Results for 'Intuitionism'

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  1.  53
    1. Intuitionistic sentential calculus with iden-tity.Intuitionistic Sentential Calculus - 1990 - Bulletin of the Section of Logic 19 (3):92-99.
  2. Fred Richman New Mexico State University.Intuitionism As Generalization - 1990 - Philosophia Mathematica (1-2):128.
  3. Intuitionism, Realism, Relativism and Rhubarb.Crispin Wright - 2006 - In Patrick Greenough & Michael Lynch (eds.), Truth and realism. Clarendon Press. pp. 38--60.
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  4. Intuitionistic Modal Algebras.Sergio A. Celani & Umberto Rivieccio - 2024 - Studia Logica 112 (3):611-660.
    Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations (...)
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  5. Ethical Intuitionism.Michael Huemer - 2005 - New York: Palgrave Macmillan.
    This book defends a form of ethical intuitionism, according to which (i) there are objective moral truths; (ii) we know some of these truths through a kind of immediate, intellectual awareness, or "intuition"; and (iii) our knowledge of moral truths gives us reasons for action independent of our desires. The author rebuts all the major objections to this theory and shows that the alternative theories about the nature of ethics all face grave difficulties.
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  6.  50
    Intuitionistic Public Announcement Logic with Distributed Knowledge.Ryo Murai & Katsuhiko Sano - 2024 - Studia Logica 112 (3):661-691.
    We develop intuitionistic public announcement logic over intuitionistic \({\textbf{K}}\), \({{\textbf{K}}}{{\textbf{T}}}\), \({{\textbf{K}}}{{\textbf{4}}}\), and \({{\textbf{S}}}{{\textbf{4}}}\) with distributed knowledge. We reveal that a recursion axiom for the distributed knowledge is _not_ valid for a frame class discussed in [ 12 ] but valid for the restricted frame class introduced in [ 20, 26 ]. The semantic completeness of the static logics for this restricted frame class is established via the concept of pseudo-model.
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  7. Revisionary intuitionism.Michael Huemer - 2008 - Social Philosophy and Policy 25 (1):368-392.
    I argue that, given evidence of the factors that tend to distort our intuitions, ethical intuitionists should disown a wide range of common moral intuitions, and that they should typically give preference to abstract, formal intuitions over more substantive ethical intuitions. In place of the common sense morality with which intuitionism has traditionally allied, the suggested approach may lead to a highly revisionary normative ethics.
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  8. Moral intuitionism and disagreement.Brian Besong - 2014 - Synthese 191 (12):2767-2789.
    According to moral intuitionism, at least some moral seeming states are justification-conferring. The primary defense of this view currently comes from advocates of the standard account, who take the justification-conferring power of a moral seeming to be determined by its phenomenological credentials alone. However, the standard account is vulnerable to a problem. In brief, the standard account implies that moral knowledge is seriously undermined by those commonplace moral disagreements in which both agents have equally good phenomenological credentials supporting their (...)
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  9. Intuitionism and the Modal Logic of Vagueness.Susanne Bobzien & Ian Rumfitt - 2020 - Journal of Philosophical Logic 49 (2):221-248.
    Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with (...)
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  10. Social intuitionists answer six questions about morality.Jonathan Haidt & Fredrik Bjorklund - 2008 - In W. Sinnott-Armstrong (ed.), Moral Psychology Vol. 2. MIT Press.
    We review the state of the art in moral psychology to answer 6 questions: 1) Where do moral beliefs and motivations come from? 2) How does moral judgment work? 3) What is the evidence for the social intuitionist model? 4) What exactly are the moral intuitions? 5) How does morality develop? And 6) Why do people vary in their morality? We describe the intuitionist approach to moral psychology. The mind makes rapid affective evaluations of everything it encounters, and these evaluations (...)
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  11.  27
    Intuitionism.A. Heyting - 1956 - Amsterdam,: North-Holland Pub. Co..
  12. Intuitionism.A. Heyting - 1971 - Amsterdam,: North-Holland Pub. Co..
  13. Ethical Intuitionism and Moral Skepticism.Clayton Littlejohn - 2011 - In Jill Graper Hernandez (ed.), The New Intuitionism.
    In this paper, I defend a non-skeptical intuitionist approach to moral epistemology from recent criticisms. Starting with Sinnott-Armstrong's skeptical attacks, I argue that a familiar sort of skeptical argument rests on a problematic conception of the evidential grounds of our moral judgments. The success of his argument turns on whether we conceive of the evidential grounds of our moral judgments as consisting entirely of non-normative considerations. While we cannot avoid skepticism if we accept this conception of our evidential grounds, that's (...)
     
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  14.  13
    Intuitionism.David Kaspar - 2012 - New York: Continuum.
    Thinking about morality -- Story of contemporary intuitionism -- Moral knowledge -- New challenges to intuitionism -- Grounds of morality -- Right and the good reconsidered -- Intuitionism's rivals -- Being moral: how and why.
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  15. Elements of Intuitionism.Michael Dummett - 1977 - New York: Oxford University Press. Edited by Roberto Minio.
    This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.
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  16.  63
    Ethical Intuitionism: Re-Evaluations.Philip Stratton-Lake (ed.) - 2002 - Oxford University Press UK.
    Ethical Intuitionism was the dominant moral theory in Britain for much of the 18th, 19th and the first third of the twentieth century. However, during the middle decades of the twentieth century ethical intuitionism came to be regarded as utterly untenable. It was thought to be either empty, or metaphysically and epistemologically extravagant, or both. This hostility led to a neglect of the central intuitionist texts, and encouraged the growth of a caricature of intuitionism that could easily (...)
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  17.  49
    Basic Intuitionistic Conditional Logic.Yale Weiss - 2019 - Journal of Philosophical Logic 48 (3):447-469.
    Conditional logics have traditionally been intended to formalize various intuitively correct modes of reasoning involving conditional expressions in natural language. Although conditional logics have by now been thoroughly studied in a classical context, they have yet to be systematically examined in an intuitionistic context, despite compelling philosophical and technical reasons to do so. This paper addresses this gap by thoroughly examining the basic intuitionistic conditional logic ICK, the intuitionistic counterpart of Chellas’ important classical system CK. I give ICK both worlds (...)
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  18.  44
    Intuitionistic logic and modality via topology.Leo Esakia - 2004 - Annals of Pure and Applied Logic 127 (1-3):155-170.
    In the pioneering article and two papers, written jointly with McKinsey, Tarski developed the so-called algebraic and topological frameworks for the Intuitionistic Logic and the Lewis modal system. In this paper, we present an outline of modern systems with a topological tinge. We consider topological interpretation of basic systems GL and G of the provability logic in terms of the Cantor derivative and the Hausdorff residue.
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  19.  28
    Intuitionistic Type Theory.Per Martin-Löf - 1980 - Bibliopolis.
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  20. Moderate intuitionism and the epistemology of moral judgment.Robert Audi - 1998 - Ethical Theory and Moral Practice 1 (1):15-44.
    This paper outlines and defends a moderate intuitionism. The point of departure is the intuitionism of W. D. Ross (1930) in The Right and the Good, conceived as ethically pluralist and epistemologically rationalist. The paper articulates a conception of self-evidence – including mediate as well as immediate kinds – appropriate to a moderate intuitionism, explores some of the resources and varieties of that position, and considers some problems and prospects for a rationalist version of intuitionism. The (...)
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  21. Moral Intuitionism Defeated?Nathan Ballantyne & Joshua C. Thurow - 2013 - American Philosophical Quarterly 50 (4):411-422.
    Walter Sinnott-Armstrong has developed and progressively refined an argument against moral intuitionism—the view on which some moral beliefs enjoy non-inferential justification. He has stated his argument in a few different forms, but the basic idea is straightforward. To start with, Sinnott-Armstrong highlights facts relevant to the truth of moral beliefs: such beliefs are sometimes biased, influenced by various irrelevant factors, and often subject to disagreement. Given these facts, Sinnott-Armstrong infers that many moral beliefs are false. What then shall we (...)
     
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  22.  45
    Complete Intuitionistic Temporal Logics for Topological Dynamics.Joseph Boudou, Martín Diéguez & David Fernández-Duque - 2022 - Journal of Symbolic Logic 87 (3):995-1022.
