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Frege

Cambridge: Harvard University Press (1973)

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  1. Minimalism and the unbearable lightness of being.John Divers & Alexander Miller - 1995 - Philosophical Papers 24 (2):127-139.
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  • Intuiting the infinite.Robin Jeshion - 2014 - Philosophical Studies 171 (2):327-349.
    This paper offers a defense of Charles Parsons’ appeal to mathematical intuition as a fundamental factor in solving Benacerraf’s problem for a non-eliminative structuralist version of Platonism. The literature is replete with challenges to his well-known argument that mathematical intuition justifies our knowledge of the infinitude of the natural numbers, in particular his demonstration that any member of a Hilbertian stroke string ω-sequence has a successor. On Parsons’ Kantian approach, this amounts to demonstrating that for an “arbitrary” or “vaguely represented” (...)
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  • Frege on Number Properties.Andrew D. Irvine - 2010 - Studia Logica 96 (2):239-260.
    In the Grundlagen , Frege offers eight main arguments, together with a series of more minor supporting arguments, against Mill’s view that numbers are “properties of external things”. This paper reviews all eight of these arguments, arguing that none are conclusive.
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  • Scientific Discovery Reloaded.Emiliano Ippoliti - 2020 - Topoi 39 (4):847-856.
    The way scientific discovery has been conceptualized has changed drastically in the last few decades: its relation to logic, inference, methods, and evolution has been deeply reloaded. The ‘philosophical matrix’ moulded by logical empiricism and analytical tradition has been challenged by the ‘friends of discovery’, who opened up the way to a rational investigation of discovery. This has produced not only new theories of discovery, but also new ways of practicing it in a rational and more systematic way. Ampliative rules, (...)
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  • Introduction.Øystein Linnebo - 2009 - Synthese 170 (3):321-329.
    Neo-Fregean logicism seeks to base mathematics on abstraction principles. But the acceptable abstraction principles are surrounded by unacceptable ones. This is the "bad company problem." In this introduction I first provide a brief historical overview of the problem. Then I outline the main responses that are currently being debated. In the course of doing so I provide summaries of the contributions to this special issue.
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  • 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 (...)
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  • Number determiners, numbers, and arithmetic.Thomas Hofweber - 2005 - Philosophical Review 114 (2):179-225.
    In his groundbreaking Grundlagen, Frege (1884) pointed out that number words like ‘four’ occur in ordinary language in two quite different ways and that this gives rise to a philosophical puzzle. On the one hand ‘four’ occurs as an adjective, which is to say that it occurs grammatically in sentences in a position that is commonly occupied by adjectives. Frege’s example was (1) Jupiter has four moons, where the occurrence of ‘four’ seems to be just like that of ‘green’ in (...)
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  • Stewart Shapiro’s Philosophy of Mathematics[REVIEW]Harold Hodes - 2002 - Philosophy and Phenomenological Research 65 (2):467–475.
    Two slogans define structuralism: contemporary mathematics studies structures; mathematical objects are places in those structures. Shapiro’s version of structuralism posits abstract objects of three sorts. A system is “a collection of objects with certain relations” between these objects. “An extended family is a system of people with blood and marital relationships.” A baseball defense, e.g., the Yankee’s defense in the first game of the 1999 World Series, is a also a system, “a collection of people with on-field spatial and ‘defensive-role’ (...)
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  • Wittgenstein’s Ignorance of Argumentation Theory and Toulmin’s Rehabilitation of Wittgenstein.Henrique Jales Ribeiro - 2024 - Philosophy International Journal 7 (2):1-5.
    The author- following his own research on the subject- argues that Wittgenstein ignores argumentation theory and in general, the problems of rhetoric and argumentation. From this point of view, he frames Stephen Toulmin’s reading of Wittgenstein, arguing that the British philosopher- who was a student of the Austrian- advocates precisely the same thesis. He explains that this happens in a very peculiar (rhetorical) context on Toulmin’s part; a context in which, in essence, Wittgenstein’s philosophy is being rehabilitated.
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  • Frege's theorem and his logicism.Hirotoshi Tabata - 2000 - History and Philosophy of Logic 21 (4):265-295.
    As is well known, Frege gave an explicit definition of number (belonging to some concept) in ?68 of his Die Grundlagen der Arithmetik.
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  • On Fundamental Differences between Dependent and Independent Meanings.Claire Ortiz Hill - 2010 - Axiomathes 20 (2-3):313-332.
