86 found
Order:
See also
  1.  31
    The Tarskian Turn. Deflationism and Axiomatic Truth.Leon Horsten - 2011 - MIT Press.
    The work of mathematician and logician Alfred Tarski (1901--1983) marks the transition from substantial to deflationary views about truth.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   36 citations  
  2. Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
    This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   27 citations  
  3. Axiomatizing Kripke's Theory of Truth.Volker Halbach & Leon Horsten - 2006 - Journal of Symbolic Logic 71 (2):677 - 712.
    We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to be true in (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   48 citations  
  4. Non-Archimedean Probability.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2013 - Milan Journal of Mathematics 81 (1):121-151.
    We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov’s axiomatization of probability is replaced by (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  5.  59
    Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia9 Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.
    Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. _1_ Introduction _2_ The Limits of Classical Probability Theory _2.1_ Classical probability functions _2.2_ Limitations _2.3_ Infinitesimals to the rescue? _3_ NAP Theory _3.1_ First four axioms of NAP _3.2_ Continuity and conditional probability _3.3_ The final axiom of NAP (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  6.  77
    Truth is Simple.Leon Horsten & Graham E. Leigh - 2017 - Mind 126 (501):195-232.
    Even though disquotationalism is not correct as it is usually formulated, a deep insight lies behind it. Specifically, it can be argued that, modulo implicit commitment to reflection principles, all there is to the notion of truth is given by a simple, natural collection of truth-biconditionals.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  7. Levity.Leon Horsten - 2009 - Mind 118 (471):555-581.
    In this article, the prospects of deflationism about the concept of truth are investigated. A new version of deflationism, called inferential deflationism, is articulated and defended. It is argued that it avoids the pitfalls of earlier deflationist views such as Horwich’s minimalist theory of truth and Field’s version of deflationism.
    No categories
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   23 citations  
  8. Hypatia's Silence.Martin Fischer, Leon Horsten & Carlo Nicolai - forthcoming - Noûs.
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  9. Cantorian Infinity and Philosophical Concepts of God.Joanna van der Veen & Leon Horsten - 2013 - European Journal for Philosophy of Religion 5 (3):117--138.
    It is often alleged that Cantor’s views about how the set theoretic universe as a whole should be considered are fundamentally unclear. In this article we argue that Cantor’s views on this subject, at least up until around 1896, are relatively clear, coherent, and interesting. We then go on to argue that Cantor’s views about the set theoretic universe as a whole have implications for theology that have hitherto not been sufficiently recognised. However, the theological implications in question, at least (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10. An Argument Concerning the Unknowable.Leon Horsten - 2009 - Analysis 69 (2):240-242.
    Williamson has forcefully argued that Fitch's argument shows that the domain of the unknowable is non-empty. And he exhorts us to make more inroads into the land of the unknowable. Concluding his discussion of Fitch's argument, he writes: " Once we acknowledge that [the domain of the unknowable] is non-empty, we can explore more effectively its extent. … We are only beginning to understand the deeper limits of our knowledge. " I shall formulate and evaluate a new argument concerning the (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  11. Impredicative Identity Criteria.Leon Horsten - 2010 - Philosophy and Phenomenological Research 80 (2):411-439.
    In this paper, a general perspective on criteria of identity of kinds of objects is developed. The question of the admissibility of impredicative or circular identitycriteria is investigated in the light of the view that is articulated. It is argued that in and of itself impredicativity docs not constitute sufficient grounds for rejecting aputative identity criterion. The view that is presented is applied to Davidson's criterion of identity for events and to the structuralist criterion of identity of placesin a structure.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  12. A Defence of Van Fraassen's Critique of Abductive Inference: Reply to Psillos.Ladyman James, Douven Igor, Horsten Leon & Fraassen Bas van - 1997 - Philosophical Quarterly 47 (188):305 - 321.
    Psillos has recently argued that van Fraassen’s arguments against abduction fail. Moreover, he claimed that, if successful, these arguments would equally undermine van Fraassen’s own constructive empiricism, for, Psillos thinks, it is only by appeal to abduction that constructive empiricism can be saved from issuing in a bald scepticism. We show that Psillos’ criticisms are misguided, and that they are mostly based on misinterpretations of van Fraassen’s arguments. Furthermore, we argue that Psillos’ arguments for his claim that constructive empiricism itself (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   23 citations  
  13. Philosophy of Mathematics.Leon Horsten - 2008 - Stanford Encyclopedia of Philosophy.
    If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case (...)
    Direct download  
     
    Export citation  
     
    Bookmark   14 citations  
  14.  98
    Reflecting on Absolute Infinity.Philip Welch & Leon Horsten - 2016 - Journal of Philosophy 113 (2):89-111.
