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  1. Conceivability, Essence, and Haecceities.Timothy Bowen - manuscript
    This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I introduce a novel epistemic two-dimensional truthmaker semantics. I argue that the interaction between the two-dimensional framework and the mereological parthood relation, which is super-rigid, enables epistemic possibilities and truthmakers with regard to parthood to be a guide to its metaphysical profile. I specify, further, a two-dimensional formula encoding the relation between the epistemic possibility and verification of essential properties obtaining (...)
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  2. Frege's Basic Law V and Cantor's Theorem.Manuel Bremer - manuscript
    The following essay reconsiders the ontological and logical issues around Frege’s Basic Law (V). If focuses less on Russell’s Paradox, as most treatments of Frege’s Grundgesetze der Arithmetik (GGA)1 do, but rather on the relation between Frege’s Basic Law (V) and Cantor’s Theorem (CT). So for the most part the inconsistency of Naïve Comprehension (in the context of standard Second Order Logic) will not concern us, but rather the ontological issues central to the conflict between (BLV) and (CT). These ontological (...)
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  3. 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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  4. Frege’s Theory of Real Numbers: A Consistent Rendering.Francesca Boccuni & Marco Panza - forthcoming - Review of Symbolic Logic:1-44.
    Frege's definition of the real numbers, as envisaged in the second volume of Grundgesetze der Arithmetik, is fatally flawed by the inconsistency of Frege's ill-fated Basic Law V. We restate Frege's definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege's own indications is possible at all.
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  5. The Primacy of the Universal Quantifier in Frege's Concept-Script.Joongol Kim - forthcoming - Dialectica.
    This paper presents three explanations of why Frege took the universal, rather than the existential, quantifier as primitive in his formalization of logic. The first two explanations provide technical reasons related to how Frege formalizes the logic of truth-functions and the logic of quantification. The third, philosophical explanation locates the reason in Frege's logicist goal of analyzing arithmetical concepts---especially the concepts of 0 and 1---in purely logical terms.
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  6. Frege meets Belnap: Basic Law V in a Relevant Logic.Shay Logan & Francesca Boccuni - forthcoming - In Andrew Tedder, Shawn Standefer & Igor Sedlar (eds.), New Directions in Relevant Logic. Springer. pp. 381-404.
    Abstractionism in the philosophy of mathematics aims at deriving large fragments of mathematics by combining abstraction principles (i.e. the abstract objects $\S e_1, \S e_2$, are identical if, and only if, an equivalence relation $Eq_\S$ holds between the entities $e_1, e_2$) with logic. Still, as highlighted in work on the semantics for relevant logics, there are different ways theories might be combined. In exactly what ways must logic and abstraction be combined in order to get interesting mathematics? In this paper, (...)
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  7. Review of "Frege: Philosophy of Mathematics". [REVIEW]Marco Antonio Ruffino - forthcoming - Manuscrito.
    In this review I briefly explain the most important points of each chapter of Dummett's book, and critically discuss some of them. Special attention is given to the criticisms of Crispin Wright's interpretation of Frege's Platonism, and also to Dummett's interpretation of the role(s) of the context principle in Frege's thought.
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  8. Logic and Sets.Marta Vlasáková - forthcoming - Logic and Logical Philosophy:1.
    The notion of the extension of a concept has been used in logic for a long time. It is usually considered to be closely connected to the intuitive notion of a set and thus seems as though it should be embedded into set theory. However, there are significant differences between this “logical” concept of set and the notion of set (class) as defined via standard axiomatic systems of set theory; it may, therefore, be quite misleading to consider the two concepts (...)
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  9. Higher-Order Metaphysics in Frege and Russell.Kevin C. Klement - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press. pp. 355-377.
    This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between objects and functions. (...)
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  10. Thin Mereological Sums, Abstraction, and Interpretational Modalities.Giorgio Lando - 2023 - Theoria 89 (3):1-18.
    Some tools introduced by Linnebo to show that mathematical entities are thin objects can also be applied to non-mathematical entities, which have been thought to be thin as well for a variety of reasons. In this paper, I discuss some difficulties and opportunities concerning the application of abstraction and interpretational modalities to mereological sums. In particular, I show that on one hand some prima facie attractive candidates for the role of an explanatory plural abstraction principle for mereological sums (in terms (...)
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  11. Frege, Thomae, and Formalism: Shifting Perspectives.Richard Lawrence - 2023 - Journal for the History of Analytical Philosophy 11 (2):1-23.
    Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that (...)
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  12. 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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  13. The Frege–Hilbert controversy in context.Tabea Rohr - 2023 - Synthese 202 (1):1-30.
