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The Principles of Mathematics

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  1. Duration Enough for Presentism.Robert E. Pezet - 2020 - Axiomathes 30 (4):391-421.
    This paper considers a problem for dynamic presentism that has received little attention: its apparent inability to accommodate the duration of events. After outlining the problem, I defend presentism from it. This defence proceeds in two stages. First, I argue the objection rests on a faulty assumption: that duration is temporal extension. The paper challenges that assumption on several different ways of conceiving of temporal extension. This is the negative case and forms the bulk of the paper. Second, after diagnosing (...)
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  • Brandom, Hegel and Inferentialism.Tom Rockmore - 2002 - International Journal of Philosophical Studies 10 (4):429 – 447.
    In the course of developing a semantics with epistemological intent, Brandom claims that his inferentialism is Hegelian. This paper argues that, even on a charitable reading, Brandom is an anti-Hegelian.
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  • Russell's Paradox in Appendix B of the Principles of Mathematics : Was Frege's Response Adequate?Kevin C. Klement - 2001 - History and Philosophy of Logic 22 (1):13-28.
    In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy (...)
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  • A New–Old Characterisation of Logical Knowledge.Ivor Grattan-Guinness - 2012 - History and Philosophy of Logic 33 (3):245 - 290.
    We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of ?sortal terms?, two theories that will feature prominently. Second, we propose that logic comprises four ?momental sectors?: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (...)
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  • Worlds and Propositions Set Free.Otávio Bueno, Christopher Menzel & Edward N. Zalta - 2014 - Erkenntnis 79 (4):797–820.
    The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent object-theoretic versions of the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory in the definition of worlds. Next the authors show that an (...)
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  • Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes From Berkeley to Russell and Beyond. [REVIEW]Mikhail G. Katz & David Sherry - 2013 - Erkenntnis 78 (3):571-625.
    Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, (...)
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  • Ten Misconceptions From the History of Analysis and Their Debunking.Piotr Błaszczyk, Mikhail G. Katz & David Sherry - 2013 - Foundations of Science 18 (1):43-74.
    The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...)
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  • Busting a Myth About Leśniewski and Definitions.Rafal Urbaniak & K. Severi Hämäri - 2012 - History and Philosophy of Logic 33 (2):159 - 189.
    A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to Le?niewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Le?niewski's published or unpublished work is known where the standard conditions are discussed. Second, Le?niewski's own logical theories allow for creative definitions. Third, Le?niewski's celebrated ?rules of definition? lay (...)
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  • The Metaphysics of Propositions.Jeffrey C. King - 2017 - Oxford Handbooks Online.
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  • The Birth of Semantics.Richard Kimberly Heck & Robert C. May - 2020 - Journal for the History of Analytical Philosophy 8 (6):1-31.
    We attempt here to trace the evolution of Frege’s thought about truth. What most frames the way we approach the problem is a recognition that hardly any of Frege’s most familiar claims about truth appear in his earliest work. We argue that Frege’s mature views about truth emerge from a fundamental re-thinking of the nature of logic instigated, in large part, by a sustained engagement with the work of George Boole and his followers, after the publication of Begriffsschrift and the (...)
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  • Does Frege Have Too Many Thoughts? A Cantorian Problem Revisited.Kevin C. Klement - 2005 - Analysis 65 (1):45–49.
    This paper continues a thread in Analysis begun by Adam Rieger and Nicholas Denyer. Rieger argued that Frege’s theory of thoughts violates Cantor’s theorem by postulating as many thoughts as concepts. Denyer countered that Rieger’s construction could not show that the thoughts generated are always distinct for distinct concepts. By focusing on universally quantified thoughts, rather than thoughts that attribute a concept to an individual, I give a different construction that avoids Denyer’s problem. I also note that this problem for (...)
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  • Peirce, Frege, the Logic of Relations, and Church's Theorem.Randall R. Dipert - 1984 - History and Philosophy of Logic 5 (1):49-66.
    In this essay, I discuss some observations by Peirce which suggest he had some idea of the substantive metalogical differences between logics which permit both quantifiers and relations, and those which do not. Peirce thus seems to have had arguments?which even De Morgan and Frege lacked?that show the superior expressiveness of relational logics.