    The language of linear temporal logic can be interpreted on the class of dynamic topological systems, giving rise to the intuitionistic temporal logic ${\sf ITL}^{\sf c}_{\Diamond \forall }$, recently shown to be decidable by Fernández-Duque. In this article we axiomatize this logic, some fragments, and prove completeness for several familiar spaces.
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  23.  35
    Intuitionistic Logic is a Connexive Logic.Davide Fazio, Antonio Ledda & Francesco Paoli - 2023 - Studia Logica 112 (1):95-139.
    We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic ($$\textrm{CHL}$$ CHL ), hereby introduced as an example of a strongly connexive logic with an intuitive semantics. We use the reverse algebraisation paradigm: $$\textrm{CHL}$$ CHL is presented as the assertional logic of a point regular variety (whose structure theory is examined in detail) that turns out to be term equivalent to the variety of Heyting algebras. We provide Hilbert-style and Gentzen-style proof systems for $$\textrm{CHL}$$ CHL ; moreover, we (...)
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  24. Brouwerian intuitionism.Michael Detlefsen - 1990 - Mind 99 (396):501-534.
    The aims of this paper are twofold: firstly, to say something about that philosophy of mathematics known as 'intuitionism' and, secondly, to fit these remarks into a more general message for the philosophy of mathematics as a whole. What I have to say on the first score can, without too much inaccuracy, be compressed into two theses. The first is that the intuitionistic critique of classical mathematics can be seen as based primarily on epistemological rather than on meaning-theoretic considerations. (...)
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  25.  64
    Intuitionism and conservatism.Mark T. Nelson - 1990 - Metaphilosophy 21 (3):282-293.
    I define ethical intuitionism as the view that it is appropriate to appeal to inferentially unsupported moral beliefs in the course of moral reasoning. I mention four common objections to this view, including the view that all such appeals to intuition make ethical theory politically and noetically conservative. I defend intuitionism from versions of this criticism expressed by R.B. Brandt, R.M. Hare and Richard Miller.
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  26. Intuitionism: An Introduction.Arend Heyting - 1956 - Amsterdam,: North-Holland Pub. Co..
  27.  34
    Intuitionistic validity in T-normal Kripke structures.Samuel R. Buss - 1993 - Annals of Pure and Applied Logic 59 (3):159-173.
    Let T be a first-order theory. A T-normal Kripke structure is one in which every world is a classical model of T. This paper gives a characterization of the intuitionistic theory T of sentences intuitionistically valid in all T-normal Kripke structures and proves the corresponding soundness and completeness theorems. For Peano arithmetic , the theory PA is a proper subtheory of Heyting arithmetic , so HA is complete but not sound for PA-normal Kripke structures.
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  28. Ethical intuitionism and the linguistic analogy.Philipp Https://Orcidorg Schwind - 2018 - Canadian Journal of Philosophy 48 (2):292-311.
    It is a central tenet of ethical intuitionism as defended by W. D. Ross and others that moral theory should reflect the convictions of mature moral agents. Hence, intuitionism is plausible to the extent that it corresponds to our well-considered moral judgments. After arguing for this claim, I discuss whether intuitionists offer an empirically adequate account of our moral obligations. I do this by applying recent empirical research by John Mikhail that is based on the idea of a (...)
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  29. Perceptual Intuitionism.Robert Cowan - 2013 - Philosophy and Phenomenological Research 90 (1):164-193.
    In the recent metaethical literature there has been significant interest in the prospects for what I am denoting ‘Perceptual Intuitionism’: the view that normal ethical agents can and do have non-inferential justification for first-order ethical beliefs by having ethical perceptual experiences, e.g., Cullison 2010, McBrayer 2010, Vayrynen 2008. If true, it promises to constitute an independent a posteriori intuitionist epistemology, providing an alternative to intuitionist accounts which posit a priori intuition and/or emotion as sources of non-inferentially justified ethical beliefs. (...)
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  30.  13
    An intuitionistic fixed point theory.Wilfried Buchholz - 1997 - Archive for Mathematical Logic 37 (1):21-27.
    In this article we prove that a certain intuitionistic version of the well-known fixed point theory \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\widehat{\rm ID}_1$\end{document} is conservative over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mbox{\sf HA}$\end{document} for almost negative formulas.
