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  1. Carnap'S. Logicism (1975). Herbert G. Bohnert. In Jaakko Hintikka (ed.), Rudolf Carnap, Logical Empiricist: Materials and Perspectives. D. Reidel Pub. Co.. 73--183.score: 30.0
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  2. Sean Walsh (2014). Logicism, Interpretability, and Knowledge of Arithmetic. Review of Symbolic Logic 7 (1):84-119.score: 24.0
    A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are representable in the logical principles. The notions of representation considered here are related to theory-based and structure-based notions of (...)
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  3. Otavio Bueno (2001). Logicism Revisited. Principia 5 (1-2):99-124.score: 24.0
    In this paper, I develop a new defense of logicism: one that combines logicism and nominalism. First, I defend the logicist approach from recent criticisms; in particular from the charge that a cruciai principie in the logicist reconstruction of arithmetic, Hume's Principle, is not analytic. In order to do that, I argue, it is crucial to understand the overall logicist approach as a nominalist view. I then indicate a way of extending the nominalist logicist approach beyond arithmetic. Finally, (...)
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  4. José Ferreirós (2009). Hilbert, Logicism, and Mathematical Existence. Synthese 170 (1):33 - 70.score: 24.0
    David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a (...)
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  5. Ian Proops (2006). Russell’s Reasons for Logicism. Journal of the History of Philosophy 44 (2):267-292.score: 24.0
    What is at stake philosophically for Russell in espousing logicism? I argue that Russell's aims are chiefly epistemological and mathematical in nature. Russell develops logicism in order to give an account of the nature of mathematics and of mathematical knowledge that is compatible with what he takes to be the uncontroversial status of this science as true, certain and exact. I argue for this view against the view of Peter Hylton, according to which Russell uses logicism to (...)
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  6. Conor Mayo-Wilson (2011). Russell on Logicism and Coherence. Journal of Bertrand Russell Studies 31 (1).score: 24.0
    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 (...)
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  7. Timothy Bays (2000). The Fruits of Logicism. Notre Dame Journal of Formal Logic 41 (4):415-421.score: 24.0
    You’ll be pleased to know that I don’t intend to use these remarks to comment on all of the papers presented at this conference. I won’t try to show that one paper was right about this topic, that another was wrong was about that topic, or that several of our conference participants were talking past one another. Nor will I try to adjudicate any of the discussions which took place in between our sessions. Instead, I’ll use these remarks to make (...)
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  8. Anders Kraal (2013). The Aim of Russell's Early Logicism: A Reinterpretation. Synthese:1-18.score: 24.0
    I argue that three main interpretations of the aim of Russell’s early logicism in The Principles of Mathematics (1903) are mistaken, and propose a new interpretation. According to this new interpretation, the aim of Russell’s logicism is to show, in opposition to Kant, that mathematical propositions have a certain sort of complete generality which entails that their truth is independent of space and time. I argue that on this interpretation two often-heard objections to Russell’s logicism, deriving from (...)
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  9. Jaime Nubiola (1996). C. S. Peirce: Pragmatism and Logicism. Philosophia Scientiae 1 (2):109-119.score: 22.0
    This paper has two separate aims, with obvious links between them. First, to present Charles S. Peirce and the pragmatist movement in a historical framework which stresses the close connections of pragmatism with the mainstream of philosophy; second, to deal with a particular controversial issue, that of the supposed logicistic orientation of Peirce's work.
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  10. Alan Garnham (1993). Is Logicist Cognitive Science Possible? Mind and Language 8 (1):49-71.score: 21.0
  11. Tom Casier (1999). From Neo-Kantianism to Logicism: Vvedenskij's Mature Years. Studies in East European Thought 51 (1):1-33.score: 21.0
    In the first two decades of the century Vvedenskij developed and defended what he took to be an original argument in support of the impossibility of metaphysical knowledge. This argument, which he hailed as a "proof," involved an examination of the four laws of thought alone. As it made no appeal to the highly technical analyses found in Kant's first Critique, Vvedenskij considered it to be more efficient and thereby effective than Kant's own arguments. Although Vvedenskij's estimation of his accomplishment (...)