    This paper aims to show that Frege’s and Hilbert’s mutual disagreement results from different notions of Anschauung and their relation to axioms. In the first section of the paper, evidence is provided to support that Frege and Hilbert were influenced by the same developments of 19th-century geometry, in particular the work of Gauss, Plücker, and von Staudt. The second section of the paper shows that Frege and Hilbert take different approaches to deal with the problems that the developments in 19th-century (...)
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  14. Frege on the introduction of real and complex numbers by abstraction and cross-sortal identity claims.Matthias Schirn - 2023 - Synthese 201 (6):1-18.
    In this article, I try to shed new light on Frege’s envisaged definitional introduction of real and complex numbers in _Die Grundlagen der Arithmetik_ (1884) and the status of cross-sortal identity claims with side glances at _Grundgesetze der Arithmetik_ (vol. I 1893, vol. II 1903). As far as I can see, this topic has not yet been discussed in the context of _Grundlagen_. I show why Frege’s strategy in the case of the projected definitions of real and complex numbers in (...)
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  15. Identity and the Cognitive Value of Logical Equations in Frege’s Foundational Project.Matthias Schirn - 2023 - Notre Dame Journal of Formal Logic 64 (4):495-544.
    In this article, I first analyze and assess the epistemological and semantic status of canonical value-range equations in the formal language of Frege’s Grundgesetze der Arithmetik. I subsequently scrutinize the relation between (a) his informal, metalinguistic stipulation in Grundgesetze I, Section 3, and (b) its formal counterpart, which is Basic Law V. One point I argue for is that the stipulation in Section 3 was designed not only to fix the references of value-range names, but that it was probably also (...)
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  16. 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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  17. The Caesar Problem — A Piecemeal Solution.J. P. Studd - 2023 - Philosophia Mathematica 31 (2):236-267.
    The Caesar problem arises for abstractionist views, which seek to secure reference for terms such as ‘the number of Xs’ or #X by stipulating the content of ‘unmixed’ identity contexts like ‘#X = #Y’. Frege objects that this stipulation says nothing about ‘mixed’ contexts such as ‘# X = Julius Caesar’. This article defends a neglected response to the Caesar problem: the content of mixed contexts is just as open to stipulation as that of unmixed contexts.
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  18. Frege’s View of the Context Principle After 1890.Krystian Bogucki - 2022 - Grazer Philosophische Studien 99 (1):1-29.
    The aim of this article is to examine Frege’s view of the context principle in his mature philosophical doctrine. Here, the author argues that the context principle is embodied in the contextual explanation of value-ranges presented in Basic Laws of Arithmetic. The contextual explanation of value-ranges plays essentially the same role as the context principle in The Foundations of Arithmetic. It is supposed to show how a reference to natural numbers is possible. Moreover, the author argues against the view that (...)
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  19. Frege's Theorem and Mathematical Cognition.Lieven Decock - 2022 - In Francesca Boccuni & Andrea Sereni (eds.), Origins and Varieties of Logicism: On the Logico-Philosophical Foundations of Logicism. New York: Routledge. pp. 372-394.
  20. Stephen Houlgate. Hegel on Being. [REVIEW]Robb Dunphy - 2022 - Idealistic Studies 52 (3):297-305.
  21. Kant Versus Frege on Arithmetic.Nora Grigore - 2022 - Axiomathes 32 (2):263-281.
    Kant's claim that arithmetical truths are synthetic is famously contradicted by Frege, who considers them to be analytical. It may seem that this is a mere dispute about linguistic labels, since both Kant and Frege agree that arithmetical truths are a priori and informative, and, therefore, it is only a matter of how one chooses to call them. I argue that the choice between calling arithmetic “synthetic” or “analytic” has a deeper significance. I claim that the dispute is not a (...)
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  22. Stipulations Missing Axioms in Frege's Grundgesetze der Arithmetik.Gregory Landini - 2022 - History and Philosophy of Logic 43 (4):347-382.
    Frege's Grundgesetze der Arithmetik offers a conception of cpLogic as the study of functions. Among functions are included those that are concepts, i.e. characteristic functions whose values are the logical objects that are the True/the False. What, in Frege's view, are the objects the True/the False? Frege's stroke functions are themselves concepts. His stipulation introducing his negation stroke mentions that it yields [...]. But curiously no accommodating axiom is given, and there is no such theorem. Why is it that some (...)
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  23. Resolving Frege’s Other Puzzle.Eric Snyder, Richard Samuels & Stewart Shapiro - 2022 - Philosophica Mathematica 30 (1):59-87.
    Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that (...)
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  24. Vagueness and Frege.Marian Călborean - 2021 - Romanian Journal of Analytic Philosophy 2:12-44.
    A constant of Frege’s writing is his rejection of indeterminate predicates as found in natural language. This paper follows Frege’s remarks on vagueness from the early "Begriffsschrift” to his mature works, drawing brief parallels with the main contemporary theories of vagueness. I critically examine Frege’s arguments for the inconsistency of natural language and argue that the inability to accommodate vagueness in his mature ontology is mainly due to heuristic rules of thumb which Frege took as essential, not to a deep (...)
