Switch to: References

Citations of:

Neo-Fregeans: In Bad Company?

In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press (1998)

Add citations

You must login to add citations.
  1. 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Linnebo on reference by abstraction.Bahram Assadian - 2023 - Analytic Philosophy 2.
    According to Øystein Linnebo's account of abstractionism, abstraction principles, received as Fregean criteria of identity, can be used to reduce facts about singular reference to objects such as directions and numbers to facts that do not involve such objects. In this article, first I show how the resources of Linnebo's metasemantics successfully handle Dummett's challenge against the referentiality of the singular terms formed by abstraction principles. Then, I argue that Linnebo's metasemantic commitments do not provide us with tools for dispelling (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • A Dilemma for Neo-Fregeanism.Robert Trueman - 2014 - Philosophia Mathematica 22 (3):361-379.
    Neo-Fregeans need their stipulation of Hume's Principle — $NxFx=NxGx \leftrightarrow \exists R (Fx \,1\hbox {-}1_R\, Gx)$ — to do two things. First, it must implicitly define the term-forming operator ‘Nx…x…’, and second it must guarantee that Hume's Principle as a whole is true. I distinguish two senses in which the neo-Fregeans might ‘stipulate’ Hume's Principle, and argue that while one sort of stipulation fixes a meaning for ‘Nx…x…’ and the other guarantees the truth of Hume's Principle, neither does both.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Life on the Ship of Neurath: Mathematics in the Philosophy of Mathematics.Stewart Shapiro - 2012 - Croatian Journal of Philosophy 26 (2):11--27.
    Some central philosophical issues concern the use of mathematics in putatively non-mathematical endeavors. One such endeavor, of course, is philosophy, and the philosophy of mathematics is a key instance of that. The present article provides an idiosyncratic survey of the use of mathematical results to provide support or counter-support to various philosophical programs concerning the foundations of mathematics.
    Download  
     
    Export citation  
     
    Bookmark  
  • Logicism and Neologicism.Neil Tennant - 2013 - Stanford Encyclopedia of Philosophy.
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • 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, I argue (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • 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 assessed. (...)
    Download  
     
    Export citation  
     
    Bookmark   62 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Hume’s Principle, Bad Company, and the Axiom of Choice.Sam Roberts & Stewart Shapiro - 2023 - Review of Symbolic Logic 16 (4):1158-1176.
    One prominent criticism of the abstractionist program is the so-called Bad Company objection. The complaint is that abstraction principles cannot in general be a legitimate way to introduce mathematical theories, since some of them are inconsistent. The most notorious example, of course, is Frege’s Basic Law V. A common response to the objection suggests that an abstraction principle can be used to legitimately introduce a mathematical theory precisely when it is stable: when it can be made true on all sufficiently (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Analysis and Interpretation in the Exact Sciences: Essays in Honour of William Demopoulos.Melanie Frappier, Derek Brown & Robert DiSalle (eds.) - 2011 - Dordrecht and London: Springer.
    The essays in this volume concern the points of intersection between analytic philosophy and the philosophy of the exact sciences. More precisely, it concern connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general. Its guiding idea is that, in contemporary philosophy of science, there are profound problems of theoretical interpretation-- problems that transcend both the methodological concerns of general philosophy of science, and the technical concerns of philosophers of (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • For Better and for Worse. Abstractionism, Good Company, and Pluralism.Andrea Sereni, Maria Paola Sforza Fogliani & Luca Zanetti - 2023 - Review of Symbolic Logic 16 (1):268-297.
    A thriving literature has developed over logical and mathematical pluralism – i.e. the views that several rival logical and mathematical theories can be equally correct. These have unfortunately grown separate; instead, they both could gain a great deal by a closer interaction. Our aim is thus to present some novel forms of abstractionist mathematical pluralism which can be modeled on parallel ways of substantiating logical pluralism (also in connection with logical anti-exceptionalism). To do this, we start by discussing the Good (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • The Metametaphysics of Neo-Fregeanism.Matti Eklund - 2020 - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. New York, NY: Routledge.
    Download  
     
    Export citation  
     
    Bookmark  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • The Principle of Equivalence as a Criterion of Identity.Ryan Samaroo - 2020 - Synthese 197 (8):3481-3505.
    In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • To Be is to Be the Object of a Possible Act of Choice.Massimiliano Carrara & Enrico Martino - 2010 - Studia Logica 96 (2):289-313.
    Aim of the paper is to revise Boolos’ reinterpretation of second-order monadic logic in terms of plural quantification ([4], [5]) and expand it to full second order logic. Introducing the idealization of plural acts of choice, performed by a suitable team of agents, we will develop a notion of plural reference . Plural quantification will be then explained in terms of plural reference. As an application, we will sketch a structuralist reconstruction of second-order arithmetic based on the axiom of infinite (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • A Vindication of Logicism.Peter Roeper - 2016 - Philosophia Mathematica 24 (3):360-378.
    Frege regarded Hume's Principle as insufficient for a logicist account of arithmetic, as it does not identify the numbers; it does not tell us which objects the numbers are. His solution, generally regarded as a failure, was to propose certain sets as the referents of numerical terms. I suggest instead that numbers are properties of pluralities, where these properties are treated as objects. Given this identification, the truth-conditions of the statements of arithmetic can be obtained from logical principles with the (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • In Good Company? On Hume’s Principle and the Assignment of Numbers to Infinite Concepts.Paolo Mancosu - 2015 - Review of Symbolic Logic 8 (2):370-410.
    In a recent article, I have explored the historical, mathematical, and philosophical issues related to the new theory of numerosities. The theory of numerosities provides a context in which to assign numerosities to infinite sets of natural numbers in such a way as to preserve the part-whole principle, namely if a set A is properly included in B then the numerosity of A is strictly less than the numerosity of B. Numerosities assignments differ from the standard assignment of size provided (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • The neo-Fregean program in the philosophy of arithmetic.William Demopoulos - 2006 - In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 87--112.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Soft Axiomatisation: John von Neumann on Method and von Neumann's Method in the Physical Sciences.Miklós Rédei & Michael Stöltzner - 2006 - In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 235--249.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Is unsaying polite?Berislav Žarnić - 2011 - In Majda Trobok, Nenad Miščević & Berislav Žarnić (eds.), Between Logic and Reality: Modeling Inference, Action and Understanding. Dordrecht and New York: Springer. pp. 201--224.
    This paper is divided in five sections. Section 11.1 sketches the history of the distinction between speech act with negative content and negated speech act, and gives a general dynamic interpretation for negated speech act. “Downdate semantics” for AGM contraction is introduced in Section 11.2. Relying on semantically interpreted contraction, Section 11.3 develops the dynamic semantics for constative and directive speech acts, and their external negations. The expressive completeness for the formal variants of natural language utterances, none of which is (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • The Company Kept by Cut Abstraction (and its Relatives).S. Shapiro - 2011 - Philosophia Mathematica 19 (2):107-138.
    This article concerns the ongoing neo-logicist program in the philosophy of mathematics. The enterprise began life, in something close to its present form, with Crispin Wright’s seminal [1983]. It was bolstered when Bob Hale [1987] joined the fray on Wright’s behalf and it continues through many extensions, objections, and replies to objections . The overall plan is to develop branches of established mathematics using abstraction principles in the form: Formula where a and b are variables of a given type , (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • 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. (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations