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  1. added 2020-05-04
    Hale and Wright on the Metaontology of Neo-Fregeanism.Matti Eklund - 2016 - In Marcus Rossberg & Philip A. Ebert (eds.), Abstractionism.
  2. added 2020-04-10
    Statements That Concern Computable Sets X⊆N and Cannot Be Formalized in ZFC Because They Refer to the Currently Known/Unknown Theorems About X.Apoloniusz Tyszka & Sławomir Kurpaska - manuscript
    Conditions (1)-(8) below concern sets X⊆N . (1) There are a large number of elements of X and it is conjectured that X is infinite. (2) No known algorithm decides the finiteness of X. (3) A known algorithm for every n∈N decides whether or not n∈X. (4) An explicitly known integer n satisfies: card(X)<ω ⇒ X⊆(-∞,n]. (5) X is widely known in number theory. (6) There is no known equality X = X_1 ∪ X_2, where X_1 and X_2 are defined (...)
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  3. added 2020-03-25
    Frege’s Theorem: AN INTRODUCTION.Richard Heck Jr - 2003 - Manuscrito 26 (2):471-503.
    Frege's work was largely devoted to an attempt to argue that the'basic laws of arithmetic' are truths of logic. That attempt had both philosophical and formal aspects. The present note offers an introduction to both of these, so that readers will be able to appreciate contemporary discussions of the philosophical significance of 'Frege's Theorem'.
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  4. added 2020-03-25
    Frege: Philosophy of Mathematics. [REVIEW]Richard Heck - 1993 - Philosophical Quarterly 43 (171):223-233.
  5. added 2020-02-11
    Frege's Philosophy of Mathematics. [REVIEW]Bob Hale - 1999 - Philosophical Quarterly 49 (194):92-104.
  6. added 2019-10-14
    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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  7. added 2019-07-04
    Ludwig Wittgenstein, Dictating Philosophy To Francis Skinner: The Wittgenstein-Skinner Manuscripts. Transcribed and Edited, with an Introduction, Introductory Chapters and Notes by Arthur Gibson.Arthur Gibson & Niamh O'Mahony (eds.) - forthcoming - Berlin, Germany: Springer.
  8. added 2019-06-06
    Logicism and the Problem of Infinity: The Number of Numbers: Articles.Gregory Landini - 2011 - Philosophia Mathematica 19 (2):167-212.
    Simple-type theory is widely regarded as inadequate to capture the metaphysics of mathematics. The problem, however, is not that some kinds of structure cannot be studied within simple-type theory. Even structures that violate simple-types are isomorphic to structures that can be studied in simple-type theory. In disputes over the logicist foundations of mathematics, the central issue concerns the problem that simple-type theory fails to assure an infinity of natural numbers as objects. This paper argues that the problem of infinity is (...)
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  9. added 2019-06-06
    Joan Weiner. Frege Explained: From Arithmetic to Analytic Philosophy. Chicago: Open Court, 2004. Pp. Xvi + 179. ISBN 0-8126-9460-0. [REVIEW]Michael Beaney - 2007 - Philosophia Mathematica 15 (1):126-128.
    This book is an expanded version of Joan Weiner's introduction to Frege's work in the Oxford University Press ‘Past Masters’ series published in 1999. The earlier book had chapters on Frege's life and character, his basic project, his new logic, his definitions of the numbers, his 1891 essay ‘Function and concept’, his 1892 essays ‘On Sinn and Bedeutung’ and ‘On concept and object’, the Grundgesetze der Arithmetik and the havoc wreaked by Russell's paradox, and a final brief chapter on Frege's (...)
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  10. added 2019-06-05
    Russell on Logicism and Coherence.Conor Mayo-Wilson - 2011 - Russell: The Journal of Bertrand Russell Studies 31 (1):89-106.
    According to Quine, Charles Parsons, Mark Steiner, and others, Russell's logicist project is important because, if successful, it would show that mathematical theorems possess desirable epistemic properties often attributed to logical theorems, such as a prioricity, necessity, and certainty. Unfortunately, Russell never attributed such importance to logicism, and such a thesis contradicts Russell's explicitly stated views on the relationship between logic and mathematics. This raises the question: what did Russell understand to be the philosophical importance of logicism? Building on recent (...)
