The oxford handbook of probability and philosophy. Oxford university press.
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  2. Nonclassical Minds and Indeterminate Survival.J. Robert G. Williams - 2014 - Philosophical Review 123 (4):379-428.
    Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same (...)
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  3. Gradational Accuracy and Nonclassical Semantics.J. Robert G. Williams - 2012 - Review of Symbolic Logic 5 (4):513-537.
    Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences of (...)
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  4. Prospects for a Naive Theory of Classes.Hartry Field, Harvey Lederman & Tore Fjetland Øgaard - 2017 - Notre Dame Journal of Formal Logic 58 (4):461-506.
    The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are (...)
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  5. The Bishop and Priest: Toward a Point-of-View Based Epistemology of True Contradictions.Eric Dietrich - 2008 - Logos Architekton 2 (2):35-58..
    True contradictions are taken increasingly seriously by philosophers and logicians. Yet, the belief that contradictions are always false remains deeply intuitive. This paper confronts this belief head-on by explaining in detail how one specific contradiction is true. The contradiction in question derives from Priest's reworking of Berkeley's argument for idealism. However, technical aspects of the explanation offered here differ considerably from Priest's derivation. The explanation uses novel formal and epistemological tools to guide the reader through a valid argument with, not (...)
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  6.  20
    Star Models and the Semantics of Infectiousness.Matthew W. G. McClure - 2020 - Undergraduate Philosophy Journal of Australasia 2 (2):35–57.
    The first degree entailment (FDE) family is a group of logics, a many-valued semantics for each system of which is obtained from classical logic by adding to the classical truth-values true and false any subset of {both, neither, indeterminate}, where indeterminate is an infectious value (any formula containing a subformula with the value indeterminate itself has the value indeterminate). In this paper, we see how to extend a version of star semantics for the logics whose many-valued semantics lack indeterminate (...)
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  7. 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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  8.  66
    Supposition and Desire in a Non-Classical Setting.J. Robert G. Williams - unknown
    *These notes were folded into the published paper "Probability and nonclassical logic*. Revising semantics and logic has consequences for the theory of mind. Standard formal treatments of rational belief and desire make classical assumptions. If we are to challenge the presuppositions, we indicate what is kind of theory is going to take their place. Consider probability theory interpreted as an account of ideal partial belief. But if some propositions are neither true nor false, or are half true, (...)
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  9. New Dimensions of the Square of Opposition.Jean-Yves Beziau & Stamatios Gerogiorgakis (eds.) - 2017 - Munich: Philosophia.
    The square of opposition is a diagram related to a theory of oppositions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantification, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has (...)
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  10. Notes on the Model Theory of DeMorgan Logics.Thomas Macaulay Ferguson - 2012 - Notre Dame Journal of Formal Logic 53 (1):113-132.
    We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's (...)
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  11. Graham Priest's «Dialetheism» -- Is It Althogether True?Lorenzo Peña - 1996 - Sorites 7:28-56.
    Graham Priest's book In Contradiction is a bold defense of the existence of true contradictions. Although Priest's case is impressive, and many of his arguments are correct, his approach is not the only one allowing for true contradictions. As against Priest's, there is at least one contradictorialist approach which establishes a link between true contradictions and degrees of truth. All in all, such an alternative is more conservative, closer to mainstream analytical philosophy. The two approaches differ as regards the floodgate (...)
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  12. On the Concept of a Notational Variant.Alexander W. Kocurek - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). pp. 284-298.
    In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The (...)
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  13. The Nonclassical Mereology of Olfactory Experiences.Błażej Skrzypulec - forthcoming - Synthese:1-20.
    While there is a growing philosophical interest in analysing olfactory experiences, the mereological structure of odours considered in respect of how they are perceptually experienced has not yet been extensively investigated. The paper argues that odours are perceptually experienced as having a mereological structure, but this structure is significantly different from the spatial mereological structure of visually experienced objects. Most importantly, in the case of the olfactory part-structure, the classical weak supplementation principle is not satisfied. This thesis is justified by (...)
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  14. A Logic for 'Because'.Benjamin Schnieder - 2011 - Review of Symbolic Logic 4 (3):445-465.
    In spite of its significance for everyday and philosophical discourse, the explanatory connective has not received much treatment in the philosophy of logic. The present paper develops a logic for based on systematic connections between and the truth-functional connectives.
