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  1. Wittgenstein and the Cognitive Science of Religion: Interpreting Human Nature and the Mind.Robert Vinten (ed.) - 2023 - London: Bloomsbury Academic.
    Advancing our understanding of one of the most influential 20th-century philosophers, Robert Vinten brings together an international line up of scholars to consider the relevance of Ludwig Wittgenstein's ideas to the cognitive science of religion. Wittgenstein's claims ranged from the rejection of the idea that psychology is a 'young science' in comparison to physics to challenges to scientistic and intellectualist accounts of religion in the work of past anthropologists. Chapters explore whether these remarks about psychology and religion undermine the frameworks (...)
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  • Logical Mistakes, Logical Aliens, and the Laws of Kant’s Pure General Logic.Tyke Nunez - 2018 - Mind 128 (512):1149-1180.
    There are two ways interpreters have tended to understand the nature of the laws of Kant’s pure general logic. On the first, these laws are unconditional norms for how we ought to think, and will govern anything that counts as thinking. On the second, these laws are formal criteria for being a thought, and violating them makes a putative thought not a thought. These traditions are in tension, in so far as the first depends on the possibility of thoughts that (...)
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  • Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.
    This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term (...)
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  • Russell, Meinong and the Origin of the Theory of Descriptions.Harm Boukema - 2007 - Russell: The Journal of Bertrand Russell Studies 27 (1):41-72.
    According to his own account, Russell was “led to” the Theory of Descriptions by “the desire to avoid Meinong’s unduly populous realm of being”. This “official view” has been subjected to severe criticism. However stimulating this criticism may be, it is too extreme and therefore not critical enough. It fails to fully acknowledge both the way it is itself opposed to Russell and the way Russell and Meinong were opposed to _their_ opponents. In order to avoid these failures, a more (...)
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  • Platitudes in mathematics.Thomas Donaldson - 2015 - Synthese 192 (6):1799-1820.
    The term ‘continuous’ in real analysis wasn’t given an adequate formal definition until 1817. However, important theorems about continuity were proven long before that. How was this possible? In this paper, I introduce and refine a proposed answer to this question, derived from the work of Frank Jackson, David Lewis and other proponents of the ‘Canberra plan’. In brief, the proposal is that before 1817 the meaning of the term ‘continuous’ was determined by a number of ‘platitudes’ which had some (...)
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  • A new perspective on the problem of applying mathematics.Christopher Pincock - 2004 - Philosophia Mathematica 12 (2):135-161.
    This paper sets out a new framework for discussing a long-standing problem in the philosophy of mathematics, namely the connection between the physical world and a mathematical domain when the mathematics is applied in science. I argue that considering counterfactual situations raises some interesting challenges for some approaches to applications, and consider an approach that avoids these challenges.
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  • The concept of “character” in Dirichlet’s theorem on primes in an arithmetic progression.Jeremy Avigad & Rebecca Morris - 2014 - Archive for History of Exact Sciences 68 (3):265-326.
    In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses ofDirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method.
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  • Frege on Sense Identity, Basic Law V, and Analysis.Philip A. Ebert - 2016 - Philosophia Mathematica 24 (1):9-29.
    The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...)
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  • Frege on Truth, Assertoric Force and the Essence of Logic.Dirk Greimann - 2014 - History and Philosophy of Logic 35 (3):272-288.
    In a posthumous text written in 1915, Frege makes some puzzling remarks about the essence of logic, arguing that the essence of logic is indicated, properly speaking, not by the word ‘true’, but by the assertoric force. William Taschek has recently shown that these remarks, which have received only little attention, are very important for understanding Frege's conception of logic. On Taschek's reconstruction, Frege characterizes logic in terms of assertoric force in order to stress the normative role that the logical (...)
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  • Moral and Semantic Innocence.Christopher Hom & Robert May - 2013 - Analytic Philosophy 54 (3):293-313.
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  • From Russell's Paradox to the Theory of Judgement: Wittgenstein and Russell on the Unity of the Proposition.Graham Stevens - 2004 - Theoria 70 (1):28-61.
