About this topic
Summary An abstraction principle (AP) allows one to introduce new singular terms by providing appropriate identity conditions. For instance, the most celebrated abstraction principle, called Hume's Principle (HP), introduces numerical terms by saying: "The number of Fs is the same as the number of Gs if and only if Fs and Gs are equinumerous (the relation of equinumerosity is definable in a second-order language without reference to numbers)." The first (and unsuccessful, because inconsistent) attempt at using APs in foundations of mathematics is due to Frege. Neo-Fregeans try to salvage Frege's project. One of the tasks is to show how various mathematical theories can be derived from appropriate APs. Another task is to develop a well-motivated acceptability criterion for APs (given that Frege's Basic Law V leads to contradiction and HP doesn't). The Bad Company objection (according to which there are separately consistent but mutually inconsistent abstraction principles) indicates that mere consistency of an AP is not enough for its acceptability. Finally neo-Fregeans have to develop a philosophically acceptable story explaining why APs can play an important role in the platonist epistemology of mathematics and what role exactly it is. 
Key works Wright 1983 is a seminal book on the topic. The consistency of arithmetic based on Hume's Principle has been proven by Boolos 1987Fine 2002 is a good survey of technical aspects of neologicism. A nice anthology of papers related to the Bad Company problem is vol. 70 no 3 of Synthese edited by Linnebo 2009. A good collection of essays related to neologicism is Wright & Hale 2001.
Introductions A good place to start is Zalta 2008 and more focused Zalta 2008 and Tennant 2013. A good introductory paper focused on philosophical motivations is  Cook 2009. A nice introduction to worries surrounding the acceptability criteria of APs is Linnebo 2009.
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  1. Hyperintensional Foundations of Mathematical Platonism.David Elohim - manuscript
    This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...)
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  2. (1 other version)Frege's theorem in plural logic.Simon Hewitt - manuscript
    A version of Frege's theorem can be proved in a plural logic with pair abstraction. We talk through this and discuss the philosophical implications of the result.
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  3. (1 other version)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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  4. Nominalist Neologicism.Rafal Urbaniak - manuscript
    The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those (...)
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  5. (1 other version)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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  6. What is neologicism?Symbolic Logic - forthcoming - Bulletin of Symbolic Logic.
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  7. Infinity, Choice, and Hume's Principle.Stephen Mackereth - forthcoming - Journal of Philosophical Logic.
    It has long been known that in the context of axiomatic second-order logic (SOL), Hume's Principle (HP) is mutually interpretable with "the universe is Dedekind infinite" (DI). I offer a more fine-grained analysis of the logical strength of HP, measured by deductive implications rather than interpretability. The main result is that HP is not deductively conservative over SOL + DI. That is, SOL + HP proves additional theorems in the language of pure second-order logic that are not provable from SOL (...)
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  8. Neologicism and Conservativeness.Stephen Mackereth - forthcoming - Journal of Philosophy.
    Neologicists have claimed that Hume's Principle (HP) may be taken as a stipulative definition of cardinal number. This claim is threatened by the fact that HP is not conservative over pure second-order logic. I argue that the dominant neologicist response to the conservativeness objection is not satisfactory. Then I propose a novel version of neologicism, based on Heck's Two-sorted Hume's Principle (2HP), which does meet the conservativeness objection—provided that conservativeness is understood semantically and not deductively. I also argue that on (...)
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  9. Explicit Abstract Objects in Predicative Settings.Sean Ebels-Duggan & Francesca Boccuni - 2024 - Journal of Philosophical Logic 53 (5):1347-1382.
    Abstractionist programs in the philosophy of mathematics have focused on abstraction principles, taken as implicit definitions of the objects in the range of their operators. In second-order logic (SOL) with predicative comprehension, such principles are consistent but also (individually) mathematically weak. This paper, inspired by the work of Boolos (Proceedings of the Aristotelian Society 87, 137–151, 1986) and Zalta (Abstract Objects, vol. 160 of Synthese Library, 1983), examines explicit definitions of abstract objects. These axioms state that there is a unique (...)