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  12. Ulrich Majer (2009). Husserl Between Frege's Logicism And Hilbert's Formalism. The Baltic International Yearbook of Cognition, Logic and Communication 4 (1):4.score: 21.0
  13. Thomas Nemeth (1999). From Neo-Kantianism to Logicism: Vvedenskij's Mature Years. Studies in East European Thought 51 (1):1 - 33.score: 21.0
    In the first two decades of the century Vvedenskij developed and defended what he took to be an original argument in support of the impossibility of metaphysical knowledge. This argument, which he hailed as a proof, involved an examination of the four laws of thought alone. As it made no appeal to the highly technical analyses found in Kant''s first Critique, Vvedenskij considered it to be more efficient and thereby effective than Kant''s own arguments. Although Vvedenskij''s estimation of his accomplishment (...)
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  14. John MacFarlane (2002). Frege, Kant, and the Logic in Logicism. Philosophical Review 111 (1):25-65.score: 18.0
    Let me start with a well-known story. Kant held that logic and conceptual analysis alone cannot account for our knowledge of arithmetic: “however we might turn and twist our concepts, we could never, by the mere analysis of them, and without the aid of intuition, discover what is the sum [7+5]” (KrV, B16). Frege took himself to have shown that Kant was wrong about this. According to Frege’s logicist thesis, every arithmetical concept can be defined in purely logical terms, and (...)
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  15. Fraser MacBride (2003). Speaking with Shadows: A Study of Neo-Logicism. British Journal for the Philosophy of Science 54 (1):103-163.score: 18.0
    According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and (...)
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  16. G. Landini (2011). Logicism and the Problem of Infinity: The Number of Numbers. Philosophia Mathematica 19 (2):167-212.score: 18.0
    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 (...)
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  17. Philip A. Ebert & Marcus Rossberg (2009). Ed Zalta's Version of Neo-Logicism: A Friendly Letter of Complaint. In Hannes Leitgeb & Alexander Hieke (eds.), Reduction – Abstraction – Analysis. Ontos. 11--305.score: 18.0
    In this short letter to Ed Zalta we raise a number of issues with regards to his version of Neo-Logicism. The letter is, in parts, based on a longer manuscript entitled “What Neo-Logicism could not be” which is in preparation. A response by Ed Zalta to our letter can be found on his website: http://mally.stanford.edu/publications.html (entry C3).
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  18. Stewart Shapiro & Alan Weir (2000). ‘Neo-Logicist‘ Logic is Not Epistemically Innocent. Philosophia Mathematica 8 (2):160--189.score: 18.0
    The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been (...)
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  19. Alexander Bird (1997). The Logic in Logicism. Dialogue 36 (02):341--60.score: 18.0
    Frege's logicism consists of two theses: (1) the truths of arithmetic are truths of logic; (2) the natural numbers are objects. In this paper I pose the question: what conception of logic is required to defend these theses? I hold that there exists an appropriate and natural conception of logic in virtue of which Hume's principle is a logical truth. Hume's principle, which states that the number of Fs is the number of Gs iff the concepts F and G (...)
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  20. Sébastien Gandon (2009). Toward a Topic-Specific Logicism? Russell's Theory of Geometry in the Principles of Mathematics. Philosophia Mathematica 17 (1):35-72.score: 18.0
    Russell's philosophy is rightly described as a programme of reduction of mathematics to logic. Now the theory of geometry developed in 1903 does not fit this picture well, since it is deeply rooted in the purely synthetic projective approach, which conflicts with all the endeavours to reduce geometry to analytical geometry. The first goal of this paper is to present an overview of this conception. The second aim is more far-reaching. The fact that such a theory of geometry was sustained (...)
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  21. William H. Hanson (1990). Second-Order Logic and Logicism. Mind 99 (393):91-99.score: 18.0
    Some widely accepted arguments in the philosophy of mathematics are fallacious because they rest on results that are provable only by using assumptions that the con- clusions of these arguments seek to undercut. These results take the form of bicon- ditionals linking statements of logic with statements of mathematics. George Boolos has given an argument of this kind in support of the claim that certain facts about second-order logic support logicism, the view that mathematics—or at least part of it—reduces (...)
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  22. Stewart Shapiro (2003). Prolegomenon to Any Future Neo-Logicist Set Theory: Abstraction and Indefinite Extensibility. British Journal for the Philosophy of Science 54 (1):59--91.score: 18.0
    The purpose of this paper is to assess the prospects for a neo-logicist development of set theory based on a restriction of Frege's Basic Law V, which we call (RV): PQ[Ext(P) = Ext(Q) [(BAD(P) & BAD(Q)) x(Px Qx)]] BAD is taken as a primitive property of properties. We explore the features it must have for (RV) to sanction the various strong axioms of Zermelo–Fraenkel set theory. The primary interpretation is where ‘BAD’ is Dummett's ‘indefinitely extensible’. 1 Background: what and why? (...)