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  15. Putnam's Naturalism and Realism Extended to Social Systems and Nonclassical Mereology.James Goetz - manuscript
    Putnam proposed liberal naturalism and metaphysical realism that extends to normative judgments and coheres with the principle of bivalence. This paper extends Putnam's naturalism and realism to a model of social systems ranging from jawless vertebrates to legal systems while the systems exhibit nonclassical mereology. The model defines types of entities and material, and focuses on natural interactions that cause organization, the dynamics of scientific entities, and the composition of social groups which includes communication and the emergence of synergy.
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  16. Logic, Form and Matter.Barry Smith & David Murray - 1981 - Aristotelian Society Supplementary Volume 55 (1):47 - 74.
    It is argued, on the basis of ideas derived from Wittgenstein's Tractatus and Husserl's Logical Investigations, that the formal comprehends more than the logical. More specifically: that there exist certain formal-ontological constants (part, whole, overlapping, etc.) which do not fall within the province of logic. A two-dimensional directly depicting language is developed for the representation of the constants of formal ontology, and means are provided for the extension of this language to enable the representation of certain materially necessary relations. (...)
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  17. The Logic of Epistemic Justification.Martin Smith - 2018 - Synthese 195 (9):3857-3875.
    Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But (...)
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  18. Logic and Semantics for Imperatives.Nate Charlow - 2014 - Journal of Philosophical Logic 43 (4):617-664.
    In this paper I will develop a view about the semantics of imperatives, which I term Modal Noncognitivism, on which imperatives might be said to have truth conditions (dispositionally, anyway), but on which it does not make sense to see them as expressing propositions (hence does not make sense to ascribe to them truth or falsity). This view stands against “Cognitivist” accounts of the semantics of imperatives, on which imperatives are claimed to express propositions, which are then enlisted in explanations (...)
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  19.  37
    Logic and Constructivism: A Model of Terminological Knowledge.Farshad Badie - 2020 - Journal of Knowledge Structures and Systems 1 (1):23-39.
    This original research hypothesises that the most fundamental building blocks of logical descriptions of cognitive, or knowledge, agents’ descriptions are expressible based on their conceptions (of the world). This article conceptually and logically analyses agents’ conceptions in order to offer a constructivist- based logical model for terminological knowledge. The most significant characteristic of [terminological] knowing is that there are strong interrelationships between terminological knowledge and the individualistic constructed, and to-be-constructed, models of knowledge. Correspondingly, I conceptually and logically analyse conception expressions (...)
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  20. The Logic of Fast and Slow Thinking.Anthia Solaki, Francesco Berto & Sonja Smets - forthcoming - Erkenntnis:1-30.
    We present a framework for epistemic logic, modeling the logical aspects of System 1 and System 2 cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the (...)
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  21. Deontic Logic.Paul McNamara - 2006 - In Dov Gabbay & John Woods (eds.), The Handbook of the History of Logic, vol. 7: Logic and the Modalities in the Twentieth Century. Elsevier Press. pp. 197-288.
    Overview of fundamental work in deontic logic.
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  22. Logic and Formal Ontology.B. Smith - 1989 - In J. N. Mohanty & W. McKenna (eds.), Husserl’s Phenomenology: A Textbook. Lanham: University Press of America. pp. 29-67.
    The current resurgence of interest in cognition and in the nature of cognitive processing has brought with it also a renewed interest in the early work of Husserl, which contains one of the most sustained attempts to come to grips with the problems of logic from a cognitive point of view. Logic, for Husserl, is a theory of science; but it is a theory which takes seriously the idea that scientific theories are constituted by the mental acts of (...)
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  23. Deviant Logic, Fuzzy Logic: Beyond the Formalism.Achille C. Varzi & Susan Haack - 1998 - Philosophical Review 107 (3):468.
    This book has three main parts. The first, longer, part is a reprint of the author's Deviant Logic, which initially appeared as a book by itself in 1974. The second and third parts include reprints of five papers originally published between 1973 and 1980. Three of them focus on the nature and justification of deductive reasoning, which are also a major concern of Deviant Logic. The other two are on fuzzy logic, and make up for a major (...)
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  24. 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 (...)
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  25. Modal Logic with Names.George Gargov & Valentin Goranko - 1993 - Journal of Philosophical Logic 22 (6):607 - 636.