    This article is concerned with reflection principles in the context of Cantor’s conception of the set-theoretic universe. We argue that within such a conception reflection principles can be formulated that confer intrinsic plausibility to strong axioms of infinity.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  15.  93
    Computational Structuralism &Dagger.Volker Halbach & Leon Horsten - 2005 - Philosophia Mathematica 13 (2):174-186.
    According to structuralism in philosophy of mathematics, arithmetic is about a single structure. First-order theories are satisfied by models that do not instantiate this structure. Proponents of structuralism have put forward various accounts of how we succeed in fixing one single structure as the intended interpretation of our arithmetical language. We shall look at a proposal that involves Tennenbaum's theorem, which says that any model with addition and multiplication as recursive operations is isomorphic to the standard model of arithmetic. On (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   14 citations  
  16.  32
    Probability for the Revision Theory of Truth.Catrin Campbell-Moore, Leon Horsten & Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (1):87-112.
    We investigate how to assign probabilities to sentences that contain a type-free truth predicate. These probability values track how often a sentence is satisfied in transfinite revision sequences, following Gupta and Belnap’s revision theory of truth. This answers an open problem by Leitgeb which asks how one might describe transfinite stages of the revision sequence using such probability functions. We offer a general construction, and explore additional constraints that lead to desirable properties of the resulting probability function. One such property (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  17.  85
    Revision Revisited.Leon Horsten, Graham E. Leigh, Hannes Leitgeb & Philip Welch - 2012 - Review of Symbolic Logic 5 (4):642-664.
    This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  18.  47
    The Expressive Power of Truth.Martin Fischer & Leon Horsten - 2015 - Review of Symbolic Logic 8 (2):345-369.
  19.  22
    A Defence of van Fraassen’s Critique of Abductive Inference: Reply to Psillos.James Ladyman, Igor Douven, Leon Horsten & Bas Fraassen - 1997 - Philosophical Quarterly 47 (188):305-321.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  20. The Deflationists' Axioms for Truth.Volker Halbach & Leon Horsten - 2005 - In J. C. Beall & Bradley Armour-Garb (eds.), Deflationism and Paradox. Oxford University Press.
  21.  83
    The Undecidability of Propositional Adaptive Logic.Leon Horsten & Philip Welch - 2007 - Synthese 158 (1):41-60.
    We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set is in general undecidable, and (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  22. Hypatia's Silence. Truth, Justification, and Entitlement.Martin Fischer, Leon Horsten & Carlo Nicolai - manuscript
    Hartry Field distinguished two concepts of type-free truth: scientific truth and disquotational truth. We argue that scientific type-free truth cannot do justificatory work in the foundations of mathematics. We also present an argument, based on Crispin Wright's theory of cognitive projects and entitlement, that disquotational truth can do justificatory work in the foundations of mathematics. The price to pay for this is that the concept of disquotational truth requires non-classical logical treatment.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  23. Godel's Disjunction: The Scope and Limits of Mathematical Knowledge.Leon Horsten & Philip Welch (eds.) - 2016 - Oxford University Press UK.
    To what extent can we hope to find answers to all mathematical questions? A famous theorem from Gödel entails that if our thinking capacities do not go beyond what an electronic computer is capable of, then there are indeed absolutely unsolvable mathematical problems. Thus it is of capital importance to find out whether human mathematicians can outstrip computers. Within this context, the contributions to this book critically examine positions about the scope and limits of human mathematical knowledge.
     
    Export citation  
     
    Bookmark   2 citations  
  24.  30
    Reasoning About Arbitrary Natural Numbers From a Carnapian Perspective.Leon Horsten & Stanislav O. Speranski - 2019 - Journal of Philosophical Logic 48 (4):685-707.
    Inspired by Kit Fine’s theory of arbitrary objects, we explore some ways in which the generic structure of the natural numbers can be presented. Following a suggestion of Saul Kripke’s, we discuss how basic facts and questions about this generic structure can be expressed in the framework of Carnapian quantified modal logic.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  25. Formal Methods in the Philosophy of Science.Leon Horsten & Igor Douven - 2008 - Studia Logica 89 (2):151-162.
    In this article, we reflect on the use of formal methods in the philosophy of science. These are taken to comprise not just methods from logic broadly conceived, but also from other formal disciplines such as probability theory, game theory, and graph theory. We explain how formal modelling in the philosophy of science can shed light on difficult problems in this domain.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  26. Earman on Underdetermination and Empirical Indistinguishability.Igor Douven & Leon Horsten - 1998 - Erkenntnis 49 (3):303-320.
    Earman (1993) distinguishes three notions of empirical indistinguishability and offers a rigorous framework to investigate how each of these notions relates to the problem of underdetermination of theory choice. He uses some of the results obtained in this framework to argue for a version of scientific anti- realism. In the present paper we first criticize Earman's arguments for that position. Secondly, we propose and motivate a modification of Earman's framework and establish several results concerning some of the notions of indistinguishability (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  27. Term Models for Abstraction Principles.Leon Horsten & Øystein Linnebo - 2016 - Journal of Philosophical Logic 45 (1):1-23.