    In “Function and Concept” and “On Concept and Object”, Frege argued that certain differences between dependent and independent meanings were inviolable and “founded deep in the nature of things” but, in those articles, he was not explicit about the actual consequences of violating such differences. However, since by creating a law that permitted one to pass from a concept to its extension, he himself mixed dependent and independent meanings, we are in a position to study some of the actual consequences (...)
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  • Semantic Realism, Actually.Simon Hewitt - 2020 - Metaphysica 21 (2):237-254.
    Michael Dummett offered a semantic characterisation of a variety of realism-antirealism debates. This approach has fallen out of fashion. This has been to the detriment of metaphysics. This paper offers an accurate characterisation of Dummett’s view, often lacking in the literature, and then defends it against a range of attacks (from Devitt, Miller and Williamson). This understanding of realism debates is resilient, and if we take it seriously the philosophical terrain looks importantly different. In particular, the philosophy of language has (...)
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  • The Priority Principle from Kant to Frege.Jeremy Heis - 2013 - Noûs 48 (2):268-297.
    In a famous passage (A68/B93), Kant writes that “the understanding can make no other use of […] concepts than that of judging by means of them.” Kant's thought is often called the thesis of the priority of judgments over concepts. We find a similar sounding priority thesis in Frege: “it is one of the most important differences between my mode of interpretation and the Boolean mode […] that I do not proceed from concepts, but from judgments.” Many interpreters have thought (...)
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  • Sir Michael Anthony Eardley Dummett, 1925-2011.R. G. Heck - 2013 - Philosophia Mathematica 21 (1):1-8.
    A remembrance of Dummett's work on philosophy of mathematcis.
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  • The Consistency of predicative fragments of frege’s grundgesetze der arithmetik.Richard G. Heck - 1996 - History and Philosophy of Logic 17 (1-2):209-220.
    As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differ...
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  • Russell Contra Sense/Reference, the ‘Mont Blanc’ Correspondence.Clare Hay - 2022 - History and Philosophy of Logic 44 (4):476-490.
    It is argued that Russell before 1905 saw no value in Frege's sense/reference distinction. This is clearest in the Mont Blanc correspondence. It is argued that Russell and Frege failed to engage because Frege lacked a grasp on the internal/external relations distinction. For Russell sense is either an external relation, objectionably separating out thought and reference, or an internal relation, so what is thought is altered such that we do not know what we are talking about. The novelty of the (...)
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  • Two Envelopes and Binding.Casper Storm Hansen - 2018 - Australasian Journal of Philosophy 96 (3):508-518.
    This paper describes a way of defending a modification of Eckhardt's [2013] solution to the Two Envelopes Paradox. The defence is based on ideas from Arntzenius, Elga, and Hawthorne [2004].
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  • Real numbers, quantities, and measurement.Bob Hale - 2002 - Philosophia Mathematica 10 (3):304-323.
    Defining the real numbers by abstraction as ratios of quantities gives prominence to then- applications in just the way that Frege thought we should. But if all the reals are to be obtained in this way, it is necessary to presuppose a rich domain of quantities of a land we cannot reasonably assume to be exemplified by any physical or other empirically measurable quantities. In consequence, an explanation of the applications of the reals, defined in this way, must proceed indirectly. (...)
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  • Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
    On the neo-Fregean approach to the foundations of mathematics, elementary arithmetic is analytic in the sense that the addition of a principle wliich may be held to IMJ explanatory of the concept of cardinal number to a suitable second-order logical basis suffices for the derivation of its basic laws. This principle, now commonly called Hume's principle, is an example of a Fregean abstraction principle. In this paper, I assume the correctness of the neo-Fregean position on elementary aritlunetic and seek to (...)
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  • Focus restored: Comments on John MacFarlane.Bob Hale & Crispin Wright - 2009 - Synthese 170 (3):457 - 482.
    In “Double Vision Two Questions about the Neo-Fregean Programme”, John MacFarlane’s raises two main questions: (1) Why is it so important to neo-Fregeans to treat expressions of the form ‘the number of Fs’ as a species of singular term? What would be lost, if anything, if they were analysed instead as a type of quantifier-phrase, as on Russell’s Theory of Definite Descriptions? and (2) Granting—at least for the sake of argument—that Hume’s Principle may be used as a means of implicitly (...)