    We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ (...)
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  26. What is a Paraconsistent Logic?Damian Szmuc, Federico Pailos & Eduardo Barrio - 2018 - In Jacek Malinowski & Walter Carnielli (eds.), Contradictions, from Consistency to Inconsistency. Springer Verlag.
    Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic (...)
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  27. Paraconsistency: Logic and Applications.Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) - 2013 - Springer.
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems (...)
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  28. Neo-Logicism and Its Logic.Panu Raatikainen - 2020 - History and Philosophy of Logic 41 (1):82-95.
    The rather unrestrained use of second-order logic in the neo-logicist program is critically examined. It is argued in some detail that it brings with it genuine set-theoretical existence assumptions and that the mathematical power that Hume’s Principle seems to provide, in the derivation of Frege’s Theorem, comes largely from the ‘logic’ assumed rather than from Hume’s Principle. It is shown that Hume’s Principle is in reality not stronger than the very weak Robinson Arithmetic Q. Consequently, only a few (...)
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  29. A Logic for Epistemic Two-Dimensional Semantics.Peter Fritz - 2013 - Synthese 190 (10):1753-1770.
    Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also (...)
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  30. Logic and the Sachverhalt.Barry Smith - 1989 - The Monist 72 (1):52-69.
    Those who conceive logic as a science have generally favoured one of two alternative conceptions as to what the subject-matter of this science ought to be. On the one hand is the nowadays somewhat old-fashioned-seeming view of logic as the science of judgment, or of thinking or reasoning activities in general. On the other hand is the view of logic as a science of ideal meanings, 'thoughts', or 'propositions in themselves'. There is, however, a third alternative conception, (...)
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  31. Vagueness, Logic and Use: Four Experimental Studies on Vagueness.Phil Serchuk, Ian Hargreaves & Richard Zach - 2011 - Mind and Language 26 (5):540-573.
    Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then (...)
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  32.  68
    Logic and Sense.Urszula Wybraniec-Skardowska - 2016 - Philosophy Study 6 (9).
    In the paper, original formal-logical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl’s ideas of pure grammar, Leśniewski-Ajukiewicz’s theory syntactic/semantic categories and in accordance with Frege’s ontological canons, Bocheński’s famous motto—syntax mirrors ontology and some ideas of Suszko: language should be a linguistic scheme of ontological reality and simultaneously a tool of its (...)
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  33. 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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  34. The Logic of Opacity.Andrew Bacon & Jeffrey Sanford Russell - 2019 - Philosophical and Phenomenological Research 99 (1):81-114.
    We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models (...)
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  35. Conservatively Extending Classical Logic with Transparent Truth.David Ripley - 2012 - Review of Symbolic Logic 5 (2):354-378.
    This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but (...)
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  36. Logic and the Autonomy of Ethics.Charles R. Pigden - 1989 - Australasian Journal of Philosophy 67 (2):127 – 151.
    My first paper on the Is/Ought issue. The young Arthur Prior endorsed the Autonomy of Ethics, in the form of Hume’s No-Ought-From-Is (NOFI) but the later Prior developed a seemingly devastating counter-argument. I defend Prior's earlier logical thesis (albeit in a modified form) against his later self. However it is important to distinguish between three versions of the Autonomy of Ethics: Ontological, Semantic and Ontological. Ontological Autonomy is the thesis that moral judgments, to be true, must answer to a realm (...)
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  37.  61
    Causal Models and the Logic of Counterfactuals.Jonathan Vandenburgh - manuscript
    Causal models provide a framework for making counterfactual predictions, making them useful for evaluating the truth conditions of counterfactual sentences. However, current causal models for counterfactual semantics face logical limitations compared to the alternative similarity-based approaches: they only apply to a limited subset of counterfactuals and the connection to counterfactual logic is not straightforward. This paper offers a causal framework for the semantics of counterfactuals which improves upon these logical issues. It extends the causal approach to counterfactuals to handle (...)
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  38. The Logic of Partitions: Introduction to the Dual of the Logic of Subsets: The Logic of Partitions.David Ellerman - 2010 - Review of Symbolic Logic 3 (2):287-350.
    Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as (...)
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  39. Logic.Susanne Bobzien - 1996 - In Simon Hornblower & A. Spawforth (eds.), The Oxford Classical Dictionary, 3rd edition. Oxford University Press.