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  10. Abstraction and grounding.Louis deRosset & Øystein Linnebo - 2023 - Philosophy and Phenomenological Research 109 (1):357-390.
    The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume's Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one‐to‐one:. The principal aim of this article is to use the notion of grounding to develop this (...)
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  11. 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 (...)
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  12. Linnebo's Abstractionism and the Bad Company Problem.J. P. Studd - 2023 - Theoria 89 (3):366-392.
    In Thin Objects: An Abstractionist Account, Linnebo offers what he describes as a “simple and definitive” solution to the bad company problem facing abstractionist accounts of mathematics. “Bad” abstraction principles can be rendered “good” by taking abstraction to have a predicative character. But the resulting predicative axioms are too weak to recover substantial portions of mathematics. Linnebo pursues two quite different strategies to overcome this weakness in the case of set theory and arithmetic. I argue that neither infinitely iterated abstraction (...)
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  13. A Logical Foundation for Potentialist Set Theory.Sharon Berry - 2022 - Cambridge University Press.
    In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist approach to develop a unified determinate conception of set-theoretic truth that vindicates many of our intuitive expectations regarding set theory. Berry further defends (...)
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  14. The incubus of inter-translatability... a realist’s nightmare?: Penelope Rush: Ontology and the foundations of mathematics: talking past each other. New York: Cambridge University Press, 2022, 46 pp, $20 PB. [REVIEW]Nicholas Danne - 2022 - Metascience 32 (1):107-110.
  15. Two-Sorted Frege Arithmetic is Not Conservative.Stephen Mackereth & Jeremy Avigad - 2022 - Review of Symbolic Logic 16 (4):1199-1232.
    Neo-Fregean logicists claim that Hume’s Principle (HP) may be taken as an implicit definition of cardinal number, true simply by fiat. A long-standing problem for neo-Fregean logicism is that HP is not deductively conservative over pure axiomatic second-order logic. This seems to preclude HP from being true by fiat. In this paper, we study Richard Kimberly Heck’s Two-Sorted Frege Arithmetic (2FA), a variation on HP which has been thought to be deductively conservative over second-order logic. We show that it isn’t. (...)
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  16. Objectivity in Mathematics, Without Mathematical Objects†.Markus Pantsar - 2021 - Philosophia Mathematica 29 (3):318-352.
    I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...)
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  17. Structuralist Neologicism†.Francesca Boccuni & Jack Woods - 2020 - Philosophia Mathematica 28 (3):296-316.
    Neofregeanism and structuralism are among the most promising recent approaches to the philosophy of mathematics. Yet both have serious costs. We develop a view, structuralist neologicism, which retains the central advantages of each while avoiding their more serious costs. The key to our approach is using arbitrary reference to explicate how mathematical terms, introduced by abstraction principles, refer. Focusing on numerical terms, this allows us to treat abstraction principles as implicit definitions determining all properties of the numbers, achieving a key (...)
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  18. The Metametaphysics of Neo-Fregeanism.Matti Eklund - 2020 - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. New York, NY: Routledge.
  19. Peacocke on magnitudes and numbers.Øystein Linnebo - 2020 - Philosophical Studies 178 (8):2717-2729.
    Peacocke’s recent The Primacy of Metaphysics covers a wide range of topics. This critical discussion focuses on the book’s novel account of extensive magnitudes and numbers. First, I further develop and defend Peacocke’s argument against nominalistic approaches to magnitudes and numbers. Then, I argue that his view is more Aristotelian than Platonist because reified magnitudes and numbers are accounted for via corresponding properties and these properties’ application conditions, and because the mentioned objects have a “shallow nature” relative to the corresponding (...)
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  20. Neo-Logicism and Its Logic.Panu Raatikainen - 2020 - History and Philosophy of Logic 41 (1):82-95.