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  • Extensions, Numbers and Frege’s Project of Logic as Universal Language.Nora Grigore - 2020 - Axiomathes 30 (5):577-588.
    Frege’s famous definition of number famously uses the concept of “extension”. Extensions, in the Fregean framework, are susceptible to bringing many difficulties, and, some say, even paradoxes. Therefore, neo-logicist programs want to avoid the problems and to replace the classical Fregean definition of number with Hume’s Principle. I argue that this move, even if it makes sense from a computational point of view, is at odds with Frege’s larger philosophical project. For Frege, I claim, extensions were an important part of (...)
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  • Was Wittgenstein Frege's heir?Karen Green - 1999 - Philosophical Quarterly 49 (196):289-308.
    This paper argues that Dummett’s interpretation of the relationship between Frege’s anti-psychologism and Wittgenstein’s doctrine that meaning is use results in a misreading of Frege. It points out that anti-mentalism is a form of anti-psychologism, but that mentalism is not the only version of psycholgism. Thus, while Frege and Wittgenstein are united in their opposition to mentalism, they are not equally opposed to psychologism, and from Frege’s point of view, the doctrine that meaning is use could also imply a version (...)
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  • What is Frege's Julius caesar problem?Dirk Greimann - 2003 - Dialectica 57 (3):261-278.
    This paper aims to determine what kind of problem Frege's famous “Julius Caesar problem” is. whether it is to be understood as the metaphysical problem of determining what kind of things abstract objects like numbers or value‐courses are, or as the epistemological problem of providing a means of recognizing these objects as the same again, or as the logical problem of providing abstract sortal concepts with a sharp delimitation in order to fulfill the law of excluded middle, or as the (...)
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  • The Context Principle and Dummett's Argument for Anti-realism.Karen Green - 2005 - Theoria 71 (2):92-117.
    Dummettian anti-realism–the refusal to endorse bivalence–is generally thought to be associated with idealism This paper argues that this is only true of the position developed by early Dummett. In a later manifestation Dummettian anti-realism is better thought of as providing the logic for anti-realisms of an error theoretic kind. Early on Dummett distinguished deep from shallow arguments for giving up bivalence: deep arguments followed a strong ‘sufficiency’ reading of Frege’s context principle, and made the sentence the primary vehicle of meaning. (...)
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  • On E.E. Constance Jones’s Account of Categorical Propositions and Her Defence of Frege.Karen Green - 2023 - Australasian Journal of Philosophy 101 (4):863-875.
    E.E.C. Jones’s early logical writings have recently been rescued from obscurity and it has been claimed that, in her works dating from the 1890s, she anticipated Frege’s distinction between sense and reference. This claim is challenged on the ground that it is based on a common but inadequate reading of Frege, which runs together his concept/object and sense/reference distinctions. It is admitted that a case can be made for Jones having anticipated something very like Frege’s analysis of categorical propositions, and (...)
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  • Indistinguishable Senses.Aidan Gray - 2018 - Noûs 54 (1):78-104.
    Fregeanism and Relationism are competing families of solutions to Frege’s Puzzle, and by extension, competing theories of propositional representation. My aim is to clarify what is at stake between them by characterizing and evaluating a Relationist argument. Relationists claim that it is cognitively possible for distinct token propositional attitudes to be, in a sense, qualitatively indistinguishable: to differ in no intrinsic representational features. The idea of an ‘intrinsic representational feature’ is not, however, made especially clear in the argument. I clarify (...)
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  • Cassirer, Schlick and 'structural' realism: The philosophy of the exact sciences in the background to early logical empiricism.Barry Gower - 2000 - British Journal for the History of Philosophy 8 (1):71 – 106.
    (2000). CASSIRER, SCHLICK AND ‘STRUCTURAL’ REALISM: THE PHILOSOPHY OF THE EXACT SCIENCES IN THE BACKGROUND TO EARLY LOGICAL EMPIRICISM. British Journal for the History of Philosophy: Vol. 8, No. 1, pp. 71-106.
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  • Quantification and realism.Michael Glanzberg - 2004 - Philosophy and Phenomenological Research 69 (3):541–572.
    This paper argues for the thesis that, roughly put, it is impossible to talk about absolutely everything. To put the thesis more precisely, there is a particular sense in which, as a matter of semantics, quantifiers always range over domains that are in principle extensible, and so cannot count as really being ‘absolutely everything’. The paper presents an argument for this thesis, and considers some important objections to the argument and to the formulation of the thesis. The paper also offers (...)
