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  1. N Eo-F Regeanism and Q Uantifier V Ariance.Katherine Hawley - 2007 - Aristotelian Society Supplementary Volume 81 (1):233-249.
    In his paper in the same volume, Sider argues that, of maximalism and quantifier variance, the latter promises to let us make better sense of neo-Fregeanism. I argue that neo-Fregeans should, and seemingly do, reject quantifier variance. If they must choose between these two options, they should choose maximalism.
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  • Hale’s Argument From Transitive Counting.Eric Snyder, Richard Samuels & Stewart Shaprio - forthcoming - Synthese:1-29.
    A core commitment of Bob Hale and Crispin Wright’s neologicism is their invocation of Frege’s Constraint—roughly, the requirement that the core empirical applications for a class of numbers be “built directly into” their formal characterization. According to these neologicists, if legitimate, Frege’s Constraint adjudicates in favor of their preferred foundation—Hume’s Principle—and against alternatives, such as the Dedekind–Peano axioms. In this paper, we consider a recent argument for legitimating Frege’s Constraint due to Hale, according to which the primary empirical application of (...)
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  • Can Semantics Guide Ontology?Katherine Ritchie - 2016 - Australasian Journal of Philosophy 94 (1):24-41.
    Since the linguistic turn, many have taken semantics to guide ontology. Here, I argue that semantics can, at best, serve as a partial guide to ontological commitment. If semantics were to be our guide, semantic data and semantic treatments would need to be taken seriously. Through an examination of plurals and their treatments, I argue that there can be multiple, equally semantically adequate, treatments of a natural language theory. Further, such treatments can attribute different ontological commitments to a theory. Given (...)
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  • Bad Company and Neo-Fregean Philosophy.Matti Eklund - 2009 - Synthese 170 (3):393-414.
    A central element in neo-Fregean philosophy of mathematics is the focus on abstraction principles, and the use of abstraction principles to ground various areas of mathematics. But as is well known, not all abstraction principles are in good standing. Various proposals for singling out the acceptable abstraction principles have been presented. Here I investigate what philosophical underpinnings can be provided for these proposals; specifically, underpinnings that fit the neo-Fregean's general outlook. Among the philosophical ideas I consider are: general views on (...)
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  • Towards a Pluralist Theory of Singular Thought.Michele Palmira - 2018 - Synthese 195 (9):3947-3974.
    This paper investigates the question of how to correctly capture the scope of singular thinking. The first part of the paper identifies a scope problem for the dominant view of singular thought maintaining that, in order for a thinker to have a singular thought about an object o, the thinker has to bear a special epistemic relation to o. The scope problem has it is that this view cannot make sense of the singularity of our thoughts about objects to which (...)
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  • Frege, Dedekind, and the Origins of Logicism.Erich H. Reck - 2013 - History and Philosophy of Logic 34 (3):242-265.
    This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise brought with it (...)
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  • Epistemological Objections to Platonism.David Liggins - 2010 - Philosophy Compass 5 (1):67-77.
    Many philosophers posit abstract entities – where something is abstract if it is acausal and lacks spatio-temporal location. Theories, types, characteristics, meanings, values and responsibilities are all good candidates for abstractness. Such things raise an epistemological puzzle: if they are abstract, then how can we have any epistemic access to how they are? If they are invisible, intangible and never make anything happen, then how can we ever discover anything about them? In this article, I critically examine epistemological objections to (...)
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  • Comparing Peano Arithmetic, Basic Law V, and Hume’s Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.
    This paper presents new constructions of models of Hume's Principle and Basic Law V with restricted amounts of comprehension. The techniques used in these constructions are drawn from hyperarithmetic theory and the model theory of fields, and formalizing these techniques within various subsystems of second-order Peano arithmetic allows one to put upper and lower bounds on the interpretability strength of these theories and hence to compare these theories to the canonical subsystems of second-order arithmetic. The main results of this paper (...)
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  • 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.
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  • Metaontology.Matti Eklund - 2006 - Philosophy Compass 1 (3):317-334.
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  • Platonism and Aristotelianism in Mathematics.Richard Pettigrew - 2008 - Philosophia Mathematica 16 (3):310-332.
    Philosophers of mathematics agree that the only interpretation of arithmetic that takes that discourse at 'face value' is one on which the expressions 'N', '0', '1', '+', and 'x' are treated as proper names. I argue that the interpretation on which these expressions are treated as akin to free variables has an equal claim to be the default interpretation of arithmetic. I show that no purely syntactic test can distinguish proper names from free variables, and I observe that any semantic (...)
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  • Tuples All the Way Down?Simon Thomas Hewitt - 2018 - Thought: A Journal of Philosophy 7 (3):161-169.
  • The Julio César Problem.Fraser MacBride - 2005 - Dialectica 59 (2):223–236.
