Results for 'logicism'

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  1. 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 rudimentary facts (...)
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  2. Logicism, Interpretability, and Knowledge of Arithmetic.Sean Walsh - 2014 - Review of Symbolic Logic 7 (1):84-119.
    A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are representable in the logical principles. The notions of representation considered here are related to theory-based and structure-based notions of (...)
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  3.  33
    Is Logicist Cognitive Science Possible?Alan Garnham - 1993 - Mind and Language 8 (1):49-71.
    This paper argues against Oaksford and Chater's claim that logicist cognitive science is not possible. It suggests that there arguments against logicist cognitive science are too closely tied to the account of Pylyshyn and of Fodor, and that the correct way of thinking about logicist cognitive science is in a mental models framework.
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  4.  69
    Against Logicist Cognitive Science.Mike Oaksford & Nick Chater - 1991 - Mind and Language 6 (1):1-38.
  5. Hilbert, Logicism, and Mathematical Existence.José Ferreirós - 2009 - Synthese 170 (1):33 - 70.
    David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a (...)
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  6.  73
    Logicism, Mental Models and Everyday Reasoning: Reply to Garnham.Nick Chater & Mike Oaksford - 1993 - Mind and Language 8 (1):72-89.
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  7.  49
    Logicism and its Philosophical Legacy.William Demopoulos - 2013 - Cambridge University Press.
    The idea that mathematics is reducible to logic has a long history, but it was Frege who gave logicism an articulation and defense that transformed it into a distinctive philosophical thesis with a profound influence on the development of philosophy in the twentieth century. This volume of classic, revised and newly written essays by William Demopoulos examines logicism's principal legacy for philosophy: its elaboration of notions of analysis and reconstruction. The essays reflect on the deployment of these ideas (...)
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  8. Logicism and the Ontological Commitments of Arithmetic.Harold T. Hodes - 1984 - Journal of Philosophy 81 (3):123-149.
  9.  85
    Plural Logicism.Francesca Boccuni - 2013 - Erkenntnis 78 (5):1051-1067.
    PG (Plural Grundgesetze) is a consistent second-order system which is aimed to derive second-order Peano arithmetic. It employs the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. George Boolos’ plural semantics is replaced with Enrico Martino’s Acts of Choice Semantics (ACS), which is developed from the notion of arbitrary reference in mathematical reasoning. Also, substitutional quantification is exploited to interpret quantification into predicate position. ACS provides a form of logicism which is (...)
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  10. ‘Neo-Logicist‘ Logic is Not Epistemically Innocent.Stewart Shapiro & Alan Weir - 2000 - Philosophia Mathematica 8 (2):160--189.
    The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been (...)
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  11. Neo-Logicism and Russell’s Logicism.Kevin C. Klement - 2012 - Russell: The Journal of Bertrand Russell Studies 32 (2):159.
    Most advocates of the so-called “neologicist” movement in the philosophy of mathematics identify themselves as “Neo-Fregeans” (e.g., Hale and Wright): presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature, and when it is, often dismissed as not really logicism at all (in lights of its assumption of axioms of infinity, reducibiity and so on). In this paper I have three aims: firstly, to identify more clearly (...)
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  12.  53
    The Logicism of Frege, Dedekind, and Russell.William Demopoulos & Peter Clark - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 129--165.
    The common thread running through the logicism of Frege, Dedekind, and Russell is their opposition to the Kantian thesis that our knowledge of arithmetic rests on spatio-temporal intuition. Our critical exposition of the view proceeds by tracing its answers to three fundamental questions: What is the basis for our knowledge of the infinity of the numbers? How is arithmetic applicable to reality? Why is reasoning by induction justified?
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  13. Neo-Logicism? An Ontological Reduction of Mathematics to Metaphysics.Edward N. Zalta - 2000 - Erkenntnis 53 (1-2):219-265.
    In this paper, we describe "metaphysical reductions", in which the well-defined terms and predicates of arbitrary mathematical theories are uniquely interpreted within an axiomatic, metaphysical theory of abstract objects. Once certain (constitutive) facts about a mathematical theory T have been added to the metaphysical theory of objects, theorems of the metaphysical theory yield both an analysis of the reference of the terms and predicates of T and an analysis of the truth of the sentences of T. The well-defined terms and (...)
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  14. Logicism Lite.Richard Jeffrey - 2002 - Philosophy of Science 69 (3):474-496.
    Logicism Lite counts number‐theoretical laws as logical for the same sort of reason for which physical laws are counted as as empirical: because of the character of the data they are responsible to. In the case of number theory these are the data verifying or falsifying the simplest equations, which Logicism Lite counts as true or false depending on the logical validity or invalidity of first‐order argument forms in which no numbertheoretical notation appears.
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  15. Natural Logicism Via the Logic of Orderly Pairing.Neil Tennant - manuscript
    The aim here is to describe how to complete the constructive logicist program, in the author’s book Anti-Realism and Logic, of deriving all the Peano-Dedekind postulates for arithmetic within a theory of natural numbers that also accounts for their applicability in counting finite collections of objects. The axioms still to be derived are those for addition and multiplication. Frege did not derive them in a fully explicit, conceptually illuminating way. Nor has any neo-Fregean done so.
     