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  • Structuralism and Its Ontology.Marc Gasser - 2015 - Ergo: An Open Access Journal of Philosophy 2:1-26.
    A prominent version of mathematical structuralism holds that mathematical objects are at bottom nothing but "positions in structures," purely relational entities without any sort of nature independent of the structure to which they belong. Such an ontology is often presented as a response to Benacerraf's "multiple reductions" problem, or motivated on hermeneutic grounds, as a faithful representation of the discourse and practice of mathematics. In this paper I argue that there are serious difficulties with this kind of view: its proponents (...)
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  • Meaning and Aesthetic Judgment in Kant.Eli Friedlander - 2006 - Philosophical Topics 34 (1-2):21-34.
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  • Book reviews. [REVIEW]Juliet Floyd - 2002 - Philosophia Mathematica 10 (1):67-88.
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  • Against the iterative conception of set.Edward Ferrier - 2019 - Philosophical Studies 176 (10):2681-2703.
    According to the iterative conception of set, each set is a collection of sets formed prior to it. The notion of priority here plays an essential role in explanations of why contradiction-inducing sets, such as the Russell set, do not exist. Consequently, these explanations are successful only to the extent that a satisfactory priority relation is made out. I argue that attempts to do this have fallen short: understanding priority in a straightforwardly constructivist sense threatens the coherence of the empty (...)
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  • Amending Frege’s Grundgesetze der Arithmetik.Fernando Ferreira - 2005 - Synthese 147 (1):3-19.
    Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this (...)
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  • Profiling interest relativity.Delia Graff Fara - 2008 - Analysis 68 (4):326-335.
    Draft (Version 1.1, October 2007): (PDF file) A reply to Jason Stanley’s Analysis criticism of my interest-relative view on vagueness.
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  • Essay Review. [REVIEW][author unknown] - 2008 - History and Philosophy of Logic 29 (2):183-193.
    W. Tait, The provenance of pure reason. Essays in the philosophy of mathematics and its history. New York: Oxford University Press, 2005. ix + 332 pp. £36.50. ISBN 0-19-514192-X. Reviewed by J. W....
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  • The good, the bad and the ugly.Philip Ebert & Stewart Shapiro - 2009 - Synthese 170 (3):415-441.
    This paper discusses the neo-logicist approach to the foundations of mathematics by highlighting an issue that arises from looking at the Bad Company objection from an epistemological perspective. For the most part, our issue is independent of the details of any resolution of the Bad Company objection and, as we will show, it concerns other foundational approaches in the philosophy of mathematics. In the first two sections, we give a brief overview of the "Scottish" neo-logicist school, present a generic form (...)
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  • Richard G. Heck Jr. Reading Frege's Grundgesetze. Oxford: Oxford University Press, 2012. ISBN: 978-0-19-923370-0 ; 978-0-19-874437-5 ; 978-0-19-165535-7 . Pp. xvii + 296. [REVIEW]Philip A. Ebert - 2015 - Philosophia Mathematica 23 (2):289-293.
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  • Frege on Sense Identity, Basic Law V, and Analysis.Philip A. Ebert - 2016 - Philosophia Mathematica 24 (1):9-29.
    The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...)
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  • Abstract Singular Terms and Thin Reference.George Duke - 2012 - Theoria 78 (4):276-292.
    The prevailing approach to the problem of the ontological status of mathematical entities such as numbers and sets is to ask in what sense it is legitimate to ascribe a reference to abstract singular terms; those expressions of our language which, taken at face value, denote abstract objects. On the basis of this approach, neo‐Fregean Abstractionists such as Hale and Wright have argued that abstract singular terms may be taken to effect genuine reference towards objects, whereas nominalists such as Field (...)
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  • Husserl and the Problem of Abstract Objects.George Duke & Peter Woelert - 2015 - Pacific Philosophical Quarterly 97 (1):27-47.
    One major difficulty confronting attempts to clarify the epistemological and ontological status of abstract objects is determining the sense, if any, in which such entities may be characterised as mind and language independent. Our contention is that the tolerant reductionist position of Michael Dummett can be strengthened by drawing on Husserl's mature account of the constitution of ideal objects and mathematical objectivity. According to the Husserlian position we advocate, abstract singular terms pick out weakly mind-independent sedimented meaning-contents. These meaning-contents serve (...)
