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Introduction to Mathematical Philosophy

London, England: Dover Publications (1919)

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  1. The Nature of Appearance in Kant’s Transcendentalism: A Seman- Tico-Cognitive Analysis.Sergey L. Katrechko - 2018 - Kantian Journal 37 (3):41-55.
  • The Role of Affect in Language Development.Stuart G. Shanker & Stanley I. Greenspan - 2010 - Theoria : An International Journal for Theory, History and Fundations of Science 20 (3):329-343.
    This paper presents the Functional/Emotional approach to language development, which explains the process leading up to the core capacities necessary for language; shows how this process leads to the formation of internal symbols; and how it shapes and is shaped by the child’s development of language.
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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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  • Metaphysical and Absolute Possibility.Justin Clarke-Doane - 2019 - Synthese 198 (Suppl 8):1861-1872.
    It is widely alleged that metaphysical possibility is “absolute” possibility Conceivability and possibility, Clarendon, Oxford, 2002, p 16; Stalnaker, in: Stalnaker Ways a world might be: metaphysical and anti-metaphysical essays, Oxford University Press, Oxford, 2003, pp 201–215; Williamson in Can J Philos 46:453–492, 2016). Kripke calls metaphysical necessity “necessity in the highest degree”. Van Inwagen claims that if P is metaphysically possible, then it is possible “tout court. Possible simpliciter. Possible period…. possib without qualification.” And Stalnaker writes, “we can agree (...)
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  • The Identity of the Categorical and the Dispositional.Galen Strawson - 2008 - Analysis 68 (4):271-282.
    Suppose that X and Y can’t possibly exist apart in reality; then—by definition—there’s no real distinction between them, only a conceptual distinction. There’s a conceptual distinction between a rectilinear figure’s triangularity and its trilaterality, for example, but no real distinction. In fundamental metaphysics there is no real distinction between an object’s categorical properties and its dispositional properties. So too there is no real distinction between an object and its properties. And in fundamental metaphysics, for X and Y to be such (...)
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  • Scientific Philosophy and the Critique of Metaphysics from Russell to Carnap to Quine.Sean Morris - 2020 - Erkenntnis 85 (4):773-799.
    In his “Wissenschaftslogik: The Role of Logic in the Philosophy of Science,” Michael Friedman argues that Carnap’s philosophy of science “is fundamentally anti-metaphysical—he aims to use the tools of mathematical logic to dissolve rather [than] solve traditional philosophical problems—and it is precisely this point that is missed by his logically-minded contemporaries such as Hempel and Quine”. In this paper, I take issue with this claim, arguing that Quine, too, is a part of this anti-metaphysical tradition. I begin in section I (...)
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  • The Child's Trigger Experience: Degree-0 Learnability.David Lightfoot - 1989 - Behavioral and Brain Sciences 12 (2):321-334.
    According to a “selective” model of human language capacity, people come to know more than they experience. The discrepancy between experience and eventual capacity is bridged by genetically provided information. Hence any hypothesis about the linguistic genotype has consequences for what experience is needed and what form people's mature capacities will take. This BBS target article discusses the “trigger experience,” that is, the experience that actually affects a child's linguistic development. It is argued that this must be a subset of (...)
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  • Ontological Commitment and Quantifiers.T. Parent - forthcoming - In Ricki Bliss & James Miller (eds.), The Routledge Handbook of Metametaphysics. New York: Routledge.
    This is a slightly opinionated review of three main factions in metaontology: Quineans, Carnapians, and Meinongians. Emphasis is given to the last camp, as the metaontological aspect of Meinongianism has been underappreciated. The final section then offers some general remarks about the legitimacy of ontology, touching on ideas I have developed in other publications.
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  • Ontology and Arbitrariness.David Builes - forthcoming - Australasian Journal of Philosophy.
    In many different ontological debates, anti-arbitrariness considerations push one towards two opposing extremes. For example, in debates about mereology, one may be pushed towards a maximal ontology (mereological universalism) or a minimal ontology (mereological nihilism), because any intermediate view seems objectionably arbitrary. However, it is usually thought that anti-arbitrariness considerations on their own cannot decide between these maximal or minimal views. I will argue that this is a mistake. Anti-arbitrariness arguments may be used to motivate a certain popular thesis in (...)