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  11. added 2019-05-28
    The Enhanced Indispensability Argument, the Circularity Problem, and the Interpretability Strategy.Jan Heylen & Lars Arthur Tump - forthcoming - Synthese:1-13.
    Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (...)
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  12. added 2019-05-28
    Review of Richard G. Heck, Jr: Reading Frege’s Grundgesetze. Oxford: Oxford University Press, 2012. [REVIEW]Marcus Rossberg - 2014 - Notre Dame Philosophical Review 11.
  13. added 2019-03-26
    Thin Objects.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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  14. added 2019-03-22
    Frege's Theorem.Richard G. Heck - 2011 - Clarendon Press.
    The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.
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  15. added 2019-03-22
    Frege’s Theorem: An Introduction.Richard Heck - 1999 - The Harvard Review of Philosophy 7 (1):56-73.
    A brief, non-technical introduction to technical and philosophical aspects of Frege's philosophy of arithmetic. The exposition focuses on Frege's Theorem, which states that the axioms of arithmetic are provable, in second-order logic, from a single non-logical axiom, "Hume's Principle", which itself is: The number of Fs is the same as the number of Gs if, and only if, the Fs and Gs are in one-one correspondence.
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  16. added 2019-03-22
    Finitude and Hume’s Principle.Richard Heck - 1997 - Journal of Philosophical Logic 26 (6):589-617.
    The paper formulates and proves a strengthening of 'Frege's Theorem', which states that axioms for second-order arithmetic are derivable in second-order logic from Hume's Principle, which itself says that the number of Fs is the same as the number of Gs just in case the Fs and Gs are equinumerous. The improvement consists in restricting this claim to finite concepts, so that nothing is claimed about the circumstances under which infinite concepts have the same number. 'Finite Hume's Principle' also suffices (...)
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  17. added 2018-09-29
    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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  18. added 2018-08-27
    13 Logicist Analysis and Conceptual Inferences L'analyse Logiciste Et les Inferences Conceptuelles.Peter Stockinger - 1990 - In Tadeusz Buksiński (ed.), Interpretation in the Humanities. Uniwersytet Im. Adama Mickiewicza W Poznaniu. pp. 71--284.
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  19. added 2018-08-27
    On Gardin's Logicist Analysis.Peter Stockinger - 1990 - In Tadeusz Buksiński (ed.), Interpretation in the Humanities. Uniwersytet Im. Adama Mickiewicza W Poznaniu. pp. 284--304.
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  20. added 2018-02-17
    Frege’s Cardinals as Concept-Correlates.Gregory Landini - 2006 - Erkenntnis 65 (2):207-243.
    In his "Grundgesetze", Frege hints that prior to his theory that cardinal numbers are objects he had an "almost completed" manuscript on cardinals. Taking this early theory to have been an account of cardinals as second-level functions, this paper works out the significance of the fact that Frege's cardinal numbers is a theory of concept-correlates. Frege held that, where n > 2, there is a one—one correlation between each n-level function and an n—1 level function, and a one—one correlation between (...)
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  21. added 2018-02-16
    Basic Laws of Arithmetic.Philip A. Ebert & Marcus Rossberg (eds.) - 2013 - Oxford University Press UK.
    This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik, with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework.
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  22. 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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  23. added 2017-08-27
    Dimension‐Based Statistical Learning Affects Both Speech Perception and Production.Matthew Lehet & Lori L. Holt - 2017 - Cognitive Science 41 (S4):885-912.
    Multiple acoustic dimensions signal speech categories. However, dimensions vary in their informativeness; some are more diagnostic of category membership than others. Speech categorization reflects these dimensional regularities such that diagnostic dimensions carry more “perceptual weight” and more effectively signal category membership to native listeners. Yet perceptual weights are malleable. When short-term experience deviates from long-term language norms, such as in a foreign accent, the perceptual weight of acoustic dimensions in signaling speech category membership rapidly adjusts. The present study investigated whether (...)