    ABSTRACT: A very brief summary presentation of western ancient logic for the non-specialized reader, from the beginnings to Boethius. For a much more detailed presentation see my "Ancient Logic" in the Stanford Encyclopedia of Philosopy (also on PhilPapers).
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  40. A Logic of Justification and Truthmaking.Alessandro Giordani - 2013 - Review of Symbolic Logic 6 (2):323-342.
    In the present paper we propose a system of propositional logic for reasoning about justification, truthmaking, and the connection between justifiers and truthmakers. The logic of justification and truthmaking is developed according to the fundamental ideas introduced by Artemov. Justifiers and truthmakers are treated in a similar way, exploiting the intuition that justifiers provide epistemic grounds for propositions to be considered true, while truthmakers provide ontological grounds for propositions to be true. This system of logic is then (...)
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  41. Logic for Exact Entailment.Kit Fine & Mark Jago - 2018 - Review of Symbolic Logic:1-21.
    An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion (...)
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  42.  50
    Logic in Opposition.Fabien Schang - 2013 - Studia Humana 2 (3):31-45.
    It is claimed hereby that, against a current view of logic as a theory of consequence, opposition is a basic logical concept that can be used to define consequence itself. This requires some substantial changes in the underlying framework, including: a non-Fregean semantics of questions and answers, instead of the usual truth-conditional semantics; an extension of opposition as a relation between any structured objects; a definition of oppositions in terms of basic negation. Objections to this claim will be reviewed.
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  43. Abstract Logic of Oppositions.Fabien Schang - 2012 - Logic and Logical Philosophy 21 (4):415--438.
    A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.
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  44. Logic and Formal Ontology.Barry Smith - 2000 - Manuscrito 23 (2):275-323.
    Revised version of chapter in J. N. Mohanty and W. McKenna (eds.), Husserl’s Phenomenology: A Textbook, Lanham: University Press of America, 1989, 29–67. -/- Logic for Husserl is a science of science, a science of what all sciences have in common in their modes of validation. Thus logic deals with universal laws relating to truth, to deduction, to verification and falsification, and with laws relating to theory as such, and to what makes for theoretical unity, both on the (...)
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  45. Dynamic Epistemic Logic and Logical Omniscience.Mattias Skipper Rasmussen - 2015 - Logic and Logical Philosophy 24 (3):377-399.
    Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning are not properly separated. In this paper, (...)
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  46. An Introduction to Partition Logic.David Ellerman - 2014 - Logic Journal of the IGPL 22 (1):94-125.
    Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the (...)
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  47. Stoic Logic.Susanne Bobzien - 2003 - In Brad Inwood (ed.), The Cambridge Companion to Stoic Philosophy. Cambridge University Press.
    ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of (...)
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  48. Imperatives, Logic Of.Peter B. M. Vranas - 2013 - In Hugh LaFollette (ed.), The International Encyclopedia of Ethics. Oxford: Blackwell. pp. 2575-2585.
    Suppose that a sign at the entrance of a hotel reads: “Don’t enter these premises unless you are accompanied by a registered guest”. You see someone who is about to enter, and you tell her: “Don’t enter these premises if you are an unaccompanied registered guest”. She asks why, and you reply: “It follows from what the sign says”. It seems that you made a valid inference from an imperative premise to an imperative conclusion. But it also seems that imperatives (...)
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  49. Modal Logic and Philosophy.Sten Lindström & Krister Segerberg - 2007 - In Patrick Blackburn, Johan van Benthem & Frank Wolter (eds.), Handbook of Modal Logic. Amsterdam, the Netherlands: Elsevier. pp. 1149-1214.
    Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on (...)
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  50. Logic, Act and Product.Jacques P. Dubucs & Wioletta Miśkiewicz - 2009 - In Giuseppe Primiero (ed.), Knowledge and Judgment. Springer Verlag.
    Logic and psychology overlap in judgment, inference and proof. The problems raised by this commonality are notoriously difficult, both from a historical and from a philosophical point of view. Sundholm has for a long time addressed these issues. His beautiful piece of work [A Century of Inference: 1837-1936] begins by summarizing the main difficulty in the usual provocative manner of the author: one can start, he says, by the act of knowledge to go to the object, as the Idealist (...)
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