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  • CRITIQUE OF IMPURE REASON: Horizons of Possibility and Meaning.Steven James Bartlett - 2021 - Salem, USA: Studies in Theory and Behavior.
    PLEASE NOTE: This is the corrected 2nd eBook edition, 2021. ●●●●● _Critique of Impure Reason_ has now also been published in a printed edition. To reduce the otherwise high price of this scholarly, technical book of nearly 900 pages and make it more widely available beyond university libraries to individual readers, the non-profit publisher and the author have agreed to issue the printed edition at cost. ●●●●● The printed edition was released on September 1, 2021 and is now available through (...)
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  • Математизирането на историята: число и битие.Vasil Penchev - 2013 - Sofia: BAS: ISSk (IPR).
    The book is a philosophical refection on the possibility of mathematical history. Are poosible models of historical phenomena so exact as those of physical ones? Mathematical models borrowed from quantum mechanics by the meditation of its interpretations are accomodated to history. The conjecture of many-variant history, alternative history, or counterfactual history is necessary for mathematical history. Conclusions about philosophy of history are inferred.
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  • Enciclopédia de Termos Lógico-Filosóficos.João Branquinho, Desidério Murcho & Nelson Gonçalves Gomes (eds.) - 2006 - São Paulo, SP, Brasil: Martins Fontes.
    Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...)
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  • Ortega y Gasset on Georg Cantor’s Theory of Transfinite Numbers.Lior Rabi - 2016 - Kairos (15):46-70.
    Ortega y Gasset is known for his philosophy of life and his effort to propose an alternative to both realism and idealism. The goal of this article is to focus on an unfamiliar aspect of his thought. The focus will be given to Ortega’s interpretation of the advancements in modern mathematics in general and Cantor’s theory of transfinite numbers in particular. The main argument is that Ortega acknowledged the historical importance of the Cantor’s Set Theory, analyzed it and articulated a (...)
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  • The Eightfold Way: Why Analyticity, Apriority and Necessity Are Independent.Douglas Ian Campbell - 2017 - Philosophers' Imprint 17:1-17.
    This paper concerns the three great modal dichotomies: (i) the necessary/contingent dichotomy; (ii) the a priori/empirical dichotomy; and (iii) the analytic/synthetic dichotomy. These can be combined to produce a tri-dichotomy of eight modal categories. The question as to which of the eight categories house statements and which do not is a pivotal battleground in the history of analytic philosophy, with key protagonists including Descartes, Hume, Kant, Kripke, Putnam and Kaplan. All parties to the debate have accepted that some categories are (...)
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  • An Account of Conscious Experience.Anil Gupta - 2012 - Analytic Philosophy 53 (1):1-29.
  • Russell and the Universalist Conception of Logic.Ian Proops - 2007 - Noûs 41 (1):1–32.
    The paper critically scrutinizes the widespread idea that Russell subscribes to a "Universalist Conception of Logic." Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results of this investigation are, for the most part, unfavorable to the Universalist interpretation.
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  • Negative existentials as corrections: a partial solution to the problem of negative existentials in segmented discourse representation theory.Lenny Clapp - 2021 - Linguistics and Philosophy 44 (6):1281-1315.
    Paradigmatic uses of negative existentials such as ‘Vulcan does not exist’ are problematic because they present the interpreter with a pragmatic paradox: a speaker who uses such a sentence seems to be asserting something that is incompatible with what she presupposes. An adequate solution must therefore explain why we interpret paradigmatic uses of negative existentials as saying something true, even though such uses present us with a pragmatic paradox. I provide such an explanation by analyzing paradigmatic uses of negative existentials (...)
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  • Analytic Philosophy.Trevor Hussey M. A. DPhil - 2002 - Nursing Philosophy 3 (1):66–69.
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  • Minds, Machines and Self-Reference.Peter Slezak - 1984 - Dialectica 38 (1):17-34.