    It is fairly well known that Wittgenstein's criticisms of Russell's multiple‐relation theory of judgement had a devastating effect on the latter's philosophical enterprise. The exact nature of those criticisms however, and the explanation for the severity of their consequences, has been a source of confusion and disagreement amongst both Russell and Wittgenstein scholars. In this paper, I offer an interpretation of those criticisms which shows them to be consonant with Wittgenstein's general critique of Russell's conception of logic and which serves (...)
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  • II. Frege as Idealist and then Realist.Michael D. Resnik - 1979 - Inquiry: An Interdisciplinary Journal of Philosophy 22 (1-4):350-357.
    Michael Dummett argued that Frege was a realist while Hans Sluga countered that he was an objective idealist in the rationalist tradition of Kant and Lotze. Sluga ties Frege's idealism to the context principle which he argues Frege never gave up. It is argued that Sluga has correctly interpreted the pre?1891 Frege while Dummett is correct concerning the later period. It is also claimed that the context principle was dropped prior to 1891 to be replaced by the doctrine of unsaturated (...)
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  • A general theory of abstraction operators.Neil Tennant - 2004 - Philosophical Quarterly 54 (214):105-133.
    I present a general theory of abstraction operators which treats them as variable-binding term- forming operators, and provides a reasonably uniform treatment for definite descriptions, set abstracts, natural number abstraction, and real number abstraction. This minimizing, extensional and relational theory reveals a striking similarity between definite descriptions and set abstracts, and provides a clear rationale for the claim that there is a logic of sets (which is ontologically non- committal). The theory also treats both natural and real numbers as answering (...)
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  • A Cantorian argument against Frege's and early Russell's theories of descriptions.Kevin C. Klement - 2008 - In Nicholas Griffin & Dale Jacquette (eds.), Russell Vs. Meinong: The Legacy of "on Denoting". London and New York: Routledge. pp. 65-77.
    It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his rejection (...)
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  • On the consistency of the Δ11-CA fragment of Frege's grundgesetze.Fernando Ferreira & Kai F. Wehmeier - 2002 - Journal of Philosophical Logic 31 (4):301-311.
    It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing Δ₁¹-comprehension (...)
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  • We hold these truths to be self-evident: But what do we mean by that?: We hold these truths to be self-evident.Stewart Shapiro - 2009 - Review of Symbolic Logic 2 (1):175-207.
    At the beginning of Die Grundlagen der Arithmetik [1884], Frege observes that “it is in the nature of mathematics to prefer proof, where proof is possible”. This, of course, is true, but thinkers differ on why it is that mathematicians prefer proof. And what of propositions for which no proof is possible? What of axioms? This talk explores various notions of self-evidence, and the role they play in various foundational systems, notably those of Frege and Zermelo. I argue that both (...)
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  • Persuading the Tortoise.Diego Marconi - 2015 - Philosophical Investigations 39 (2):123-137.
    In On Certainty, Wittgenstein addressed the issue of beliefs that are not to be argued for, either because any grounds we could produce are less certain than the belief they are supposed to ground, or because our interlocutors would not accept our reasons. However, he did not address the closely related issue of justifying a conclusion to interlocutors who do not see that it follows from premises they accept. In fact, Wittgenstein had discussed the issue in the Remarks on the (...)
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  • Models, Models, and Models.Gregory Wheeler - 2013 - Metaphilosophy 44 (3):293-300.
    Michael Dummett famously maintained that analytic philosophy was simply philosophy that followed Frege in treating the philosophy of language as the basis for all other philosophy (1978, 441). But one important insight to emerge from computer science is how difficult it is to animate the linguistic artifacts that the analysis of thought produces. Yet, modeling the effects of thought requires a new skill that goes beyond analysis: procedural literacy. Some of the most promising research in philosophy makes use of a (...)
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  • Introduction to Foundations of Logic & Mathematics, Special Issue.Fraser MacBride - 2004 - Philosophical Quarterly 54 (214):1 - 15.