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  23. Maria Carla Galavotti (2003). Harold Jeffreys' Probabilistic Epistemology: Between Logicism and Subjectivism. British Journal for the Philosophy of Science 54 (1):43-57.score: 18.0
    Harold Jeffreys' ideas on the interpretation of probability and epistemology are reviewed. It is argued that with regard to the interpretation of probability, Jeffreys embraces a version of logicism that shares some features of the subjectivism of Ramsey and de Finetti. Jeffreys also developed a probabilistic epistemology, characterized by a pragmatical and constructivist attitude towards notions such as ‘objectivity’, ‘reality’ and ‘causality’. 1 Introductory remarks 2 The interpretation of probability 3 Jeffreys' probabilistic epistemology.
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  24. Marcus Rossberg & Philip A. Ebert (2007). What is the Purpose of Neo-Logicism? Traveaux de Logique 18:33-61.score: 18.0
    This paper introduces and evaluates two contemporary approaches of neo-logicism. Our aim is to highlight the differences between these two neo-logicist programmes and clarify what each projects attempts to achieve. To this end, we first introduce the programme of the Scottish school – as defended by Bob Hale and Crispin Wright1 which we believe to be a..
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  25. Kevin C. Klement (2012). Neo-Logicism and Russell’s Logicism. Russell 32 (127):159.score: 18.0
    Most advocates of the so-called “neologicist” movement in the philosophy of mathematics identify themselves as “Neo-Fregeans” (e.g., Hale and Wright): presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature, and when it is, often dismissed as not really logicism at all (in lights of its assumption of axioms of infinity, reducibiity and so on). In this paper I have three aims: firstly, to identify more clearly (...)
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  26. Matthias Schirn (2014). Frege's Logicism and the Neo-Fregean Project. Axiomathes 24 (2):207-243.score: 18.0
    Neo-logicism is, not least in the light of Frege’s logicist programme, an important topic in the current philosophy of mathematics. In this essay, I critically discuss a number of issues that I consider to be relevant for both Frege’s logicism and neo-logicism. I begin with a brief introduction into Wright’s neo-Fregean project and mention the main objections that he faces. In Sect. 2, I discuss the Julius Caesar problem and its possible Fregean and neo-Fregean solution. In Sect. (...)
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  27. John Burgess, Logicism: A New Look.score: 18.0
    Adapated from talks at the UCLA Logic Center and the Pitt Philosophy of Science Series. Exposition of material from Fixing Frege, Chapter 2 (on predicative versions of Frege’s system) and from “Protocol Sentences for Lite Logicism” (on a form of mathematical instrumentalism), suggesting a connection. Provisional version: references remain to be added. To appear in Mathematics, Modality, and Models: Selected Philosophical Papers, coming from Cambridge University Press.
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  28. Roy T. Cook (2002). The State of the Economy: Neo-Logicism and Inflationt. Philosophia Mathematica 10 (1):43-66.score: 18.0
    In this paper I examine the prospects for a successful neo–logicist reconstruction of the real numbers, focusing on Bob Hale's use of a cut-abstraction principle. There is a serious problem plaguing Hale's project. Natural generalizations of this principle imply that there are far more objects than one would expect from a position that stresses its epistemological conservativeness. In other words, the sort of abstraction needed to obtain a theory of the reals is rampantly inflationary. I also indicate briefly why this (...)
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  29. Sébastien Gandon (2008). Which Arithmetization for Which Logicism? Russell on Relations and Quantities in The Principles of Mathematics. History and Philosophy of Logic 29 (1):1-30.score: 18.0
    This article aims first at showing that Russell's general doctrine according to which all mathematics is deducible 'by logical principles from logical principles' does not require a preliminary reduction of all mathematics to arithmetic. In the Principles, mechanics (part VII), geometry (part VI), analysis (part IV-V) and magnitude theory (part III) are to be all directly derived from the theory of relations, without being first reduced to arithmetic (part II). The epistemological importance of this point cannot be overestimated: Russell's (...) does not only contain the claim that mathematics is no more than logic, it also contains the claim that the differences between the various mathematical sciences can be logically justified?and thus, that, contrary to the arithmetization stance, analysis, geometry and mechanics are not merely outgrowths of arithmetic. The second aim of this article is to set out the neglected Russellian theory of quantity. The topic is obviously linked with the first, since the mere existence of a doctrine of magnitude, in a work dated from 1903, is a sign of a distrust vis-à-vis the arithmetization programme. After having shown that, despite the works of Cantor, Dedekind and Weierstrass, many mathematicians at the end of the 19th Century elaborated various axiomatic theories of the magnitude, I will try to define the peculiarity of the Russellian approach. I will lay stress on the continuity of the logicist's thought on this point: Whitehead, in the Principia, deepens and generalizes the first Russellian 1903 theory. (shrink)
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  30. Francesca Boccuni (2013). Plural Logicism. Erkenntnis 78 (5):1051-1067.score: 18.0
    PG (Plural Grundgesetze) is a consistent second-order system which is aimed to derive second-order Peano arithmetic. It employs the notion of plural quantification and a few Fregean devices, among which the infamous Basic Law V. George Boolos’ plural semantics is replaced with Enrico Martino’s Acts of Choice Semantics (ACS), which is developed from the notion of arbitrary reference in mathematical reasoning. Also, substitutional quantification is exploited to interpret quantification into predicate position. ACS provides a form of logicism which is (...)