    One version of the Julius Caesar problem arises when we demand assurance that expressions drawn from different theories or stretches of discourse refer to different things. The counter‐Caesar problem arises when assurance is demanded that expressions drawn from different theories . refer to the same thing. The Julio César problem generalises from the counter‐Caesar problem. It arises when we seek reassurance that expressions drawn from different languages refer to the same kind of things . If the Julio César problem is (...)
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  • Categories for the Neologicist.Shay Allen Logan - 2017 - Philosophia Mathematica 25 (1):26-44.
    Abstraction principles provide implicit definitions of mathematical objects. In this paper, an abstraction principle defining categories is proposed. It is unsatisfiable and inconsistent in the expected ways. Two restricted versions of the principle which are consistent are presented.
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  • Neo-Fregean Ontology.Matti Eklund - 2006 - Philosophical Perspectives 20 (1):95–121.
    Neo-Fregeanism in the philosophy of mathematics consists of two main parts: the logicist thesis, that mathematics (or at least branches thereof, like arithmetic) all but reduce to logic, and the platonist thesis, that there are abstract, mathematical objects. I will here focus on the ontological thesis, platonism. Neo-Fregeanism has been widely discussed in recent years. Mostly the discussion has focused on issues specific to mathematics. I will here single out for special attention the view on ontology which underlies the neo-Fregeans’ (...)
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  • Weyl on Fregean Implicit Definitions: Between Phenomenology and Symbolic Construction.Demetra Christopoulou - 2014 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (1):35-47.
    This paper aims to investigate certain aspects of Weyl’s account of implicit definitions. The paper takes under consideration Weyl’s approach to a certain kind of implicit definitions i.e. abstraction principles introduced by Frege.ion principles are bi-conditionals that transform certain equivalence relations into identity statements, defining thereby mathematical terms in an implicit way. The paper compares the analytic reading of implicit definitions offered by the Neo-Fregean program with Weyl’s account which has phenomenological leanings. The paper suggests that Weyl’s account should be (...)
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  • The Status of Value-Ranges in the Argument of Basic Laws of Arithmetic I §10.Thomas Lockhart - 2017 - History and Philosophy of Logic 38 (4):345-363.
    Frege's concern in GGI §10 is neither with the epistemological issue of how we come to know about value-ranges, nor with the semantic-metaphysical issue of whether we have said enough about such objects in order to ensure that any kind of reference to them is possible. The problem which occupies Frege in GGI §10 is the general problem according to which we ‘cannot yet decide’, for any arbitrary function, what value ‘’ has if ‘ℵ’ is a canonical value-range name. This (...)
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  • Singular Terms Revisited.Robert Schwartzkopff - 2016 - Synthese 193 (3).
    Neo-Fregeans take their argument for arithmetical realism to depend on the availability of certain, so-called broadly syntactic tests for whether a given expression functions as a singular term. The broadly syntactic tests proposed in the neo-Fregean tradition are the so-called inferential test and the Aristotelian test. If these tests are to subserve the neo-Fregean argument, they must be at least adequate, in the sense of correctly classifying paradigm cases of singular terms and non-singular terms. In this paper, I pursue two (...)
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  • Abstraction and Identity.Roy T. Cook & Philip A. Ebert - 2005 - Dialectica 59 (2):121–139.
    A co-authored article with Roy T. Cook forthcoming in a special edition on the Caesar Problem of the journal Dialectica. We argue against the appeal to equivalence classes in resolving the Caesar Problem.
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  • Neo-Fregeanism and Quantifier Variance.Theodore Sider - 2007 - Aristotelian Society Supplementary Volume 81 (1):201–232.
    NeoFregeanism is an intriguing but elusive philosophy of mathematical existence. At crucial points, it goes cryptic and metaphorical. I want to put forward an interpretation of neoFregeanism—perhaps not one that actual neoFregeans will embrace—that makes sense of much of what they say. NeoFregeans should embrace quantifier variance.
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  • The Julio César Problem.Fraser MacBride - 2005 - Dialectica 59 (2):223-236.
    One version of the Julius Caesar problem arises when we demand assurance that expressions drawn from different theories or stretches of discourse refer to different things. The counter‐Caesar problem arises when assurance is demanded that expressions drawn from different theories. refer to the same thing. The Julio César problem generalises from the counter‐Caesar problem. It arises when we seek reassurance that expressions drawn from different languages refer to the same kind of things. If the Julio César problem is not resolved (...)
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  • Abstraction Reconceived.J. P. Studd - 2016 - British Journal for the Philosophy of Science 67 (2):579-615.
    Neologicists have sought to ground mathematical knowledge in abstraction. One especially obstinate problem for this account is the bad company problem. The leading neologicist strategy for resolving this problem is to attempt to sift the good abstraction principles from the bad. This response faces a dilemma: the system of ‘good’ abstraction principles either falls foul of the Scylla of inconsistency or the Charybdis of being unable to recover a modest portion of Zermelo–Fraenkel set theory with its intended generality. This article (...)
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  • 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 (...)
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  • Abstractionist Categories of Categories.Shay Allen Logan - 2015 - Review of Symbolic Logic 8 (4):705-721.
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