    Frege attempted to provide arithmetic with a foundation in logic. But his attempt to do so was confounded by Russell's discovery of paradox at the heart of Frege's system. The papers collected in this special issue contribute to the on-going investigation into the foundations of mathematics and logic. After sketching the historical background, this introduction provides an overview of the papers collected here, tracing some of the themes that connect them.
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  • Hilbert, logicism, and mathematical existence.José Ferreirós - 2009 - Synthese 170 (1):33 - 70.
    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 new (...)
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  • Frege on the psychological significance of definitions.John F. Horty - 1993 - Philosophical Studies 72 (2-3):223 - 263.
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  • A Typology of Conceptual Explications.Dirk Greimann - 2012 - Disputatio 4 (34):645-670.
    Greimann-Dirk_A-typology-of-conceptual-explications.
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  • Sense, Reference and Hybridity.Wolfgang Künne - 2010 - Dialectica 64 (4):529-551.
    In his paper on ‘Frege's Theory of Sense and Reference’ Saul Kripke remarks: “Like the present account, Künne stresses that for Frege times, persons, etc. can be part of the expression of the thought. However, his reading is certainly not mine in significant respects . . .”. On both counts, he is right. As regards the differences between our readings, in some respects I shall confess to having made a mistake, in several others I shall remain stubbornly unmoved. Thus I (...)
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  • Mathematical aspects of the periodic law.Guillermo Restrepo & Leonardo Pachón - 2006 - Foundations of Chemistry 9 (2):189-214.
    We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the periodic system includes number theory, information theory, order theory, set theory and topology. Each theory used shows that it is possible to provide the Periodic Law with a mathematical structure. We also show that it is possible to study the (...)
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  • Wahrheit und selbstrückbezüglichkeit.Jesus Padilla-Galvez - 1991 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 22 (1):111-132.
    Summary This paper is intended to discuss the problems occurring in the relation between the notion of truth and the question of self-reference. To do this, we shall review Tarski's (T) convention and its related terminology. We shall clarify the relation between truth and extension in order to lead into the question of semantic paradoxes appearing in the theoretical models concerned with truth. Subsequently, we shall review the logical system which develops in the reformulation of the modal proposal of the (...)
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  • Success by default?Augustín Rayo - 2003 - Philosophia Mathematica 11 (3):305-322.
    I argue that Neo-Fregean accounts of arithmetical language and arithmetical knowledge tacitly rely on a thesis I call [Success by Default]—the thesis that, in the absence of reasons to the contrary, we are justified in thinking that certain stipulations are successful. Since Neo-Fregeans have yet to supply an adequate defense of [Success by Default], I conclude that there is an important gap in Neo-Fregean accounts of arithmetical language and knowledge. I end the paper by offering a naturalistic remedy.
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  • Wittgenstein, formalism, and symbolic mathematics.Anderson Luis Nakano - 2020 - Kriterion: Journal of Philosophy 61 (145):31-53.
    ABSTRACT In a recent essay, Sören Stenlund tries to align Wittgenstein’s approach to the foundations and nature of mathematics with the tradition of symbolic mathematics. The characterization of symbolic mathematics made by Stenlund, according to which mathematics is logically separated from its external applications, brings it closer to the formalist position. This raises naturally the question whether Wittgenstein holds a formalist position in philosophy of mathematics. The aim of this paper is to give a negative answer to this question, defending (...)
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  • Cocchiarella’s Formal Ontology and the Paradoxes of Hyperintensionality.Gregory Landini - 2009 - Axiomathes 19 (2):115-142.
    This is a critical discussion of Nino B. Cocchiarella’s book “Formal Ontology and Conceptual Realism.” It focuses on paradoxes of hyperintensionality that may arise in formal systems of intensional logic.
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  • Wittgenstein et le logicisme de Russell : Remarques critiques sur « A Mathematical Proof Must be Surveyable » de F. Mühlhölzer.Sébastien Gandon - 2012 - Philosophiques 39 (1):163-187.