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  31. Richard Jeffrey (2002). Logicism Lite. Philosophy of Science 69 (3):474-496.score: 18.0
    Logicism Lite counts number‐theoretical laws as logical for the same sort of reason for which physical laws are counted as as empirical: because of the character of the data they are responsible to. In the case of number theory these are the data verifying or falsifying the simplest equations, which Logicism Lite counts as true or false depending on the logical validity or invalidity of first‐order argument forms in which no numbertheoretical notation appears.
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  32. Neil Tennant (2014). Logic, Mathematics, and the A Priori, Part II: Core Logic as Analytic, and as the Basis for Natural Logicism. Philosophia Mathematica:nku009.score: 18.0
    We examine the sense in which logic is a priori, and explain how mathematical theories can be dichotomized non-trivially into analytic and synthetic portions. We argue that Core Logic contains exactly the a-priori-because-analytically-valid deductive principles. We introduce the reader to Core Logic by explaining its relationship to other logical systems, and stating its rules of inference. Important metatheorems about Core Logic are reported, and its important features noted. Core Logic can serve as the basis for a foundational program that could (...)
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  33. Matthias Schirn (2014). Erratum To: Frege's Logicism and the Neo-Fregean Project. Axiomathes 24 (2):245-245.score: 18.0
    Erratum to: Axiomathes DOI 10.1007/s10516-013-9222-7In the online publication, page 13, line 27, after the sentence “Hence, neo-logicism is doomed to failure.”, the following two sentences were missing:This argument was developed by Robert Trueman in a draft of his paper ‘Sham Names andion’. A revised version of this paper is forthcoming in Philosophia Mathematica under the tile ‘A Dilemma for Neo-Fregeanism’.
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  34. Neil Tennant, Natural Logicism Via the Logic of Orderly Pairing.score: 18.0
    The aim here is to describe how to complete the constructive logicist program, in the author’s book Anti-Realism and Logic, of deriving all the Peano-Dedekind postulates for arithmetic within a theory of natural numbers that also accounts for their applicability in counting finite collections of objects. The axioms still to be derived are those for addition and multiplication. Frege did not derive them in a fully explicit, conceptually illuminating way. Nor has any neo-Fregean done so.
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  35. I. Grattan-Guinness (1984). Notes on the Fate of Logicism Fromprincipia Mathematicato Gödel's Incompletability Theorem. History and Philosophy of Logic 5 (1):67-78.score: 18.0
    An outline is given of the development of logicism from the publication of the first edition of Whitehead and Russell's Principia mathematica (1910-1913) through the contributions of Wittgenstein, Ramsey and Chwistek to Russell's own modifications made for the second edition of the work (1925) and the adoption of many of its logical techniques by the Vienna Circle. A tendency towards extensionalism is emphasised.
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  36. Erich H. Reck (2013). Frege, Dedekind, and the Origins of Logicism. History and Philosophy of Logic 34 (3):242-265.score: 18.0
    This paper has a two-fold objective: to provide a balanced, multi-faceted account of the origins of logicism; to rehabilitate Richard Dedekind as a main logicist. Logicism should be seen as more deeply rooted in the development of modern mathematics than typically assumed, and this becomes evident by reconsidering Dedekind's writings in relation to Frege's. Especially in its Dedekindian and Fregean versions, logicism constitutes the culmination of the rise of ?pure mathematics? in the nineteenth century; and this rise (...)
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  37. José Ferreiros (1997). Notes on Types, Sets, and Logicism, 1930-1950. Theoria 12 (1):91-124.score: 18.0
    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 (...)
