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  1. 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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  2. added 2018-09-24
    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 aprioricity, 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 work (...)
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  3. 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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  4. 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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  5. 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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  6. 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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  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 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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  9. 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.
  10. 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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  11. 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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  12. 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.
  13. 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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  14. 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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  15. 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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  16. 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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  17. 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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  18. 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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  19. added 2017-01-27
    Frege’s Theorem by Richard G. Heck, Jr. [REVIEW]John P. Burgess - 2012 - Journal of Philosophy 109 (12):728-732.
  20. added 2017-01-27
    Logical Problems Suggested by Logicism.J. W. Degen - 2006 - Vienna Circle Institute Yearbook 12:123-138.
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  21. 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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  22. added 2017-01-26
    New Logicism in Theoretical Legal Thinking.Pavel Holländer - 2006 - Rechtstheorie 37 (2):131-138.
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  23. 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.
  24. 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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  25. added 2017-01-23
    Richard G. Heck, Jr.: Frege’s Theorem. [REVIEW]John P. Burgess - 2012 - Journal of Philosophy 109 (12):728-733.
  26. 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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  27. added 2017-01-19
    Notes on Types, Sets, and Logicism, 1930-1950.José Ferreiros - 1997 - Theoria 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 (with particular attention to Carnap and Tarski), Quine’s work is our central concern, since he was seemingly (...)
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  28. 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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  29. added 2017-01-16
    Aquinas on Being and Logicism.Steven A. Long - 2005 - New Blackfriars 86 (1003):323-347.
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  30. added 2017-01-15
    Minimal Logicism.Francesca Boccuni - 2014 - Philosophia Scientae 18:81-94.
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  31. added 2017-01-15
    A Non Reductionist Logicism with Explicit Definitions.Pierre Joray - 2013 - In . Les Cahiers D'Ithaque.
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  32. 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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  33. 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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  34. 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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  35. 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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  36. 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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  37. added 2016-12-08
    Meaning and Method: Essays in Honor of Hilary Putnam.Hilary Putnam & George Boolos (eds.) - 1990 - Cambridge University Press.
    In this festschrift for the eminent philosopher Hilary Putnam, a team of distinguished philosophers write on a broad range of topics and thus reflect the remarkably fertile and provocative research of Putnam himself. The volume is not merely a celebration of a man, but also a report on the state of philosophy in a number of significant areas. The essays fall naturally into three groups: a central core on the theme of conventionality and content in the philosophy of mind, language, (...)
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  38. added 2016-12-05
    Logicism and its Philosophical Legacy.William Demopoulos - 2015 - Cambridge University Press.
    The idea that mathematics is reducible to logic has a long history, but it was Frege who gave logicism an articulation and defense that transformed it into a distinctive philosophical thesis with a profound influence on the development of philosophy in the twentieth century. This volume of classic, revised and newly written essays by William Demopoulos examines logicism's principal legacy for philosophy: its elaboration of notions of analysis and reconstruction. The essays reflect on the deployment of these ideas by the (...)
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  39. added 2016-11-30
    What Russell Should Have Said to Burali–Forti.Salvatore Florio & Graham Leach-Krouse - 2017 - Review of Symbolic Logic 10 (4):682-718.
    The paradox that appears under Burali-Forti’s name in many textbooks of set theory is a clever piece of reasoning leading to an unproblematic theorem. The theorem asserts that the ordinals do not form a set. For such a set would be—absurdly—an ordinal greater than any ordinal in the set of all ordinals. In this article, we argue that the paradox of Burali-Forti is first and foremost a problem about concept formation by abstraction, not about sets. We contend, furthermore, that some (...)
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  40. added 2016-10-07
    Essays on Frege's Basic Laws of Arithmetic.Philip A. Ebert & Marcus Rossberg (eds.) - forthcoming - Oxford University Press.
  41. added 2016-10-03
    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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  42. added 2016-10-03
    Frege Meets Brouwer.Stewart Shapiro & Øystein Linnebo - 2015 - Review of Symbolic Logic 8 (3):540-552.