    Ce texte discute certaines conclusions d’un article récent de F. Mülhölzer et vise à montrer que le logicisme russellien a les moyens de résister à la critique que Wittgenstein lui adresse dans la partie III des Remarques sur les fondements desmathématiques.This paper discusses some conclusions of a recent article from F.Mülhölzer. It aims at showing that Russell’s logicism has the means to overcome the criticisms Wittgenstein expounded in Remarks on the Foundations of Mathematics, part III.
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  • Frege’s Logicism and the Neo-Fregean Project.Matthias Schirn - 2014 - Axiomathes 24 (2):207-243.
    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. 3, I raise (...)
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  • 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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  • Peano as logician.Wlllard Van Orman Quine - 1987 - History and Philosophy of Logic 8 (1):15-24.
    Peano's contributions to logic are surveyed under several headings. His use of class abstraction is considered first, together with his recognition of the distinction between membership and inclusion. Then his strategy of notational inversion is appraised. Finally, class abstraction is considered again, from ontological points of view; and Peano's achievements are compared with Frege's.
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  • Logicism as Making Arithmetic Explicit.Vojtěch Kolman - 2015 - Erkenntnis 80 (3):487-503.
    This paper aims to shed light on the broader significance of Frege’s logicism against the background of discussing and comparing Wittgenstein’s ‘showing/saying’-distinction with Brandom’s idiom of logic as the enterprise of making the implicit rules of our linguistic practices explicit. The main thesis of this paper is that the problem of Frege’s logicism lies deeper than in its inconsistency : it lies in the basic idea that in arithmetic one can, and should, express everything that is implicitly presupposed so that (...)
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  • Desperately seeking ψ.Charles Travis - 2011 - Philosophical Issues 21 (1):505-557.
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  • Frege Meets Aristotle: Points as Abstracts.Stewart Shapiro & Geoffrey Hellman - 2015 - Philosophia Mathematica:nkv021.
    There are a number of regions-based accounts of space/time, due to Whitehead, Roeper, Menger, Tarski, the present authors, and others. They all follow the Aristotelian theme that continua are not composed of points: each region has a proper part. The purpose of this note is to show how to recapture ‘points’ in such frameworks via Scottish neo-logicist abstraction principles. The results recapitulate some Aristotelian themes. A second agenda is to provide a new arena to help decide what is at stake (...)
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  • Metaphors for Mathematics from Pasch to Hilbert.Dirk Schlimm - 2016 - Philosophia Mathematica 24 (3):308-329.
    How mathematicians conceive of the nature of mathematics is reflected in the metaphors they use to talk about it. In this paper I investigate a change in the use of metaphors in the late nineteenth and early twentieth centuries. In particular, I argue that the metaphor of mathematics as a tree was used systematically by Pasch and some of his contemporaries, while that of mathematics as a building was deliberately chosen by Hilbert to reflect a different view of mathematics. By (...)
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  • Our knowledge of numbers as self-subsistent objects.William Demopoulos - 2005 - Dialectica 59 (2):141–159.
    A feature of Frege's philosophy of arithmetic that has elicited a great deal of attention in the recent secondary literature is his contention that numbers are ‘self‐subsistent’ objects. The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to Kreisel's folk‐lore observation that the central problem in the philosophy of mathematics is not the existence of mathematical objects, but the objectivity of mathematics. Although Frege was undoubtedly concerned with both questions, a goal of (...)
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  • The Issue of Linguistic Ambiguities in Wittgenstein’s Second Philosophy and in Schachter’s Critical Grammar.Krzysztof Rotter - 2004 - Studia Semiotyczne—English Supplement 25:176-209.
    By a seemingly strange twist of fate, the formalist approach to language became popular after Hilbert’s project of providing a formalist foundation for mathematics foundered on G¨odel’s famous incompleteness theorems. Even in September 1930, during the congress in K¨onigsberg, where G¨odel presented his results for the first time, Carnap still defended logicism against the intuitionist and formalist views on the foundations of mathematics. Furthermore in linguistics, the formalist approach to syntactic issues had only become disseminated in the 1930s, due to (...)
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