    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 a few rudimentary facts (...)
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  21. Thin Objects: An Abstractionist Account, by Øystein Linnebo. [REVIEW]J. P. Studd - 2020 - Mind 129 (514):646-656.
    Thin Objects: Anionist Account, by LinneboØystein. Oxford: Oxford University Press, 2018. Pp. xviii + 238.
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  22. Abstract objects and semantics: An essay on prospects and problems with abstraction principles as a means of justifying reference to abstract objects.Gnatek Zuzanna - 2020 - Dissertation, Trinity College, Dublin
  23. The Basic Laws of Cardinal Number.Richard Kimberly Heck - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press. pp. 1-30.
    An overview of what Frege accomplishes in Part II of Grundgesetze, which contains proofs of axioms for arithmetic and several additional results concerning the finite, the infinite, and the relationship between these notions. One might think of this paper as an extremely compressed form of Part II of my book Reading Frege's Grundgesetze.
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  24. 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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  25. The Problem of Fregean Equivalents.Joongol Kim - 2019 - Dialectica 73 (3):367-394.
    It would seem that some statements like ‘There are exactly four moons of Jupiter’ and ‘The number of moons of Jupiter is four’ have the same truth-conditions and yet differ in ontological commitment. One strategy to resolve this paradoxical phenomenon is to insist that the statements have not only the same truth-conditions but also the same ontological commitments; the other strategy is to reject the presumption that they have the same truth-conditions. This paper critically examines some popular versions of these (...)
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  26. Hale’s argument from transitive counting.Eric Snyder, Richard Samuels & Stewart Shapiro - 2019 - Synthese 198 (3):1905-1933.
    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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  27. Cardinality and Acceptable Abstraction.Roy T. Cook & Øystein Linnebo - 2018 - Notre Dame Journal of Formal Logic 59 (1):61-74.
    It is widely thought that the acceptability of an abstraction principle is a feature of the cardinalities at which it is satisfiable. This view is called into question by a recent observation by Richard Heck. We show that a fix proposed by Heck fails but we analyze the interesting idea on which it is based, namely that an acceptable abstraction has to “generate” the objects that it requires. We also correct and complete the classification of proposed criteria for acceptable abstraction.
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  28. Being Necessary: Themes of Ontology and Modality from the Work of Bob Hale.Ivette Fred Rivera & Jessica Leech (eds.) - 2018 - Oxford, England: Oxford University Press.
    Edited by Ivette Fred-Rivera and Jessica Leech. What is the relationship between ontology and modality: between what there is, and what there could be, must be, or might have been? Throughout a distinguished career, Bob Hale’s work has addressed this question on a number of fronts, through the development of a Fregean approach to ontology, an essentialist theory of modality, and in his work on neo-logicism in the philosophy of mathematics. This collection of new essays engages with these themes in (...)
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  29. The generous ontology of thin objects: Øystein Linnebo: Thin objects: an abstractionist account. New York: Oxford University Press, xvii + 231 pp, $50.00 HB. [REVIEW]Nathaniel Gan - 2018 - Metascience 28 (1):167-169.
  30. Logicism, Ontology, and the Epistemology of Second-Order Logic.Richard Kimberly Heck - 2018 - In Ivette Fred Rivera & Jessica Leech (eds.), Being Necessary: Themes of Ontology and Modality from the Work of Bob Hale. Oxford, England: Oxford University Press. pp. 140-169.
    In two recent papers, Bob Hale has attempted to free second-order logic of the 'staggering existential assumptions' with which Quine famously attempted to saddle it. I argue, first, that the ontological issue is at best secondary: the crucial issue about second-order logic, at least for a neo-logicist, is epistemological. I then argue that neither Crispin Wright's attempt to characterize a `neutralist' conception of quantification that is wholly independent of existential commitment, nor Hale's attempt to characterize the second-order domain in terms (...)