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  16. 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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  17. Arithmetic, Logicism, and Frege’s Definitions.Timothy Perrine - 2021 - International Philosophical Quarterly 61 (1):5-25.
    This paper describes both an exegetical puzzle that lies at the heart of Frege’s writings—how to reconcile his logicism with his definitions and claims about his definitions—and two interpretations that try to resolve that puzzle, what I call the “explicative interpretation” and the “analysis interpretation.” This paper defends the explicative interpretation primarily by criticizing the most careful and sophisticated defenses of the analysis interpretation, those given my Michael Dummett and Patricia Blanchette. Specifically, I argue that Frege’s text either are (...)
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  18. The Logicist Foundations of Mathematics.Rudolf Carnap - 1931 - In Paul Benacerraf & Hilary Putnam (eds.), Philosophy of Mathematics: Selected Readings. Cambridge University Press. pp. 41--52.
  19.  54
    Logicism Revisited.Alan Musgrave - 1977 - British Journal for the Philosophy of Science 28 (2):99-127.
  20.  56
    Epistemic Logicism & Russell's Regressive Method.A. D. Irvine - 1989 - Philosophical Studies 55 (3):303 - 327.
  21.  41
    Logicism and Neologicism.Neil Tennant - 2013 - Stanford Encyclopedia of Philosophy.
  22. Inferentialism, Logicism, Harmony, and a Counterpoint.Neil Tennant - manuscript
    Inferentialism is explained as an attempt to provide an account of meaning that is more sensitive (than the tradition of truth-conditional theorizing deriving from Tarski and Davidson) to what is learned when one masters meanings.
     
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  23. Epistemic Logicism and Russell's Regressive Method'.A. D. Irvine - 1999 - In Bertrand Russell: Critical Assessments. Routledge. pp. 2.
     