    Kripke’s notion of groundedness plays a central role in many responses to the semantic paradoxes. Can the notion of groundedness be brought to bear on the paradoxes that arise in connection with abstraction principles? We explore a version of grounded abstraction whereby term models are built up in a ‘grounded’ manner. The results are mixed. Our method solves a problem concerning circularity and yields a ‘grounded’ model for the predicative theory based on Frege’s Basic Law V. However, the method is (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  28.  61
    No Future.Leon Horsten & Hannes Leitgeb - 2001 - Journal of Philosophical Logic 30 (3):259-265.
    The difficulties with formalizing the intensional notions necessity, knowability and omniscience, and rational belief are well-known. If these notions are formalized as predicates applying to (codes of) sentences, then from apparently weak and uncontroversial logical principles governing these notions, outright contradictions can be derived. Tense logic is one of the best understood and most extensively developed branches of intensional logic. In tense logic, the temporal notions future and past are formalized as sentential operators rather than as predicates. The question therefore (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  29.  26
    Triangulating Non-Archimedean Probability.Hazel Brickhill & Leon Horsten - 2018 - Review of Symbolic Logic 11 (3):519-546.
    We relate Popper functions to regular and perfectly additive such non-Archimedean probability functions by means of a representation theorem: every such non-Archimedean probability function is infinitesimally close to some Popper function, and vice versa. We also show that regular and perfectly additive non-Archimedean probability functions can be given a lexicographic representation. Thus Popper functions, a specific kind of non-Archimedean probability functions, and lexicographic probability functions triangulate to the same place: they are in a good sense interchangeable.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  30. Closer.Rafael De Clercq & Leon Horsten - 2005 - Synthese 146 (3):371 - 393.
    Criteria of identity should mirror the identity relation in being reflexive, symmetrical, and transitive. However, this logical requirement is only rarely met by the criteria that we are most inclined to propose as candidates. The present paper addresses the question how such obvious candidates are best approximated by means of relations that have all of the aforementioned features, i.e., which are equivalence relations. This question divides into two more basic questions. First, what is to be considered a ‘best’ approximation. And (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  31. Perceptual Indiscriminability: In Defence of Wright's Proof.Rafael de Clercq & Leon Horsten - 2004 - Philosophical Quarterly 54 (216):439-444.
    A series of unnoticeably small changes in an observable property may add up to a noticeable change. Crispin Wright has used this fact to prove that perceptual indiscriminability is a non-transitive relation. Delia Graff has recently argued that there is a 'tension' between Wright's assumptions. But Graff has misunderstood one of these, that 'phenomenal continua' are possible; and the other, that our powers of discrimination are finite, is sound. If the first assumption is properly understood, it is not in tension (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  32.  17
    Principles of Truth.Volker Halbach & Leon Horsten (eds.) - 2002 - Hänsel-Hohenhausen.
  33. Perceptual Indiscriminability and the Concept of a Color Shade.Leon Horsten - 2010 - In Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds: Vaguenesss, its Nature and its Logic. Oxford University Press.
  34. Strict Conditionals: A Negative Result.Jan Heylen & Leon Horsten - 2006 - Philosophical Quarterly 56 (225):536–549.
    Jonathan Lowe has argued that a particular variation on C.I. Lewis' notion of strict implication avoids the paradoxes of strict implication. We show that Lowe's notion of implication does not achieve this aim, and offer a general argument to demonstrate that no other variation on Lewis' notion of constantly strict implication describes the logical behaviour of natural-language conditionals in a satisfactory way.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  35.  70
    In Defense of Epistemic Arithmetic.Leon Horsten - 1998 - Synthese 116 (1):1-25.
    This paper presents a defense of Epistemic Arithmetic as used for a formalization of intuitionistic arithmetic and of certain informal mathematical principles. First, objections by Allen Hazen and Craig Smorynski against Epistemic Arithmetic are discussed and found wanting. Second, positive support is given for the research program by showing that Epistemic Arithmetic can give interesting formulations of Church's Thesis.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  36. The Semantical Paradoxes, the Neutrality of Truth and the Neutrality of the Minimalist Theory of Truth.Leon Horsten - 1995 - In P. Cartois (ed.), The Many Problems of Realism (Studies in the General Philosophy of Science: Volume 3). Tilberg University Press.
  37.  77
    On the Quantitative Scalar or-Implicature.Leon Horsten - 2005 - Synthese 146 (1-2):111-127.
