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  1. added 2019-06-05
    Number Words as Number Names.Friederike Moltmann - 2017 - Linguistics and Philosophy 40 (4):331-345.
    This paper criticizes the view that number words in argument position retain the meaning they have on an adjectival or determiner use, as argued by Hofweber :179–225, 2005) and Moltmann :499–534, 2013a, 2013b). In particular the paper re-evaluates syntactic evidence from German given in Moltmann to that effect.
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  2. added 2019-02-04
    Content Recarving as Subject Matter Restriction.Vincenzo Ciccarelli - forthcoming - Manuscrito: Revista Internacional de Filosofía 42 (1).
    In this article I offer an explicating interpretation of the procedure of content recarving as described by Frege in §64 of the Foundations of Arithmetic. I argue that the procedure of content recarving may be interpreted as an operation that while restricting the subject matter of a sentence, performs a generalization on what the sentence says about its subject matter. The characterization of the recarving operation is given in the setting of Yablo’s theory of subject matter and it is based (...)
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  3. added 2018-04-30
    Tuples All the Way Down?Simon Thomas Hewitt - 2018 - Thought: A Journal of Philosophy 7 (3):161-169.
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  4. added 2018-03-05
    Composition as Abstraction.Jeffrey Sanford Russell - 2017 - Journal of Philosophy 114 (9):453-470.
    The existence of mereological sums can be derived from an abstraction principle in a way analogous to numbers. I draw lessons for the thesis that “composition is innocent” from neo-Fregeanism in the philosophy of mathematics.
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  5. added 2018-03-01
    Priority, Platonism, and the Metaontology of Abstraction.Michele Lubrano - 2016 - Dissertation, University of Turin
    In this dissertation I examine the NeoFregean metaontology of mathematics. I try to clarify the relationship between what is sometimes called Priority Thesis and Platonism about mathematical entities. I then present three coherent ways in which one might endorse both these stances, also answering some possible objections. Finally I try to show which of these three ways is the most promising.
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  6. added 2018-02-17
    Neo-Logicism and Russell’s Logicism.Kevin C. Klement - 2012 - Russell: The Journal of Bertrand Russell Studies 32 (2):159.
    Most advocates of the so-called “neologicist” movement in the philosophy of mathematics identify themselves as “Neo-Fregeans” (e.g., Hale and Wright): presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature, and when it is, often dismissed as not really logicism at all (in lights of its assumption of axioms of infinity, reducibiity and so on). In this paper I have three aims: firstly, to identify more clearly the primary metaontological (...)
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  7. added 2018-01-17
    Tuples All the Way Down?Simon Hewitt - manuscript
    We can introduce singular terms for ordered pairs by means of an abstraction principle. Doing so proves useful for a number of projects in the philosophy of mathematics. However there is a question whether we can appeal to the abstraction principle in good faith, since a version of the Caesar Problem can be generated, posing the worry that abstraction fails to introduce expressions which refer determinately to the requisite sort of object. In this short paper I will pose the difficulty, (...)
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  8. added 2016-03-06
    Logical Indefinites.Jack Woods - 2014 - Logique Et Analyse -- Special Issue Edited by Julien Murzi and Massimiliano Carrara 227: 277-307.
    I argue that we can and should extend Tarski's model-theoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles.
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  9. added 2015-03-22
    Neo-Logicism and its Logic.Panu Raatikainen - forthcoming - History and Philosophy of Logic.
    The rather unrestrained use of second-order logic in the neo-logicist program is critically examined. It is argued in some detail that it brings with it genuine set-theoretical existence assumptions, and that the mathematical power that Hume’s Principle seems to provide, in the derivation of Frege’s Theorem, comes largely from the “logic” assumed rather than from Hume’s principle. It is shown that Hume’s principle is in reality not stronger than the very weak Robinson Arithmetic Q. Consequently, only few rudimentary facts of (...)
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  10. added 2013-11-28
    Abstraction Relations Need Not Be Reflexive.Jonathan Payne - 2013 - Thought: A Journal of Philosophy 2 (2):137-147.
    Neo-Fregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of non-reflexive abstraction relations to restricted abstraction principles.
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  11. added 2011-11-21
    The Number of Planets, a Number-Referring Term?Friederike Moltmann - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics. Oxford University Press. pp. 113-129.
    The question whether numbers are objects is a central question in the philosophy of mathematics. Frege made use of a syntactic criterion for objethood: numbers are objects because there are singular terms that stand for them, and not just singular terms in some formal language, but in natural language in particular. In particular, Frege (1884) thought that both noun phrases like the number of planets and simple numerals like eight as in (1) are singular terms referring to numbers as abstract (...)
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