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  31.  30
    Intuitionistic Fixed Point Theories for Strictly Positive Operators.Christian Rüede & Thomas Strahm - 2002 - Mathematical Logic Quarterly 48 (2):195-202.
    In this paper it is shown that the intuitionistic .xed point theory equation image for α times iterated fixed points of strictly positive operator forms is conservative for negative arithmetic and equation image sentences over the theory equation image for α times iterated arithmetic comprehension without set parameters.This generalizes results previously due to Buchholz [5] and Arai [2].
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  32.  16
    Intuitionistic notions of boundedness in ℕ.Fred Richman - 2009 - Mathematical Logic Quarterly 55 (1):31-36.
    We consider notions of boundedness of subsets of the natural numbers ℕ that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ℕ to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. Most (...)
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  33. Truth-Maker Semantics for Intuitionistic Logic.Kit Fine - 2014 - Journal of Philosophical Logic 43 (2-3):549-577.
    I propose a new semantics for intuitionistic logic, which is a cross between the construction-oriented semantics of Brouwer-Heyting-Kolmogorov and the condition-oriented semantics of Kripke. The new semantics shows how there might be a common semantical underpinning for intuitionistic and classical logic and how intuitionistic logic might thereby be tied to a realist conception of the relationship between language and the world.
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  34.  56
    Semi-intuitionistic Logic.Juan Manuel Cornejo - 2011 - Studia Logica 98 (1-2):9-25.
    The purpose of this paper is to define a new logic $${\mathcal {SI}}$$ called semi-intuitionistic logic such that the semi-Heyting algebras introduced in [ 4 ] by Sankappanavar are the semantics for $${\mathcal {SI}}$$ . Besides, the intuitionistic logic will be an axiomatic extension of $${\mathcal {SI}}$$.
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  35. logicism, intuitionism, and formalism - What has become of them?Sten Lindstr©œm, Erik Palmgren, Krister Segerberg & Viggo Stoltenberg-Hansen (eds.) - 2008 - Berlin, Germany: Springer.
    The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating (...)
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  36. Intuitionism in Moral Epistemology.Elizabeth Tropman - 2017 - In Tristram Colin McPherson & David Plunkett (eds.), The Routledge Handbook of Metaethics. New York: Routledge. pp. 472-483.
    Attributions of moral knowledge are common in everyday life. We say that we know that some actions are morally right or wrong, permitted or required. Yet, how do we know such moral claims? Moral intuitionism is a family of theories in moral epistemology that tries to answer this question. Intuitionists are not skeptics about moral knowledge. They think that there are moral truths for us to know, and further, that knowledge of these truths is possible. What distinguishes intuitionism (...)
     
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  37.  67
    Intuitionistic Epistemic Logic, Kripke Models and Fitch’s Paradox.Carlo Proietti - 2012 - Journal of Philosophical Logic 41 (5):877-900.
    The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of (...)
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  38.  33
    Intuitionistic logic, model theory and forcing.Melvin Fitting - 1969 - Amsterdam,: North-Holland Pub. Co..
  39.  6
    Craig Interpolation Theorem Fails in Bi-Intuitionistic Predicate Logic.Grigory K. Olkhovikov & Guillermo Badia - 2024 - Review of Symbolic Logic 17 (2):611-633.
    In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urquhart for intuitionistic predicate logic with constant domains [13]. More precisely, we show that there is a valid implication $\phi \rightarrow \psi $ with no interpolant. Importantly, this result does not contradict the unfortunately named ‘Craig interpolation’ theorem established by Rauszer in [24] since that article is about the property more correctly named ‘deductive interpolation’ (see (...)
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  40.  78
    Evolutionary Intuitionism: A Theory of the Origin and Nature of Moral Facts.Brian Edward Zamulinski - 2007 - Ithaca: Mcgill-Queen's University Press.
    It seems impossible that organisms selected to maximize their genetic legacy could also be moral agents in a world in which taking risks for strangers is sometimes morally laudable. Brian Zamulinski argues that it is possible if morality is an evolutionary by-product rather than an adaptation.Evolutionary Intuitionism presents a new evolutionary theory of human morality. Zamulinski explains the evolution of foundational attitudes, whose relationships to acts constitute moral facts. With foundational attitudes and the resulting moral facts in place, he (...)