    We show that, by choosing definitions carefully, a version of Frege's theorem can be proved in intuitionistic logic.
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  43. added 2016-09-30
    NeoFregean Metaontology.Fraser MacBride - 2016 - In P. Ebert & M. Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics. Oxford, U.K.: Oxford University Press. pp. 94-112.
    According to neo-Fregeans, an expression that is syntactically singular and figures in a true sentence is guaranteed to have some existing thing in the world to pick out. But this approach is confronted by a dilemma. If reality is crystalline, has a structure fixed independently of language, then the view that reality is guaranteed to contain a sufficient plenitude of objects to supply referents for the relevant expressions is left hostage to cosmological fortune. Whereas if reality is plastic then it (...)
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  44. added 2016-09-09
    Russell’s Method of Analysis and the Axioms of Mathematics.Lydia Patton - 2017 - In Sandra Lapointe Christopher Pincock (ed.), Innovations in the History of Analytical Philosophy. London: Palgrave-Macmillan. pp. 105-126.
    In the early 1900s, Russell began to recognize that he, and many other mathematicians, had been using assertions like the Axiom of Choice implicitly, and without explicitly proving them. In working with the Axioms of Choice, Infinity, and Reducibility, and his and Whitehead’s Multiplicative Axiom, Russell came to take the position that some axioms are necessary to recovering certain results of mathematics, but may not be proven to be true absolutely. The essay traces historical roots of, and motivations for, Russell’s (...)
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  45. added 2016-07-29
    Dedekind's Logicism.Ansten Mørch Klev - 2015 - Philosophia Mathematica:nkv027.
    A detailed argument is provided for the thesis that Dedekind was a logicist about arithmetic. The rules of inference employed in Dedekind's construction of arithmetic are, by his lights, all purely logical in character, and the definitions are all explicit; even the definition of the natural numbers as the abstract type of simply infinite systems can be seen to be explicit. The primitive concepts of the construction are logical in their being intrinsically tied to the functioning of the understanding.
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  46. added 2016-03-22
    Thin Objects.Øystein Linnebo - 2009 - In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. pp. 11--227.
  47. added 2016-02-26
    The Good, the Bad and the Ugly.Philip A. Ebert & Stewart Shapiro - 2009 - Synthese 170 (3):415-441.
    This paper discusses the neo-logicist approach to the foundations of mathematics by highlighting an issue that arises from looking at the Bad Company objection from an epistemological perspective. For the most part, our issue is independent of the details of any resolution of the Bad Company objection and, as we will show, it concerns other foundational approaches in the philosophy of mathematics. In the first two sections, we give a brief overview of the "Scottish" neo-logicist school, present a generic form (...)
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  48. added 2016-02-25
    The Strength of Abstraction with Predicative Comprehension.Sean Walsh - 2016 - Bulletin of Symbolic Logic 22 (1):105–120.
    Frege's theorem says that second-order Peano arithmetic is interpretable in Hume's Principle and full impredicative comprehension. Hume's Principle is one example of an abstraction principle, while another paradigmatic example is Basic Law V from Frege's Grundgesetze. In this paper we study the strength of abstraction principles in the presence of predicative restrictions on the comprehension schema, and in particular we study a predicative Fregean theory which contains all the abstraction principles whose underlying equivalence relations can be proven to be equivalence (...)
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  49. added 2015-12-02
    Singular Terms and Arithmetical Logicism.Ian Rumfitt - 2003 - Philosophical Books 44 (3):193--219.
    This article is a critical notice of Bob Hale and Crispin Wright's *The Reason's Proper Study* (OUP). It focuses particularly on their attempts (crucial to their neo-logicist project) to say what a singular term is. I identify problems for their account but include some constructive suggestions about how it might be improved.
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  50. added 2015-10-06
    The Arché Papers on the Mathematics of Abstraction.Roy T. Cook (ed.) - 2007 - Springer.
    Unique in presenting a thoroughgoing examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns).
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