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  • Poincaré Against the Logicians.Michael Detlefsen - 1992 - Synthese 90 (3):349 - 378.
    Poincaré was a persistent critic of logicism. Unlike most critics of logicism, however, he did not focus his attention on the basic laws of the logicists or the question of their genuinely logical status. Instead, he directed his remarks against the place accorded to logical inference in the logicist's conception of mathematical proof. Following Leibniz, traditional logicist dogma (and this is explicit in Frege) has held that reasoning or inference is everywhere the same — that there are no principles of (...)
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  • Epistemic Modality, Mind, and Mathematics.Hasen Khudairi - 2017 - Gutenberg.
    This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how phenomenal consciousness and gradational possible-worlds models in Bayesian perceptual psychology relate to epistemic modal space. The book demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; the types of mathematical modality; to the epistemic status (...)
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  • Introduction to Foundations of Logic & Mathematics, Special Issue.Fraser MacBride - 2004 - Philosophical Quarterly 54 (214):1 - 15.
    Frege attempted to provide arithmetic with a foundation in logic. But his attempt to do so was confounded by Russell's discovery of paradox at the heart of Frege's system. The papers collected in this special issue contribute to the on-going investigation into the foundations of mathematics and logic. After sketching the historical background, this introduction provides an overview of the papers collected here, tracing some of the themes that connect them.
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  • Frege's Approach to the Foundations of Analysis (1874–1903).Matthias Schirn - 2013 - History and Philosophy of Logic 34 (3):266-292.
    The concept of quantity (Größe) plays a key role in Frege's theory of real numbers. Typically enough, he refers to this theory as ?theory of quantity? (?Größenlehre?) in the second volume of his opus magnum Grundgesetze der Arithmetik (Frege 1903). In this essay, I deal, in a critical way, with Frege's treatment of the concept of quantity and his approach to analysis from the beginning of his academic career until Frege 1903. I begin with a few introductory remarks. In Section (...)
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  • Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus.Alexandre Borovik & Mikhail G. Katz - 2012 - Foundations of Science 17 (3):245-276.
    Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, (...)
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  • Two Models of Propositional Structure.Filip Kawczyński - 2017 - Studia Semiotyczne—English Supplement 29:82-106.
    This paper is a comparison of two structural theories of propositions: the theory proposed by Kazimierz Ajdukiewicz in the 1960s and the theory developed by Jeffrey King at the beginning of the 21st century. The first section of the paper is an overview of these theories. The second part is a detailed discussion of significant similarities shared by them. In this section, I also identify and analyze ways in which these theories differ and attempt to determine if these differences are (...)
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  • Gottlob Frege, One More Time.Claude Imbert & tr Bontea, Adriana - 2000 - Hypatia 15 (4):156-173.
    : Frege's philosophical writings, including the "logistic project," acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing (...)
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  • The Grammatical Background of Kant's General Logic.Kurt Mosser - 2008 - Kantian Review 13 (1):116-140.
    In the Critique of Pure Reason, Kant conceives of general logic as a set of universal and necessary rules for the possibility of thought, or as a set of minimal necessary conditions for ascribing rationality to an agent . Such a conception, of course, contrasts with contemporary notions of formal, mathematical or symbolic logic. Yet, in so far as Kant seeks to identify those conditions that must hold for the possibility of thought in general, such conditions must hold a fortiori (...)
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  • Frege, Gottlob (1848-1925).Nikolay Milkov - 2020 - Bloomsbury Encyclopedia of Philosophers.
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  • Frege, Dedekind, and the Modern Epistemology of Arithmetic.Markus Pantsar - 2016 - Acta Analytica 31 (3):297-318.
    In early analytic philosophy, one of the most central questions concerned the status of arithmetical objects. Frege argued against the popular conception that we arrive at natural numbers with a psychological process of abstraction. Instead, he wanted to show that arithmetical truths can be derived from the truths of logic, thus eliminating all psychological components. Meanwhile, Dedekind and Peano developed axiomatic systems of arithmetic. The differences between the logicist and axiomatic approaches turned out to be philosophical as well as mathematical. (...)