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  38. Francisco Rodríguez Consuegra (1987). Russell's Logicist Definitions of Numbers, 1898–1913: Chronology and Significance. History and Philosophy of Logic 8 (2):141-169.score: 18.0
    According to the received view, Russell rediscovered about 1900 the logical definition of cardinal number given by Frege in 1884. In the same way, we are told, he stated and developed independently the idea of logicism, using the principle of abstraction as the philosophical ground. Furthermore, the role commonly ascribed in this to Peano was only to invent an appropriate notation to be used as mere instrument. In this paper I hold that the study of Russell's unpublished manuscripts and (...)
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  39. G. S. Axtell (1990). Logicism, Pragmatism, and Metascience: Towards a Pancritical Pragmatic Theory of Meta-Level Discourse. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:39 - 49.score: 18.0
    The faults of logical empiricist accounts of metascientific discourse are examined through a study of the modifications Carnap makes to his version of the program over four decades. As empiricists acquiesced on the distinction between theory and observation, Carnap attempted to retain and insulate an equally suspect sharp distinction between the theoretic and the pragmatic. Carnap's later philosophy was understood as a modification of the program in the direction of pragmatism. But neither the key notion of "external questions" nor an (...)
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  40. Georg Schiemer (2014). Logicism and Ramsification. Metascience 23 (2):255-261.score: 18.0
    This excellent book presents a collection of eleven articles, all but one of which were written by William Demopoulos over the period of the last 19 years. The book comprises eight published articles, some of which have appeared only recently, as well as three new articles. The thematic scope of the topics investigated here is broad and ranges from Frege’s original logicist program outlined in his Grundlagen der Arithmetik (Frege 1884) to Carnap’s mature work on the logical reconstruction of scientific (...)
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  41. Arthur Sullivan (ed.) (2003). Logicism and the Philosophy of Language: Selections From Frege and Russell. Broadview Press.score: 18.0
    Logicism and the Philosophy of Language brings together the core works by Gottlob Frege and Bertrand Russell on logic and language. In their separate efforts to clarify mathematics through the use of logic in the late nineteenth and early twentieth century, Frege and Russell both recognized the need for rigorous and systematic semantic analysis of language. It was their turn to this style of analysis that would establish the philosophy of language as an autonomous area of inquiry. This anthology (...)
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  42. Peter M. Simons (1985). Multicategorial Ontology and Logicism. Conceptus 19:87-99.score: 18.0
    This paper discusses the philosophical background to the paper by lejewski in this issue. lejewski offers an ontologically neutral logic for the first two types (individuals and classes thereof). some peculiarities of the logic used are noted, in particular the distinction between empty individual terms, empty class terms, and non-empty class terms designating the empty class. lejewski ends by denying the truth of the formula meaning "there are classes," but we argue that the way in which truth-conditions for formulae containing (...)
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  43. Harold T. Hodes (1984). Logicism and the Ontological Commitments of Arithmetic. Journal of Philosophy 81 (3):123-149.score: 15.0
  44. Paul Benacerraf (1981). Frege: The Last Logicist. Midwest Studies in Philosophy 6 (1):17-36.score: 15.0
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  45. Sten Lindström, Erik Palmgren, Krister Segerberg & Viggo Stoltenberg-Hansen (eds.) (2009). Logicism, Intuitionism, and Formalism - What has Become of Them? Springer.score: 15.0
    These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics.A special section is concerned with constructive ...
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  46. Alberto Coffa (1982). Kant, Bolzano, and the Emergence of Logicism. Journal of Philosophy 79 (11):679-689.score: 15.0
  47. Warren D. Goldfarb (1982). Logicism and Logical Truth. Journal of Philosophy 79 (11):692-695.score: 15.0
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  48. Geoffrey Hellman (1981). How to Godel a Frege-Russell: Godel's Incompleteness Theorems and Logicism. Noûs 15 (4):451-468.score: 15.0
  49. Gianluigi Oliveri (2009). Stefano Donati. I Fondamenti Della Matematica Nel Logicismo di Bertrand Russell [the Foundations of Mathematics in the Logicism of Bertrand Russell]. Philosophia Mathematica 17 (1):109-113.score: 15.0
  50. Neil Tennant, Inferentialism, Logicism, Harmony, and a Counterpoint.score: 15.0
    Inferentialism is explained as an attempt to provide an account of meaning that is more sensitive (than the tradition of truth-conditional theorizing deriving from Tarski and Davidson) to what is learned when one masters meanings.
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