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  24. added 2017-03-20
    A Framework for Implicit Definitions and the A Priori.Philip A. Ebert - 2016 - In Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism. Oxford: Oxford University Press. pp. 133--160.
  25. added 2017-02-23
    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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  26. added 2017-02-13
    Logicism 2000: A Mini-Manifesto.Richard Jeffrey - 1996 - In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell. pp. 160--164.
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  27. added 2017-02-12
    Notes on Types, Sets, and Logicism, 1930-1950.José Ferreirós Domínguez - 1997 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 12 (1):91-124.
  28. added 2017-02-08
    Peano, Russell, and Logicism.Herbert Hochberg - 1955 - Analysis 16 (5):118 - 120.
    The author addresses the question as to whether russell and whitehead "provide an explication of the idea that arithmetical truths are tautologies." he thinks their achievement was in developing an axiomatic system in which the "interpreted propositions are tautologies," but not in proving this of mathematics. He thinks the real problem here is the attempt to explicate ordinary language via formally constructed languages. (staff).
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  29. added 2017-01-30
    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 (...)
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  30. added 2017-01-29
    Foundations of Mathematics and Logicism.Ivor Grattan-Guinness - 2008 - In Michel Weber (ed.), Handbook of Whiteheadian Process Thought. De Gruyter. pp. 97-104.
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  31. added 2017-01-29
    Logicism Reconsidered.Patricia A. Blanchette - 1990 - Dissertation, Stanford University
    This thesis is an examination of Frege's logicism, and of a number of objections which are widely viewed as refutations of the logicist thesis. In the view offered here, logicism is designed to provide answers to two questions: that of the nature of arithmetical truth, and that of the source of arithmetical knowledge. ;The first objection dealt with here is the view that logicism is not an epistemologically significant thesis, due to the fact that the epistemological status of logic itself (...)
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  32. added 2017-01-28
    Andrea Pedeferri, Editor. Frege E Il Neologicismo. Milan: FrancoAngeli, 2005. ISBN 88-464-6944-5. Pp. 270. [REVIEW]Andrea Pedeferr - 2006 - Philosophia Mathematica 14 (2):268.
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  33. added 2017-01-27
    William Demopoulos Logicism and its Philosophical Legacy.Bob Hale - 2015 - British Journal for the Philosophy of Science 66 (2):459-463.
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  34. added 2017-01-27
    Frege’s Theorem by Richard G. Heck, Jr. [REVIEW]John P. Burgess - 2012 - Journal of Philosophy 109 (12):728-732.
  35. added 2017-01-27
    Logical Problems Suggested by Logicism.J. W. Degen - 2006 - Vienna Circle Institute Yearbook 12:123-138.
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  36. added 2017-01-27
    Frege, Neo-Logicism and Applied Mathematics.Peter Clark - 2004 - Vienna Circle Institute Yearbook 11:169-183.
    A little over one hundred years ago , Frege wrote to Russell in the following terms1: I myself was long reluctant to recognize ranges of values and hence classes; but I saw no other possibility of placing arithmetic on a logical foundation. But the question is how do we apprehend logical objects? And I have found no other answer to it than this, We apprehend them as extensions of concepts, or more generally, as ranges of values of functions. I have (...)
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  37. added 2017-01-26
    New Logicism in Theoretical Legal Thinking.Pavel Holländer - 2006 - Rechtstheorie 37 (2):131-138.
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  38. added 2017-01-26
    Mathematics in and Behind Russell's Logicism and its Reception'.I. Grattan-Guinness - 2003 - In Nicholas Griffin (ed.), Bulletin of Symbolic Logic. Cambridge University Press. pp. 51.
  39. added 2017-01-25
    The Predicative Frege Hierarchy.Albert Visser - 2009 - Annals of Pure and Applied Logic 160 (2):129-153.