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  31. (1 other version)Tuples all the Way Down?Simon Thomas Hewitt - 2018 - Thought: A Journal of Philosophy 7 (3):161-169.
    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 note I will pose the difficulty, and (...)
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  32. Thin Objects: An Abstractionist Account.Øystein Linnebo - 2018 - Oxford: Oxford University Press.
    Are there objects that are “thin” in the sense that their existence does not make a substantial demand on the world? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. This book attempts to develop the (...)
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  33. The Limits of Reconstructive Neologicist Epistemology.Eileen S. Nutting - 2018 - Philosophical Quarterly 68 (273):717-738.
    Wright claims that his and Hale’s abstractionist neologicist project is primarily epistemological in aim. Its epistemological aims include establishing the possibility of a priori mathematical knowledge, and establishing the possibility of reference to abstract mathematical objects. But, as Wright acknowledges, there is a question of how neologicist epistemology applies to actual, ordinary mathematical beliefs. I take up this question, focusing on arithmetic. Following a suggestion of Hale and Wright, I consider the possibility that the neologicist account provides an idealised reconstruction (...)
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  34. Neo-Fregeanism and the Burali-Forti Paradox.Ian Rumfitt - 2018 - In Ivette Fred Rivera & Jessica Leech (eds.), Being Necessary: Themes of Ontology and Modality from the Work of Bob Hale. Oxford, England: Oxford University Press. pp. 188-223.
    Philip Jourdain put this question to Frege in a letter of 28 January 1909. Frege had, indeed, next to nothing to say about ordinals, and in this respect Bob Hale has followed the master. As I hope this chapter will show, though, the topic is worth addressing. The natural abstraction principle for ordinals combines with full, impredicative second-order logic to engender a contradiction, the so-called Burali-Forti Paradox. I shall contend that the best solution involves a retreat to a predicative logic. (...)
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  35. Thin Reference, Metaontological Minimalism and Abstraction Principles: The Prospects for Tolerant Reductionism.Andrea Sereni - 2018 - In Annalisa Coliva, Paolo Leonardi & Sebastiano Moruzzi (eds.), Eva Picardi on Language, Analysis and History. Londra, Regno Unito: Palgrave. pp. 161-181.
    A standard understanding of abstraction principles elicits two opposite readings: Intolerant Reductionism, where abstractions are seen as reducing talk of abstract objects to talk about non-problematic domains, and Robustionism, where newly introduced terms genuinely refer to abstract objects. Against this dichotomy between such “austere” and “robust” readings, Dummett suggested ways to steer intermediate paths. We explore different options for intermediate stances, by reviewing metaontological strategies and semantic ones. Based on Dummett’s and Picardi’s understanding of the Context Principle, the paper acknowledges (...)
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  36. Abstraction and Four Kinds of Invariance.Roy T. Cook - 2017 - Philosophia Mathematica 25 (1):3–25.
    Fine and Antonelli introduce two generalizations of permutation invariance — internal invariance and simple/double invariance respectively. After sketching reasons why a solution to the Bad Company problem might require that abstraction principles be invariant in one or both senses, I identify the most fine-grained abstraction principle that is invariant in each sense. Hume’s Principle is the most fine-grained abstraction principle invariant in both senses. I conclude by suggesting that this partially explains the success of Hume’s Principle, and the comparative lack (...)
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  37. Introduction to Special Issue: Abstraction Principles.Salvatore Florio - 2017 - Philosophia Mathematica 25 (1):1-2.
    Introduction to a special issue on abstraction principles.
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  38. A Generic Russellian Elimination of Abstract Objects.Kevin C. Klement - 2017 - Philosophia Mathematica 25 (1):91-115.
    In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as ‘incomplete symbols’, using Russell's no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Richard Heck's charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in a system (...)
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  39. Identity and Sortals.Ansten Klev - 2017 - Erkenntnis 82 (1):1-16.