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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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  • Frege and the rigorization of analysis.William Demopoulos - 1994 - Journal of Philosophical Logic 23 (3):225 - 245.
    This paper has three goals: (i) to show that the foundational program begun in the Begriffsschroft, and carried forward in the Grundlagen, represented Frege's attempt to establish the autonomy of arithmetic from geometry and kinematics; the cogency and coherence of 'intuitive' reasoning were not in question. (ii) To place Frege's logicism in the context of the nineteenth century tradition in mathematical analysis, and, in particular, to show how the modern concept of a function made it possible for Frege to pursue (...)
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  • The Middle Wittgenstein’s Critique of Frege.Piotr Dehnel - 2020 - International Journal of Philosophical Studies 28 (1):75-95.
    This article aims to analyse Wittgenstein’s 1929–1932 notes concerning Frege’s critique of what is referred to as old formalism in the philosophy of mathematics. Wittgenstein disagreed with Frege’s critique and, in his notes, outlined his own assessment of formalism. First of all, he approvingly foregrounded its mathematics-game comparison and insistence that rules precede the meanings of expressions. In this article, I recount Frege’s critique of formalism and address Wittgenstein’s assessment of it to show that his remarks are not so much (...)
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  • Why are (some) Platonists so insouciant?William Lane Craig - 2011 - Philosophy 86 (2):213-229.
    Some platonists truly agonize over the ontological commitments which their platonism demands of them. Peter van Inwagen, for example, confesses candidly,I am happy to admit that I am uneasy about believing in the existence of ‘causally irrelevant’ objects. The fact that abstract objects, if they exist, can be neither causes or [sic] effects is one of the many features of abstract objects that make nominalism so attractive. I should very much like to be a nominalist, but I don't see how (...)
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  • Extending Everything with Nothing.Filippo Costantini - 2020 - Philosophia 48 (4):1413-1436.
    In this paper we offer a new solution to the old paradox of nothingness. This new solution develops in two steps. The first step consists in showing how to resolve the contradiction generated by the notion of nothingness by claiming that the contradiction shows the indefinite extensibility of the concept of object. The second step consists in showing that, having accepted the idea of indefinite extensibility, we can have absolute generality without the emergence of the contradiction connected to the absolute (...)
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  • PATRICIA A. BLANCHETTE. Frege's Conception of Logic. Oxford University Press, 2012. ISBN 978-0-19-926925-9 . Pp. xv + 256. [REVIEW]Roy T. Cook - 2014 - Philosophia Mathematica 22 (1):108-120.
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  • Structuralism as a philosophy of mathematical practice.Jessica Carter - 2008 - Synthese 163 (2):119 - 131.
    This paper compares the statement ‘Mathematics is the study of structure’ with the actual practice of mathematics. We present two examples from contemporary mathematical practice where the notion of structure plays different roles. In the first case a structure is defined over a certain set. It is argued firstly that this set may not be regarded as a structure and secondly that what is important to mathematical practice is the relation that exists between the structure and the set. In the (...)
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  • Dadaism: Restrictivism as Militant Quietism.Tim Button - 2010 - Proceedings of the Aristotelian Society 110 (3pt3):387-398.
    Can we quantify over everything: absolutely, positively, definitely, totally, every thing? Some philosophers have claimed that we must be able to do so, since the doctrine that we cannot is self-stultifying. But this treats restrictivism as a positive doctrine. Restrictivism is much better viewed as a kind of militant quietism, which I call dadaism. Dadaists advance a hostile challenge, with the aim of silencing everyone who holds a positive position about ‘absolute generality’.
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  • Frege on knowing the foundation.Tyler Burge - 1998 - Mind 107 (426):305-347.
    The paper scrutinizes Frege's Euclideanism - his view of arithmetic and geometry as resting on a small number of self-evident axioms from which non-self-evident theorems can be proved. Frege's notions of self-evidence and axiom are discussed in some detail. Elements in Frege's position that are in apparent tension with his Euclideanism are considered - his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that understanding is closely associated with inferential (...)
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  • Charles S. Chihara. A structural account of mathematics. Oxford: Oxford university press, 2004. Pp. XIV + 380. ISBN 0-19-926753-. [REVIEW]John P. Burgess - 2005 - Philosophia Mathematica 13 (1):78-90.
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