    SummaryJ.R. Lucas has argued that it follows from Godel's Theorem that the mind cannot be a machine or represented by any formal system. Although this notorious argument against the mechanism thesis has received considerable attention in the literature, it has not been decisively rebutted, even though mechanism is generally thought to be the only plausible view of the mind. In this paper I offer an analysis of Lucas's argument which shows that it derives its persuasiveness from a subtle confusion. In (...)
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  • Bootstrapping the Mind: Analogical Processes and Symbol Systems.Dedre Gentner - 2010 - Cognitive Science 34 (5):752-775.
    Human cognition is striking in its brilliance and its adaptability. How do we get that way? How do we move from the nearly helpless state of infants to the cognitive proficiency that characterizes adults? In this paper I argue, first, that analogical ability is the key factor in our prodigious capacity, and, second, that possession of a symbol system is crucial to the full expression of analogical ability.
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  • Accommodating the Informal Notion of Class Within the Framework of Lesaniewski's Ontology.Czestaw Lejewski - 1985 - Dialectica 39 (3):217-241.
    SummaryInterpreted distributively the sentence‘Indiana is a member of the class of American federal states’means the same as‘Indiana is an American federal state’. In accordance with the collective sense of class expressions the sentence can be understood as implying that Indiana is a part of the country whose capital city is Washington. Neither interpretation appears to accommodate all the intuitions connected with the informal notion of class. A closer accommodation can be achieved, it seems, if class expressions are interpreted as verb‐like (...)
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  • Russell on Incomplete Symbols.Bryan Pickel - 2013 - Philosophy Compass 8 (10):909-923.
    Russell's notion of an incomplete symbol has become a standard against which philosophers compare their views on the relationship between language and the world. But Russell's exact characterization of incomplete symbols and the role they play in his philosophy are still disputed. In this paper, I trace the development of the notion of an incomplete symbol in Russell's philosophy. I suggest – against Kaplan, Evans, and others – that Russell's many characterizations of the notion of an incomplete symbol are compatible. (...)
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  • Replies to Bricker, Divers, and Sullivan.Timothy Williamson - 2014 - Philosophy and Phenomenological Research 88 (3):744-764.
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  • A Descriptivist Refutation of Kripke's Modal Argument and of Soames's Defence.Chen Bo - 2012 - Theoria 78 (3):225-260.
    This article systematically challenges Kripke's modal argument and Soames's defence of this argument by arguing that, just like descriptions, names can take narrow or wide scopes over modalities, and that there is a big difference between the wide scope reading and the narrow scope reading of a modal sentence with a name. Its final conclusions are that all of Kripke's and Soames's arguments are untenable due to some fallacies or mistakes; names are not “rigid designators”; if there were rigid designators, (...)
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  • Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different.Allen P. Hazen & Francis Jeffry Pelletier - 2014 - Studia Logica 102 (6):1103-1142.
    Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...)
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  • Bolzano and Kant on the Nature of Logic.Clinton Tolley - 2012 - History and Philosophy of Logic 33 (4):307-327.
    Here I revisit Bolzano's criticisms of Kant on the nature of logic. I argue that while Bolzano is correct in taking Kant to conceive of the traditional logic as a science of the activity of thinking rather than the content of thought, he is wrong to charge Kant with a failure to identify and examine this content itself within logic as such. This neglects Kant's own insistence that traditional logic does not exhaust logic as such, since it must be supplemented (...)
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  • A New–Old Characterisation of Logical Knowledge.Ivor Grattan-Guinness - 2012 - History and Philosophy of Logic 33 (3):245 - 290.
    We seek means of distinguishing logical knowledge from other kinds of knowledge, especially mathematics. The attempt is restricted to classical two-valued logic and assumes that the basic notion in logic is the proposition. First, we explain the distinction between the parts and the moments of a whole, and theories of ?sortal terms?, two theories that will feature prominently. Second, we propose that logic comprises four ?momental sectors?: the propositional and the functional calculi, the calculus of asserted propositions, and rules for (...)
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  • You Reap What You Sow: How MBA Programs Undermine Ethics.Matthias Philip Hühn - 2014 - Journal of Business Ethics 121 (4):527-541.