    In this paper, we characterize the strength of the predicative Frege hierarchy, , introduced by John Burgess in his book [J. Burgess, Fixing frege, in: Princeton Monographs in Philosophy, Princeton University Press, Princeton, 2005]. We show that and are mutually interpretable. It follows that is mutually interpretable with Q. This fact was proved earlier by Mihai Ganea in [M. Ganea, Burgess’ PV is Robinson’s Q, The Journal of Symbolic Logic 72 619–624] using a different proof. Another consequence of the our (...)
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  40. added 2017-01-23
    Richard G. Heck, Jr.: Frege’s Theorem. [REVIEW]John P. Burgess - 2012 - Journal of Philosophy 109 (12):728-733.
  41. added 2017-01-23
    Chateaubriand's Logicism.Abel Casanave - 2004 - Manuscrito 27 (1):13-20.
    In his doctoral dissertation, O. Chateaubriand favored Dedekind’s analysis of the notion of number; whereas in Logical Forms, he favors a fregean approach to the topic. My aim in this paper is to examine the kind of logicism he defends. Three aspects will be considered: the concept of analysis; the universality of arithmetical properties and their definability; the irreducibility of arithmetical objects.
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  42. added 2017-01-17
    Notes on Types, Sets, and Logicism, 1930-1950.José Ferreiros - 1997 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 12 (1):91-124.
    The present paper is a contribution to the history of logic and its philosophy toward the mid-20th century. It examines the interplay between logic, type theory and set theory during the 1930s and 40s, before the reign of first-order logic, and the closely connected issue of the fate of logicism. After a brief presentation of the emergence of logicism, set theory, and type theory, Quine’s work is our central concern, since he was seemingly the most outstanding logicist around 1940, though (...)
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  43. added 2017-01-16
    Aquinas on Being and Logicism.Steven A. Long - 2005 - New Blackfriars 86 (1003):323-347.
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  44. added 2017-01-15
    Minimal Logicism.Francesca Boccuni - 2014 - Philosophia Scientae 18:81-94.
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  45. added 2017-01-15
    A Non Reductionist Logicism with Explicit Definitions.Pierre Joray - 2013 - In . Les Cahiers D'Ithaque.
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  46. added 2017-01-14
    Subregular Tetrahedra.John Corcoran - 2008 - Bulletin of Symbolic Logic 14 (3):411-2.
    This largely expository lecture deals with aspects of traditional solid geometry suitable for applications in logic courses. Polygons are plane or two-dimensional; the simplest are triangles. Polyhedra [or polyhedrons] are solid or three-dimensional; the simplest are tetrahedra [or triangular pyramids, made of four triangles]. -/- A regular polygon has equal sides and equal angles. A polyhedron having congruent faces and congruent [polyhedral] angles is not called regular, as some might expect; rather they are said to be subregular—a word coined for (...)
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  47. added 2017-01-10
    Meaning, Presuppositions, Truth-Relevance, Gödel's Sentence and the Liar Paradox.X. Y. Newberry - manuscript
    Section 1 reviews Strawson’s logic of presuppositions. Strawson’s justification is critiqued and a new justification proposed. Section 2 extends the logic of presuppositions to cases when the subject class is necessarily empty, such as (x)((Px & ~Px) → Qx) . The strong similarity of the resulting logic with Richard Diaz’s truth-relevant logic is pointed out. Section 3 further extends the logic of presuppositions to sentences with many variables, and a certain valuation is proposed. It is noted that, given this valuation, (...)
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  48. added 2016-12-08
    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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  49. added 2016-12-08
    Solving the Caesar Problem Without Categorical Sortals.Nikolaj Jang Pedersen - 2009 - Erkenntnis 71 (2):141-155.
    The neo-Fregean account of arithmetical knowledge is centered around the abstraction principle known as Hume’s Principle: for any concepts X and Y , the number of X ’s is the same as the number of Y ’s just in case there is a 1–1 correspondence between X and Y . The Caesar Problem, originally raised by Frege in §56 of Die Grundlagen der Arithmetik , emerges in the context of the neo-Fregean programme, because, though Hume’s Principle provides a criterion of (...)
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  50. added 2016-12-08
    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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