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  24. Logicism, Ontology, and the Epistemology of Second-Order Logic.Richard Kimberly Heck - 2018 - In Ivette Fred-Rivera & Jessica Leach (eds.), Being Necessary: Themes of Ontology and Modality from the Work of Bob Hale. Oxford: Oxford University Press. pp. 140-169.
    In two recent papers, Bob Hale has attempted to free second-order logic of the 'staggering existential assumptions' with which Quine famously attempted to saddle it. I argue, first, that the ontological issue is at best secondary: the crucial issue about second-order logic, at least for a neo-logicist, is epistemological. I then argue that neither Crispin Wright's attempt to characterize a `neutralist' conception of quantification that is wholly independent of existential commitment, nor Hale's attempt to characterize the second-order domain in terms (...)
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  25. Logicism Revisited.Otávio Bueno - 2001 - Principia 5 (1-2):99-124.
    In this paper, I develop a new defense of logicism: one that combines logicism and nominalism. First, I defend the logicist approach from recent criticisms; in particular from the charge that a cruciai principie in the logicist reconstruction of arithmetic, Hume's Principle, is not analytic. In order to do that, I argue, it is crucial to understand the overall logicist approach as a nominalist view. I then indicate a way of extending the nominalist logicist approach beyond arithmetic. Finally, (...)
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  26.  34
    Russell, Logicism, and the Choice of Logical Constants.Michael Byrd - 1989 - Notre Dame Journal of Formal Logic 30 (3):343-361.
  27. Russell on Logicism and Coherence.Conor Mayo-Wilson - 2011 - Russell: The Journal of Bertrand Russell Studies 31 (1):89-106.
    According to Quine, Charles Parsons, Mark Steiner, and others, Russell's logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as a prioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell's explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of logicism? Building (...)
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  28.  74
    Singular Terms and Arithmetical Logicism.Ian Rumfitt - 2003 - Philosophical Books 44 (3):193--219.
    This article is a critical notice of Bob Hale and Crispin Wright's *The Reason's Proper Study* (OUP). It focuses particularly on their attempts (crucial to their neo-logicist project) to say what a singular term is. I identify problems for their account but include some constructive suggestions about how it might be improved.
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  29.  16
    Logicism, Pragmatism, and Metascience: Towards a Pancritical Pragmatic Theory of Meta-Level Discourse.G. S. Axtell - 1990 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:39 - 49.
    The faults of logical empiricist accounts of metascientific discourse are examined through a study of the modifications Carnap makes to his version of the program over four decades. As empiricists acquiesced on the distinction between theory and observation, Carnap attempted to retain and insulate an equally suspect sharp distinction between the theoretic and the pragmatic. Carnap's later philosophy was understood as a modification of the program in the direction of pragmatism. But neither the key notion of "external questions" nor an (...)
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  30. Logicism and the Problem of Infinity: The Number of Numbers: Articles.Gregory Landini - 2011 - Philosophia Mathematica 19 (2):167-212.
    Simple-type theory is widely regarded as inadequate to capture the metaphysics of mathematics. The problem, however, is not that some kinds of structure cannot be studied within simple-type theory. Even structures that violate simple-types are isomorphic to structures that can be studied in simple-type theory. In disputes over the logicist foundations of mathematics, the central issue concerns the problem that simple-type theory fails to assure an infinity of natural numbers as objects. This paper argues that the problem of infinity is (...)
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  31. Logicism and Logical Truth.Warren D. Goldfarb - 1982 - Journal of Philosophy 79 (11):692-695.
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  32.  39
    The Logicist Manifesto: At Long Last Let Logic-Based Artificial Intelligence Become a Field Unto Itself.Selmer Bringsjord - 2008 - Journal of Applied Logic 6 (4):502-525.
  33.  4
    Carnap, Logicism, and Ontological Commitment.Otávio Bueno - 2016 - In Sorin Costreie (ed.), Early Analytic Philosophy – New Perspectives on the Tradition. Springer. pp. 337--352.
    Throughout most of his career, Rudolf Carnap attempted to articulate an empiricist view. Central to this project is the understanding of how empiricism can be made compatible with abstract objects that seem to be invoked in mathematics. In this paper, I discuss and critically evaluate three moves made by Carnap to accommodate mathematical talk within his empiricist program: the “weak logicism” in the Aufbau; the combination of formalism and logicism in the Logische Syntax; and the distinction between internal (...)
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  34.  43
    Logicism.John Kekes - 1982 - Idealistic Studies 12 (1):1-13.
    Logicism is the fallacy of making exaggerated claims for logic. My aim here is to expose and criticize that fallacy as it occurs in the relation between logic and philosophy.
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  35. Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
    According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and (...)
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  36.  67
    Logic, Logicism, and Intuitions in Mathematics.Besim Karakadılar - 2001 - Dissertation, Middle East Technical University
    In this work I study the main tenets of the logicist philosophy of mathematics. I deal, basically, with two problems: (1) To what extent can one dispense with intuition in mathematics? (2) What is the appropriate logic for the purposes of logicism? By means of my considerations I try to determine the pros and cons of logicism. My standpoint favors the logicist line of thought. -/- .
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  37. Logicism, Quantifiers, and Abstraction.Aldo Antonelli - manuscript
    With the aid of a non-standard (but still first-order) cardinality quantifier and an extra-logical operator representing numerical abstraction, this paper presents a formalization of first-order arithmetic, in which numbers are abstracta of the equinumerosity relation, their properties derived from those of the cardinality quantifier and the abstraction operator.
     