    This paper argues that the MBA, probably the most successful academic program of the last 50 years, negatively affects the theory and practice of management with regard to ethics through its pedagogy, structure, and its underlying epistemic assumptions. In particular I seek to demonstrate how the syllabus, the pedagogy and the epistemological assumptions of MBA programs together make managers/leaders unable and unwilling to deal with ethics. I also argue that while the what and the how play a very important role, (...)
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  • Propositions, Meaning, and Names.Tristan Grøtvedt Haze - 2018 - Philosophical Forum 49 (3):335-362.
    The object of this paper is to sketch an approach to propositions, meaning and names. The key ingredients are a Twin-Earth-inspired distinction between internal and external meaning, and a middle-Wittgenstein-inspired conception of internal meaning as role in language system. I show how the approach offers a promising solution to the problem of the meaning of proper names. This is a plea for a neglected way of thinking about these topics.
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  • Frege's Changing Conception of Number.Kevin C. Klement - 2012 - Theoria 78 (2):146-167.
    I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...)
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  • Invariance, Structure, Measurement – Eino Kaila and the History of Logical Empiricism.Matthias Neuber - 2012 - Theoria 78 (4):358-383.
    Eino Kaila's thought occupies a curious position within the logical empiricist movement. Along with Hans Reichenbach, Herbert Feigl, and the early Moritz Schlick, Kaila advocates a realist approach towards science and the project of a “scientific world conception”. This realist approach was chiefly directed at both Kantianism and Poincaréan conventionalism. The case in point was the theory of measurement. According to Kaila, the foundations of physical reality are characterized by the existence of invariant systems of relations, which he called structures. (...)
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  • Consulting The Reference Book.Kent Bach - 2014 - Mind and Language 29 (4):455-474.
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  • Programs as Causal Models: Speculations on Mental Programs and Mental Representation.Nick Chater & Mike Oaksford - 2013 - Cognitive Science 37 (6):1171-1191.
    Judea Pearl has argued that counterfactuals and causality are central to intelligence, whether natural or artificial, and has helped create a rich mathematical and computational framework for formally analyzing causality. Here, we draw out connections between these notions and various current issues in cognitive science, including the nature of mental “programs” and mental representation. We argue that programs (consisting of algorithms and data structures) have a causal (counterfactual-supporting) structure; these counterfactuals can reveal the nature of mental representations. Programs can also (...)
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  • Cognitivism: A New Theory of Singular Thought?Sarah Sawyer - 2012 - Mind and Language 27 (3):264-283.
    In a series of recent articles, Robin Jeshion has developed a theory of singular thought which she calls ‘cognitivism’. According to Jeshion, cognitivism offers a middle path between acquaintance theories—which she takes to impose too strong a requirement on singular thought, and semantic instrumentalism—which she takes to impose too weak a requirement. In this article, I raise a series of concerns about Jeshion's theory, and suggest that the relevant data can be accommodated by a version of acquaintance theory that distinguishes (...)
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  • Modal Objectivity1.Clarke-Doane Justin - 2019 - Noûs:266-295.
    It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically significant” about (...)
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  • On Neutral Relations.Richard Gaskin & Daniel J. Hill - 2012 - Dialectica 66 (1):167-186.
    Is there an explanation of why the state of x's bearing the non-symmetric binary relation R to y is different from its differential opposite, the state of y's bearing R to x? One traditional view has it that the explanation is that non-symmetric relations hold of objects in an essentially directional way, ordering the relevant relata. We call this view ‘directionalism’. Kit Fine has suggested that this approach is subject to significant metaphysical difficulties, sufficient to motivate seeking an alternative analysis. (...)
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  • Metaphilosophy in the Systems of Metatheories.Georg Brutian - 2012 - Metaphilosophy 43 (3):294-305.
    This article discusses the essence and form of various types of metatheory, paying special attention to metaphilosophy. It suggests the idea of the metatheoretical model—a completely new approach in philosophical discussion—and considers this concept with regard to the Platonic model and the Rhodian model. These models permit two different systems of metatheoretical construction. The paradigms of modern science allow the formation of metatheories that help further the development of logical, mathematical, and similar sciences. The Rhodian model allows the discovery of (...)