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  41.  65
    Full intuitionistic linear logic.Martin Hyland & Valeria de Paiva - 1993 - Annals of Pure and Applied Logic 64 (3):273-291.
    In this paper we give a brief treatment of a theory of proofs for a system of Full Intuitionistic Linear Logic. This system is distinct from Classical Linear Logic, but unlike the standard Intuitionistic Linear Logic of Girard and Lafont includes the multiplicative disjunction par. This connective does have an entirely natural interpretation in a variety of categorical models of Intuitionistic Linear Logic. The main proof-theoretic problem arises from the observation of Schellinx that cut elimination fails outright for an intuitive (...)
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  42. Intuitionistic mereology.Paolo Maffezioli & Achille C. Varzi - 2021 - Synthese 198 (Suppl 18):4277-4302.
    Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.
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  43. An Intuitionistic Theory of Types: Predicative Part.Per Martin-Löf - 1975 - In ¸ Iterose1975. North Holland.
  44. An intuitionistic defence of Berkeley’s master argument.Conor McGlynn - 2019 - Analysis 79 (2):236-242.
    Berkeley’s ‘master argument’ for idealism has been the subject of extensive criticism. Two of his strongest critics, A.N. Prior and J.L. Mackie, argue that due to various logical confusions on the part of Berkeley, the master argument fails to establish his idealist conclusion. Prior argues that Berkeley’s argument ‘proves too little’ in its conclusion, while Mackie contends that Berkeley confuses two different kinds of self-refutation in his argument. This paper proposes a defence of the master argument based on intuitionistic argument. (...)
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  45.  37
    Intuitionism and proof theory.A. Kino, John Myhill & Richard Eugene Vesley (eds.) - 1970 - Amsterdam,: North-Holland Pub. Co..
    Our first aim is to make the study of informal notions of proof plausible. Put differently, since the raison d'étre of anything like existing proof theory seems to rest on such notions, the aim is nothing else but to make a case for proof theory; ...
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  46.  55
    Intuitionistic logic with strong negation.Yuri Gurevich - 1977 - Studia Logica 36 (1-2):49 - 59.
    This paper is a reaction to the following remark by grzegorczyk: "the compound sentences are not a product of experiment. they arise from reasoning. this concerns also negations; we see that the lemon is yellow, we do not see that it is not blue." generally, in science the truth is ascertained as indirectly as falsehood. an example: a litmus-paper is used to verify the sentence "the solution is acid." this approach gives rise to a (very intuitionistic indeed) conservative extension of (...)
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  47.  14
    An Intuitionistic Axiomatisation of Real Closed Fields.Erik Palmgren - 2002 - Mathematical Logic Quarterly 48 (2):297-299.
    We give an intuitionistic axiomatisation of real closed fields which has the constructive reals as a model. The main result is that this axiomatisation together with just the decidability of the order relation gives the classical theory of real closed fields. To establish this we rely on the quantifier elimination theorem for real closed fields due to Tarski, and a conservation theorem of classical logic over intuitionistic logic for geometric theories.
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  48.  2
    Intuitionistic fuzzy aggregation and clustering.Zeshui Xu - 2012 - New York: Springer.
    Intuitionistic fuzzy aggregation techniques -- Intuitionistic fuzzy clustering algorithms.
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  49.  52
    Inquisitive Intuitionistic Logic.Wesley H. Holliday - 2020 - In Nicola Olivetti & Rineke Verbrugge (eds.), Advances in Modal Logic, Vol. 11. College Publications. pp. 329-348.
    Inquisitive logic is a research program seeking to expand the purview of logic beyond declarative sentences to include the logic of questions. To this end, inquisitive propositional logic extends classical propositional logic for declarative sentences with principles governing a new binary connective of inquisitive disjunction, which allows the formation of questions. Recently inquisitive logicians have considered what happens if the logic of declarative sentences is assumed to be intuitionistic rather than classical. In short, what should inquisitive logic be on an (...)
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  50.  34
    Mathematical Intuitionism and Intersubjectivity. A Critical Exposition of Arguments for Intuitionism.Tomasz Placek - 1999 - Bulletin of Symbolic Logic 8 (4):518-520.
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