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  38. 13 Logicist Analysis and Conceptual Inferences L'analyse Logiciste Et les Inferences Conceptuelles.Peter Stockinger - 1990 - In Tadeusz Buksiński (ed.), Interpretation in the Humanities. Uniwersytet Im. Adama Mickiewicza W Poznaniu. pp. 71--284.
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  39.  52
    Logicism and Formal Necessity: Reflections on Kant’s Modal Metaphysics.James Van Cleve - 2018 - Kantian Review 23 (3):449-459.
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  40. Logicism: Fregean and Neo-Fregean.Marco Ruffino - 1998 - Manuscrito 21:149-188.
  41.  20
    Logicism and the Philosophy of Language: Selections From Frege and Russell.Arthur Sullivan (ed.) - 2003 - Broadview Press.
    Logicism and the Philosophy of Language brings together the core works by Gottlob Frege and Bertrand Russell on logic and language. In their separate efforts to clarify mathematics through the use of logic in the late nineteenth and early twentieth century, Frege and Russell both recognized the need for rigorous and systematic semantic analysis of language. It was their turn to this style of analysis that would establish the philosophy of language as an autonomous area of inquiry. This anthology (...)
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  42. Logicism Reconsidered.Patricia A. Blanchette - 1990 - Dissertation, Stanford University
    This thesis is an examination of Frege's logicism, and of a number of objections which are widely viewed as refutations of the logicist thesis. In the view offered here, logicism is designed to provide answers to two questions: that of the nature of arithmetical truth, and that of the source of arithmetical knowledge. ;The first objection dealt with here is the view that logicism is not an epistemologically significant thesis, due to the fact that the epistemological status (...)
     
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  43. Logicism, Structuralism and Objectivity.Elaine Landry - 2001 - Topoi 20 (1):79-95.
  44.  26
    Minimal Logicism.Francesca Boccuni - 2014 - Philosophia Scientae 18:81-94.
    PLV (Plural Basic Law V) is a consistent second-order system which is aimed to derive second-order Peano arithmetic. It employs the notion of plural quantification and a first-order formulation of Frege's infamous Basic Law V. George Boolos' plural semantics is replaced with Enrico Martino's Acts of Choice Semantics (ACS), which is developed from the notion of arbitrary reference in mathematical reasoning. ACS provides a form of logicism which is radically alternative to Frege's and which is grounded on the existence (...)
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  45.  59
    Logicist Responses to Kant: (Early) Frege and (Early) Russell.Michael Kremer - 2006 - Philosophical Topics 34 (1/2):163-188.
  46.  79
    The Logic in Logicism.Alexander Bird - 1997 - Dialogue 36 (2):341--60.
    Frege's logicism consists of two theses: the truths of arithmetic are truths of logic; the natural numbers are objects. In this paper I pose the question: what conception of logic is required to defend these theses? I hold that there exists an appropriate and natural conception of logic in virtue of which Hume's principle is a logical truth. Hume's principle, which states that the number of Fs is the number of Gs iff the concepts F and G are equinumerous (...)
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  47. Logicism, Some Considerations.Paul Benacerraf - 1960 - Dissertation, Princeton University
     
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  48.  19
    Logicism and Ramsification: William Demopoulos: Logicism and its Philosophical Legacy. Cambridge: Cambridge University Press, 2013, Xii+272pp, $99.00 HB. [REVIEW]Georg Schiemer - 2014 - Metascience 23 (2):255-261.
    This excellent book presents a collection of eleven articles, all but one of which were written by William Demopoulos over the period of the last 19 years. The book comprises eight published articles, some of which have appeared only recently, as well as three new articles. The thematic scope of the topics investigated here is broad and ranges from Frege’s original logicist program outlined in his Grundlagen der Arithmetik (Frege 1884) to Carnap’s mature work on the logical reconstruction of scientific (...)
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  49. Logicism: A New Look.John Burgess - manuscript
    Adapated from talks at the UCLA Logic Center and the Pitt Philosophy of Science Series. Exposition of material from Fixing Frege, Chapter 2 (on predicative versions of Frege’s system) and from “Protocol Sentences for Lite Logicism” (on a form of mathematical instrumentalism), suggesting a connection. Provisional version: references remain to be added. To appear in Mathematics, Modality, and Models: Selected Philosophical Papers, coming from Cambridge University Press.
     
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  50.  42
    Logicism and Carnap's Logical Syntax.Adrian Frey - 2011 - .
    Although logicism played a significant role in Carnap's philosophical thinking, the relation of his philosophy of mathematics to the main tenets of the logicist tradition is complex and variable. is paper examines one aspect of this relation by discussing the following question: What elements of Carnap's Logical Syntax of Language, if any at all, indicate a real commitment to that tradition? It will be shown that although important aspects of Frege-Russell logicism are incorporated into the framework developed in (...)
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