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  25. Frege on intuition and objecthood in projective geometry.Günther Eder - 2021 - Synthese 199 (3-4):6523-6561.
    In recent years, several scholars have been investigating Frege’s mathematical background, especially in geometry, in order to put his general views on mathematics and logic into proper perspective. In this article I want to continue this line of research and study Frege’s views on geometry in their own right by focussing on his views on a field which occupied center stage in nineteenth century geometry, namely, projective geometry.
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  26. Frege's Curiously Two-Dimensional Concept-Script.Landon D. C. Elkind - 2021 - Journal for the History of Analytical Philosophy 9 (11).
    In this paper I argue that the two-dimensional character of Frege’s Begriffsschrift plays an epistemological role in his argument for the analyticity of arithmetic. First, I motivate the claim that its two-dimensional character needs a historical explanation. Then, to set the stage, I discuss Frege’s notion of a Begriffsschrift and Kant’s epistemology of mathematics as synthetic a priori and partly grounded in intuition, canvassing Frege’s sharp disagreement on these points. Finally, I argue that the two-dimensional character of Frege’s notations play (...)
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  27. A filosofia da matemática de Frege no contexto do neokantismo.Gottfried Gabriel, Sven Schlotter, Lucas A. D. Amaral & Rafael R. Garcia - 2021 - Kant E-Prints 16 (2):363-376.
    Há muitos pontos de concordância entre Frege e os neokantianos. Isso vale especialmente para os representantes do neokantismo da teoria do valor ou do Sudoeste alemão na tradição de Hermann Lotze. Não discutiremos aqui todos os aspectos dessa proximidade; de acordo com o tema que propomos, ficaremos restritos à filosofia da matemática. A primeira parte do artigo tratará da relação entre aritmética e geometria, mostrando surpreendentes semelhanças entre Frege e o neokantiano Otto Liebmann. A segunda parte discutirá as diferentes recepções (...)
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  28. Arithmetic, Logicism, and Frege’s Definitions.Timothy Perrine - 2021 - International Philosophical Quarterly 61 (1):5-25.
    This paper describes both an exegetical puzzle that lies at the heart of Frege’s writings—how to reconcile his logicism with his definitions and claims about his definitions—and two interpretations that try to resolve that puzzle, what I call the “explicative interpretation” and the “analysis interpretation.” This paper defends the explicative interpretation primarily by criticizing the most careful and sophisticated defenses of the analysis interpretation, those given my Michael Dummett and Patricia Blanchette. Specifically, I argue that Frege’s text either are inconsistent (...)
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  29. Mr. Frege, The Platonist.Daniel Sierra - 2021 - Logiko-Filosofskie Studii 2 (Vol 19):136-144.
    Even though Frege is a major figure in the history of analytic philosophy, it is not surprising that there are still issues surrounding his views, interpreting them, and labeling them. Frege’s view on numbers is typically termed as ‘Platonistic’ or at least a type of Platonism (Reck 2005). Still, the term ‘Platonism’ has views and assumptions ascribed to it that may be misleading and leads to mischaracterizations of Frege’s outlook on numbers and ideas. So, clarification of the term ‘Platonism’ is (...)
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  30. Saying Something about a Concept: Frege on Statements of Number.Mark Textor - 2021 - History and Philosophy of Logic 42 (1):60-71.
    The paper gives a historically informed reconstruction of Frege's view of statements of number. The reconstruction supports Frege's claim that a statement can be 'about a concept' although it does not contain a singular term referring to the concept. Hence, Frege's philosophy of number is not subject to the problems Frege sees for singular reference to concepts.
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  31. Why did Frege reject the theory of types?Wim Vanrie - 2021 - British Journal for the History of Philosophy 29 (3):517-536.
    I investigate why Frege rejected the theory of types, as Russell presented it to him in their correspondence. Frege claims that it commits one to violations of the law of excluded middle, but this complaint seems to rest on a dogmatic refusal to take Russell’s proposal seriously on its own terms. What is at stake is not so much the truth of a law of logic, but the structure of the hierarchy of the logical categories, something Frege seems to neglect. (...)
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  32. The Bad Company Objection and the Extensionality of Frege’s Logic.Vincenzo Ciccarelli - 2020 - Perspectiva Filosófica 47 (2):231-247.
    According to the Bad Company objection, the fact that Frege’s infamous Basic Law V instantiates the general definitional pattern of higher-order abstraction principles is a good reason to doubt the soundness of this sort of definitions. In this paper I argue against this objection by showing that the definitional pattern of abstraction principles – as extrapolated from §64 of Frege’s Grundlagen– includes an additional requirement (which I call the specificity condition) that is not satisfied by the Basic Law V while (...)