    . Two simple generalized conversational implicatures are investigated :(1) the quantitative scalar implicature associated with ‘or’, and (2) the ‘not-and’-implicature, which is the dual to (1). It is argued that it is more fruitful to consider these implicatures as rules of interpretation and to model them in an algebraic fashion than to consider them as nonmonotonic rules of inference and to model them in a proof-theoretic way.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  38.  82
    One Hundred Years of Semantic Paradox.Leon Horsten - 2015 - Journal of Philosophical Logic (6):1-15.
    This article contains an overview of the main problems, themes and theories relating to the semantic paradoxes in the twentieth century. From this historical overview I tentatively draw some lessons about the way in which the field may evolve in the next decade.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  39.  41
    Canonical Naming Systems.Leon Horsten - 2004 - Minds and Machines 15 (2):229-257.
    This paper outlines a framework for the abstract investigation of the concept of canonicity of names and of naming systems. Degrees of canonicity of names and of naming systems are distinguished. The structure of the degrees is investigated, and a notion of relative canonicity is defined. The notions of canonicity are formally expressed within a Carnapian system of second-order modal logic.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  40.  94
    Probabilist antirealism.Igor Douven, Leon Horsten & Jan-Willem Romeijn - 2010 - Pacific Philosophical Quarterly 91 (1):38-63.
    Until now, antirealists have offered sketches of a theory of truth, at best. In this paper, we present a probabilist account of antirealist truth in some formal detail, and we assess its ability to deal with the problems that are standardly taken to beset antirealism.
    Direct download (5 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   2 citations  
  41.  47
    Generic Structures†.Leon Horsten - 2019 - Philosophia Mathematica 27 (3):362-380.
    In this article ideas from Kit Fine’s theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generis mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine’s sense.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  42. Reflecting in Epistemic Arithmetic.Leon Horsten - 1996 - Journal of Symbolic Logic 61 (3):788-801.
    An epistemic formalization of arithmetic is constructed in which certain non-trivial metatheoretical inferences about the system itself can be made. These inferences involve the notion of provability in principle, and cannot be made in any consistent extensions of Stewart Shapiro's system of epistemic arithmetic. The system constructed in the paper can be given a modal-structural interpretation.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  43.  75
    Truth and Existence.Jan Heylen & Leon Horsten - 2017 - Thought: A Journal of Philosophy 6 (1):106-114.
    Halbach has argued that Tarski biconditionals are not ontologically conservative over classical logic, but his argument is undermined by the fact that he cannot include a theory of arithmetic, which functions as a theory of syntax. This article is an improvement on Halbach's argument. By adding the Tarski biconditionals to inclusive negative free logic and the universal closure of minimal arithmetic, which is by itself an ontologically neutral combination, one can prove that at least one thing exists. The result can (...)
    No categories
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  44.  15
    An Axiomatic Investigation of Provability as a Primitive Predicate.Leon Horsten - 2003 - In Leon Horsten & Volker Halbach (eds.), Principles of Truth. De Gruyter. pp. 203-220.
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
  45.  28
    Modal-Epistemic Variants of Shapiro’s System of Epistemic Arithmetic.Leon Horsten - 1994 - Notre Dame Journal of Formal Logic 35 (2):284-291.
  46.  68
    On the Exclusivity Implicature of ‘Or’ or on the Meaning of Eating Strawberries.Liza Verhoeven & Leon Horsten - 2005 - Studia Logica 81 (1):19-24.
    This paper is a contribution to the program of constructing formal representations of pragmatic aspects of human reasoning. We propose a formalization within the framework of Adaptive Logics of the exclusivity implicature governing the connective 'or'.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  47.  42
    Human-Effective Computability†.Marianna Antonutti Marfori & Leon Horsten - 2019 - Philosophia Mathematica 27 (1):61-87.
    We analyse Kreisel’s notion of human-effective computability. Like Kreisel, we relate this notion to a concept of informal provability, but we disagree with Kreisel about the precise way in which this is best done. The resulting two different ways of analysing human-effective computability give rise to two different variants of Church’s thesis. These are both investigated by relating them to transfinite progressions of formal theories in the sense of Feferman.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  48.  46
    Bas C. Van Fraassen, The Empirical Stance. [REVIEW]Leon Horsten - 2004 - International Studies in the Philosophy of Science 18 (1):95-97.
  49. Having an Interpretation. [REVIEW]Leon Horsten - 2010 - Philosophical Studies 150 (3):449 - 459.
    I investigate what it means to have an interpretation of our language, how we manage to bestow a determinate interpretation to our utterances, and to which extent our interpretation of the world is determinate. All this is done in dialogue with van Fraassen's insightful discussion of Putnam's model-theoretic argument and of scientific structuralism.
    No categories
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  50.  6
    Models for the Logic of Possible Proofs.Leon Horsten - 2000 - Pacific Philosophical Quarterly 81 (1):49-66.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   4 citations  
1 — 50 / 86