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  • Frege’s Logicism and the Neo-Fregean Project.Matthias Schirn - 2014 - Axiomathes 24 (2):207-243.
    Neo-logicism is, not least in the light of Frege’s logicist programme, an important topic in the current philosophy of mathematics. In this essay, I critically discuss a number of issues that I consider to be relevant for both Frege’s logicism and neo-logicism. I begin with a brief introduction into Wright’s neo-Fregean project and mention the main objections that he faces. In Sect. 2, I discuss the Julius Caesar problem and its possible Fregean and neo-Fregean solution. In Sect. 3, I raise (...)
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  • Hume’s Principle and Axiom V Reconsidered: Critical Reflections on Frege and His Interpreters.Matthias Schirn - 2006 - Synthese 148 (1):171-227.
    In this paper, I shall discuss several topics related to Frege's paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege's notion of evidence and its interpretation by Jeshion, the introduction (...)
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  • Natural Numbers and Infinitesimals: A Discussion Between Benno Kerry and Georg Cantor.Carlo Proietti - 2008 - History and Philosophy of Logic 29 (4):343-359.
    During the first months of 1887, while completing the drafts of his Mitteilungen zur Lehre vom Transfiniten, Georg Cantor maintained a continuous correspondence with Benno Kerry. Their exchange essentially concerned two main topics in the philosophy of mathematics, namely, (a) the concept of natural number and (b) the infinitesimals. Cantor's and Kerry's positions turned out to be irreconcilable, mostly because of Kerry's irremediably psychologistic outlook, according to Cantor at least. In this study, I will examine and reconstruct the main points (...)
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  • Decompositions and Transformations: Conceptions of Analysis in the Early Analytic and Phenomenological Traditions.Michael Beaney - 2002 - Southern Journal of Philosophy 40 (S1):53-99.
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  • Cantor's Power-Set Theorem Versus Frege's Double-Correlation Thesis.Nino B. Cocciharella - 1992 - History and Philosophy of Logic 13 (2):179-201.
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  • What It is to Be an Intentional Object.Nicola Spinelli - 2016 - Disputatio 8 (42):93-112.
    This paper is about a certain view of intentionality, a problem faced by the view, and two ways in which, it has been proposed, the problem might be solved. The view is that every intentional state has an intentional object. The problem is that the putative intentional objects of some intentional states do not, or even cannot, exist. The two strategies to solve the problem and secure the view are those implemented by Tim Crane in his article “Intentional Objects”. In (...)
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  • John Cook Wilson.Mathieu Marion - 2010 - Stanford Encyclopedia of Philosophy.
    John Cook Wilson (1849–1915) was Wykeham Professor of Logic at New College, Oxford and the founder of ‘Oxford Realism’, a philosophical movement that flourished at Oxford during the first decades of the 20th century. Although trained as a classicist and a mathematician, his most important contribution was to the theory of knowledge, where he argued that knowledge is factive and not definable in terms of belief, and he criticized ‘hybrid’ and ‘externalist’ accounts. He also argued for direct realism in perception, (...)
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  • Gingerbread Nuts and Pebbles: Frege and the Neo-Kantians–Two Recently Discovered Documents.Sven Schlotter & Kai F. Wehmeier - 2013 - British Journal for the History of Philosophy 21 (3):591 - 609.
    (2012). Gingerbread Nuts and Pebbles: Frege and the Neo-Kantians – Two Recently Discovered Documents. British Journal for the History of Philosophy. ???aop.label???. doi: 10.1080/09608788.2012.692665.
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  • The Truth and Nothing but the Truth, yet Never the Whole Truth: Frege, Russell and the Analysis of Unities.Graham Stevens - 2003 - History and Philosophy of Logic 24 (3):221-240.
    It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there (...)
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  • PM's Circumflex, Syntax and Philosophy of Types.Kevin C. Klement - 2013 - In Bernard Linsky & Nicholas Griffin (eds.), The Palgrave Centenary Companion to Principia Mathematica. Palgrave-Macmillan. pp. 218-246.
    Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is (...)
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  • The Unnameable.Alasdair Urquhart - 2008 - Canadian Journal of Philosophy 38 (S1):119-135.