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  33. The Metametaphysics of Neo-Fregeanism.Matti Eklund - 2020 - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. New York, NY: Routledge.
  34. Quine’s proxy-function argument for the indeterminacy of reference and frege’s caesar problem.Dirk Greimann - 2020 - Manuscrito 44 (3):70-108.
    In his logical foundation of arithmetic, Frege faced the problem that the semantic interpretation of his system does not determine the reference of the abstract terms completely. The contextual definition of number, for instance, does not decide whether the number 5 is identical to Julius Caesar. In a late writing, Quine claimed that the indeterminacy of reference established by Frege’s Caesar problem is a special case of the indeterminacy established by his proxy-function argument. The present paper aims to show that (...)
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  35. 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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  36. 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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  37. 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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  38. Reflections on Frege’s Theory of Real Numbers†.Peter Roeper - 2020 - Philosophia Mathematica 28 (2):236-257.
    ABSTRACT Although Frege’s theory of real numbers in Grundgesetze der Arithmetik, Vol. II, is incomplete, it is possible to provide a logicist justification for the approach he is taking and to construct a plausible completion of his account by an extrapolation which parallels his theory of cardinal numbers.
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  39. 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 (...)
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  40. 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
  41. Frege on Referentiality and Julius Caesar in Grundgesetze Section 10.Bruno Bentzen - 2019 - Notre Dame Journal of Formal Logic 60 (4):617-637.
    This paper aims to answer the question of whether or not Frege's solution limited to value-ranges and truth-values proposed to resolve the "problem of indeterminacy of reference" in section 10 of Grundgesetze is a violation of his principle of complete determination, which states that a predicate must be defined to apply for all objects in general. Closely related to this doubt is the common allegation that Frege was unable to solve a persistent version of the Caesar problem for value-ranges. It (...)
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  42. Hilbertian Structuralism and the Frege-Hilbert Controversy†.Fiona T. Doherty - 2019 - Philosophia Mathematica 27 (3):335-361.
    ABSTRACT This paper reveals David Hilbert’s position in the philosophy of mathematics, circa 1900, to be a form of non-eliminative structuralism, predating his formalism. I argue that Hilbert withstands the pressing objections put to him by Frege in the course of the Frege-Hilbert controversy in virtue of this early structuralist approach. To demonstrate that this historical position deserves contemporary attention I show that Hilbertian structuralism avoids a recent wave of objections against non-eliminative structuralists to the effect that they cannot distinguish (...)
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  43. 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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  44. 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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  45. 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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  46. Frege’s Constraint and the Nature of Frege’s Foundational Program.Marco Panza & Andrea Sereni - 2019 - Review of Symbolic Logic 12 (1):97-143.
    Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$and on whether it (...)
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  47. Frege’s philosophy of geometry.Matthias Schirn - 2019 - Synthese 196 (3):929-971.
    In this paper, I critically discuss Frege’s philosophy of geometry with special emphasis on his position in The Foundations of Arithmetic of 1884. In Sect. 2, I argue that that what Frege calls faculty of intuition in his dissertation is probably meant to refer to a capacity of visualizing geometrical configurations structurally in a way which is essentially the same for most Western educated human beings. I further suggest that according to his Habilitationsschrift it is through spatial intuition that we (...)
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  48. On the Philosophical Significance of Frege’s Constraint.Andrea Sereni - 2019 - Philosophia Mathematica 27 (2):244–275.
    Foundational projects disagree on whether pure and applied mathematics should be explained together. Proponents of unified accounts like neologicists defend Frege’s Constraint (FC), a principle demanding that an explanation of applicability be provided by mathematical definitions. I reconsider the philosophical import of FC, arguing that usual conceptions are biased by ontological assumptions. I explore more reasonable weaker variants — Moderate and Modest FC — arguing against common opinion that ante rem structuralism (and other) views can meet them. I dispel doubts (...)
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  49. Neologicism for Real – Are We There Yet?Rafal Urbaniak - 2019 - In Bartłomiej Skowron (ed.), Contemporary Polish Ontology. Berlin: De Gruyter. pp. 181-204.
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  50. The geometrical basis of arithmetical knowledge: Frege & Dehaene.Sorin Costreie - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):361-370.
    Frege writes in Numbers and Arithmetic about kindergarten-numbers and “an a priori mode of cognition” that they may have “a geometrical source.” This resembles recent findings on arithmetical cognition. In my paper, I explore this resemblance between Gottlob Frege’s later position concerning the geometrical source of arithmetical knowledge, and some current positions in the literature dedicated to arithmetical cognition, especially that of Stanislas Dehaene. In my analysis, I shall try to mainly see to what extent logicism is compatible with intuitionism.
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