    According to the sortal conception of the universe of individuals every individual falls under a highest sortal, or category. It is argued here that on this conception the identity relation is defined between individuals a and b if and only if a and b fall under a common category. Identity must therefore be regarded as a relation of the form \, with three arguments x, y, and Z, where Z ranges over categories, and where the range of x and y (...)
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  40. 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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  41. 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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  42. 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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  43. The Breadth of the Paradox.Patricia Blanchette - 2016 - Philosophia Mathematica 24 (1):30-49.
    This essay examines Frege's reaction to Russell's Paradox and his views about the grounding of existence claims in mathematics. It is argued that Frege's strict requirements on existential proofs would rule out the attempt to ground arithmetic in. It is hoped that this discussion will help to clarify the ways in which Frege's position is both coherent and significantly different from the neo-logicist position on the issues of: what's required for proofs of existence; the connection between models, consistency, and existence; (...)
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  44. Necessity, Necessitism, and Numbers.Roy T. Cook - 2016 - Philosophical Forum 47 (3-4):385-414.
    Timothy Williamson’s Modal Logic as Metaphysics is a book-length defense of necessitism about objects—roughly put, the view that, necessarily, any object that exists, exists necessarily. In more formal terms, Williamson argues for the validity of necessitism for objects (NO: ◻︎∀x◻︎∃y(x=y)). NO entails both the (first-order) Barcan formula (BF: ◇∃xΦ → ∃x◇Φ, for any formula Φ) and the (first-order) converse Barcan formula (CBF: ∃x◇Φ → ◇∃xΦ, for any formula Φ). The purpose of this essay is not to assess Williamson’s arguments either (...)
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  45. Frege's Cardinals and Neo-Logicism.Roy T. Cook - 2016 - Philosophia Mathematica 24 (1):60-90.
    Gottlob Frege defined cardinal numbers in terms of value-ranges governed by the inconsistent Basic Law V. Neo-logicists have revived something like Frege's original project by introducing cardinal numbers as primitive objects, governed by Hume's Principle. A neo-logicist foundation for set theory, however, requires a consistent theory of value-ranges of some sort. Thus, it is natural to ask whether we can reconstruct the cardinal numbers by retaining Frege's definition and adopting an alternative consistent principle governing value-ranges. Given some natural assumptions regarding (...)
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  46. Frege's Recipe.Roy T. Cook & Philip A. Ebert - 2016 - Journal of Philosophy 113 (7):309-345.
    In this paper, we present a formal recipe that Frege followed in his magnum opus “Grundgesetze der Arithmetik” when formulating his definitions. This recipe is not explicitly mentioned as such by Frege, but we will offer strong reasons to believe that Frege applied it in developing the formal material of Grundgesetze. We then show that a version of Basic Law V plays a fundamental role in Frege’s recipe and, in what follows, we will explicate what exactly this role is and (...)
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  47. Introduction to Abstractionism.Philip A. Ebert & Marcus Rossberg - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics. Oxford, England: Oxford University Press UK. pp. 3-33.
  48. Hale and Wright on the Metaontology of Neo-Fregeanism.Matti Eklund - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics. Oxford, England: Oxford University Press UK.
  49. 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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  50. The Number of Moons Is Not a Number. Towards a Comprehensive Linguistic Approach to Frege's Commitment Puzzle.Borys Jastrzębski - 2016 - Filozofia Nauki 24 (2 (94)):31-49.
    Comprehensive Linguistic Approach to Frege's Commitment Puzzle There is a puzzle, noticed by Frege, about inferences from sentences like (F1) "Jupiter has four moons" to sentences like (F2) "The number of moons of Jupiter is four". They seem to be truth-conditionally equivalent but, apparently, they say something about completely different things. (F1) seems to be about moons, while (F2) about numbers. This phenomenon raises several puzzles about semantics, syntax, and is one of main tools of easy ontology. Recently, new linguistic (...)
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