    Hans Herzberger as a philosopher and logician has shown deep interest both in the philosophy of Gottlob Frege, and in the topic of the inexpressible and the ineffable. In the fall of 1982, he taught at the University of Toronto, together with André Gombay, a course on Frege's metaphysics, philosophy of language, and foundations of arithmetic. Again, in the fall of 1986, he taught a seminar on the philosophy of language that dealt with 'the limits of discursive symbolism in several (...)
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  • Mctaggart and the Unreality of Time.Rögnvaldur Ingthorsson - 1998 - Axiomathes 9 (3):287-306.
    McTaggart's argument for the unreality of time is generally believed to be a self-contained argument independent of McTaggart's idealist ontology. I argue that this is mistaken. It is really a demonstration of a contradiction in the appearance of time, on the basis of certain a priori ontological axioms, in particular the thesis that all times exist in parity. When understood in this way, the argument is neither obscure or unfounded, but arguably does not address those versions of the A-theory that (...)
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  • Composition and Identities.Manuel Lechthaler - 2017 - Dissertation, University of Otago
    Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation which comes in a variety of (...)
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  • Photographic Representation and Depiction of Temporal Extension.Jiri Benovsky - 2012 - Inquiry: An Interdisciplinary Journal of Philosophy 55 (2):194-213.
    The main task of this paper is to understand if and how static images like photographs can represent and/or depict temporal extension (duration). In order to do this, a detour will be necessary to understand some features of the nature of photographic representation and depiction in general. This important detour will enable us to see that photographs (can) have a narrative content, and that the skilled photographer can 'tell a story' in a very clear sense, as well as control and (...)
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  • Gottlob Frege, One More Time.Claude Imbert - 2000 - Hypatia 15 (4):156-173.
    Frege's philosophical writings, including the “logistic project,” acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing their (...)
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  • Objectivity and Reality in Lotze and Frege.Michael Dummett - 1982 - Inquiry: An Interdisciplinary Journal of Philosophy 25 (1):95 – 114.
    Frege held that logical objects are objective but not wirklich, and that psychologism follows from the mistake of believing whatever is not wirklich to be subjective. It has been suggested that Frege's use of the terms ?objective? and ?wirklich? is in line with that found in Lotze's Logic; from this it has been inferred that Frege's doctrines have been misinterpreted as being ontological in character, but that they really belong to epistemology. In fact, Lotze held that something may be the (...)
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  • Formal Arithmetic Before Grundgesetze.Richard Kimberly Heck - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 497-537.
    A speculative investigation of how Frege's logical views change between Begriffsschrift and Grundgesetze and how this might have affected the formal development of logicism.
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  • Hume’s Principle and Axiom V Reconsidered: Critical Reflections on Frege and His Interpreters.Matthias Schirn - 2006 - Synthese 148 (1):171 - 227.
    In this paper, I shall discuss several topics related to Frege’s paradigms of second-order abstraction principles and his logicism. The discussion includes a critical examination of some controversial views put forward mainly by Robin Jeshion, Tyler Burge, Crispin Wright, Richard Heck and John MacFarlane. In the introductory section, I try to shed light on the connection between logical abstraction and logical objects. The second section contains a critical appraisal of Frege’s notion of evidence and its interpretation by Jeshion, the introduction (...)
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  • El Principio Fregeano Del Contexto En Die Grundlagen Der Arithmetik: Una Revisión a la Interpretación de Dummett.María Gabriela Fulugonio - 2008 - Análisis Filosófico 28 (2):205-238.
    En su obra de 1884, Die Grundlagen der Arithmetik [Gl.], Frege establece el principio del contexto como uno de sus principios fundamentales y propone valerse de él para dar con el concepto adecuado de número. Así, ofrece una definición de tipo contextual de número cardinal, pero ante una objeción que le resulta insalvable se decide por una definición explicita. La cuestión acerca de cuál ha sido entonces el sentido de establecer con tanto énfasis el principio del contexto admite más de (...)
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  • Decomposition and Analysis in Frege’s Grundgesetze.Gregory Landini - 1996 - History and Philosophy of Logic 17 (1-2):121-139.
    Frege seems to hold two incompatible theses:(i) that sentences differing in structure can yet express the same sense; and (ii) that the senses of the meaningful parts of a complex term are determinate parts of the sense of the term. Dummett offered a solution, distinguishing analysis from decomposition. The present paper offers an embellishment of Dummett?s distinction by providing a way of depicting the internal structures of complex senses?determinate structures that yield distinct decompositions. Decomposition is then shown to be adequate (...)
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  • Frege’s Cardinals as Concept-Correlates.Gregory Landini - 2006 - Erkenntnis 65 (2):207-243.
    In his "Grundgesetze", Frege hints that prior to his theory that cardinal numbers are objects he had an "almost completed" manuscript on cardinals. Taking this early theory to have been an account of cardinals as second-level functions, this paper works out the significance of the fact that Frege's cardinal numbers is a theory of concept-correlates. Frege held that, where n > 2, there is a one—one correlation between each n-level function and an n—1 level function, and a one—one correlation between (...)
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  • Is Frege's Definition of the Ancestral Adequate.Richard Heck - 2016 - Philosophia Mathematica 24 (1):91-116.
    Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of arithmetical induction. This (...)
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  • Our Knowledge of Numbers as Self-Subsistent Objects.William Demopoulos - 2005 - Dialectica 59 (2):141–159.
    A feature of Frege's philosophy of arithmetic that has elicited a great deal of attention in the recent secondary literature is his contention that numbers are ‘self‐subsistent’ objects. The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to Kreisel's folk‐lore observation that the central problem in the philosophy of mathematics is not the existence of mathematical objects, but the objectivity of mathematics. Although Frege was undoubtedly concerned with both questions, a goal of (...)
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  • Kerry und Frege über Begriff und Gegenstand.Eva Picardi - 1994 - History and Philosophy of Logic 15 (1):9-32.
    After describing the philosophical background of Kerry's work, an account is given of the way Kerry proposed to supplement Bolzano's conception of logic with a psychological account of the mental acts underlying mathematical judgements.In his writings Kerry criticized Frege's work and Kerry's views were then attacked by Frege.The following two issues were central to this controversy: (a) the relation between the content of a concept and the object of a concept; (b) the logical roles of the definite article. Not only (...)
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  • Scharp on Replacing Truth.Andrew Bacon - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (4):370-386.
    ABSTRACTKevin Scharp’s ‘Replacing Truth’ is an ambitious and far reaching account of the semantic paradoxes. In this critical discussion we examine one the books central claims: to have provided a theory of truth that avoids the revenge paradoxes. In the first part we assess this claim, and in the second part we investigate some features of Scharp’s preferred theory of truth, ADT, and compare it with existing theories such as the Kripke–Feferman theory. In the appendix a simple model of Scharp’s (...)
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  • Impossible Worlds.Franz Berto & Mark Jago - 2013 - Oxford: Oxford University Press.
    We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the leading philosophical (...)
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  • On the “Gray’s Elegy” Argument and its Bearing on Frege’s Theory of Sense.James Levine - 2004 - Philosophy and Phenomenological Research 69 (2):251–295.
    In his recent book, "The Metaphysicians of Meaning" (2000), Gideon Makin argues that in the so-called "Gray's Elegy" argument (the GEA) in "On Denoting", Russell provides decisive arguments against not only his own theory of denoting concepts but also Frege's theory of sense. I argue that by failing to recognize fundamental differences between the two theories, Makin fails to recognize that the GEA has less force against Frege's theory than against Russell's own earlier theory. While I agree with many aspects (...)
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  • Grundlagen, Section 64: Frege's Discussion of Definitions by Abstraction in Historical Context.Paolo Mancosu - 2015 - History and Philosophy of Logic 36 (1):62-89.
    I offer in this paper a contextual analysis of Frege's Grundlagen, section 64. It is surprising that with so much ink spilled on that section, the sources of Frege's discussion of definitions by abstraction have remained elusive. I hope to have filled this gap by providing textual evidence coming from, among other sources, Grassmann, Schlömilch, and the tradition of textbooks in geometry for secondary schools . In addition, I put Frege's considerations in the context of a widespread debate in Germany (...)
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