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  • The Barcan Formula in Metaphysics.Ori Simchen - 2013 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 28 (3):375-392.
    The Barcan formula (BF) is commonly paraphrased as the schematic conditional that if it is possible that there be a phi then something or other is possibly a phi. It is validated by the most straightforward systems of quantified modal logic. It is also widely considered to pose a threat to the commonsensical metaphysical view that there are no non-actual (or ‘merely possible’) things. I show how BF can be cleared of such a charge by construing it as a bridge (...)
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  • Concept Referentialism and the Role of Empty Concepts.Kevan Edwards - 2010 - Mind and Language 25 (1):89-118.
    This paper defends a reference-based approach to concept individuation against the objection that such an approach is unable to make sense of concepts that fail to refer. The main line of thought pursued involves clarifying how the referentialist should construe the relationship between a concept's (referential) content and its role in mental processes. While the central goal of the paper is to defend a view aptly titled Concept Referentialism , broader morals are drawn regarding reference-based approaches in general. The paper (...)
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  • Aristotle, Hume and the Goals of Medicine.David Misselbrook - 2016 - Journal of Evaluation in Clinical Practice 22 (4):544-549.
  • The Cambridge Revolt Against Idealism: Was There Ever an Eden?Fraser Macbride - 2012 - Metaphilosophy 43 (1-2):135-146.
    According to one creation myth, analytic philosophy emerged in Cambridge when Moore and Russell abandoned idealism in favour of naive realism: every word stood for something; it was only after “the Fall,” Russell's discovery of his theory of descriptions, that they realized some complex phrases (“the present King of France”) didn't stand for anything. It has become a commonplace of recent scholarship to object that even before the Fall, Russell acknowledged that such phrases may fail to denote. But we need (...)
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  • Descriptions Which Have Grown Capital Letters.Brian Rabern - 2015 - Mind and Language 30 (3):292-319.
    Almost entirely ignored in the linguistic theorising on names and descriptions is a hybrid form of expression which, like definite descriptions, begin with 'the' but which, like proper names, are capitalised and seem to lack descriptive content. These are expressions such as the following, 'the Holy Roman Empire', 'the Mississippi River', or 'the Space Needle'. Such capitalised descriptions are ubiquitous in natural language, but to which linguistic categories do they belong? Are they simply proper names? Or are they definite descriptions (...)
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  • The but Not All: A Partitive Account of Plural Definite Descriptions.Berit Brogaard - 2007 - Mind and Language 22 (4):402–426.
    A number of authors in favor of a unitary account of singular descriptions have alleged that the unitary account can be extrapolated to account for plural definite descriptions. In this paper I take a closer look at this suggestion. I argue that while the unitary account is clearly onto something right, it is in the end empirically inadequate. At the end of the paper I offer a new partitive account of plural definite descriptions that avoids the problems with both the (...)
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  • Improvements in Human Reasoning and an Error in L. J. Cohen's.David H. Krantz - 1981 - Behavioral and Brain Sciences 4 (3):340-340.
  • A Language for the Description of God.David Graves & Ilai Alon - 1994 - International Journal for Philosophy of Religion 36 (3):169-186.
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  • It Adds Up After All: Kant’s Philosophy of Arithmetic in Light of the Traditional Logic.R. Lanier Anderson - 2004 - Philosophy and Phenomenological Research 69 (3):501–540.
    Officially, for Kant, judgments are analytic iff the predicate is "contained in" the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia(e). Hierarchies afford a straightforward sense of containment: (...)
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  • The Persistence of Cognitive Illusions.Persi Diaconis & David Freedman - 1981 - Behavioral and Brain Sciences 4 (3):333-334.
  • Matching Parameters to Simple Triggers.David Lightfoot - 1989 - Behavioral and Brain Sciences 12 (2):364-375.
  • Against the Russellian Open Future.Anders J. Schoubye & Brian Rabern - 2017 - Mind 126 (504): 1217–1237.
    Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the form 'will(φ)', that is based on the classic Russellian analysis of definite descriptions. Todd's analysis is supposed to vindicate the claim that the future is metaphysically open while retaining a simple Ockhamist semantics of future contingents and the principles of classical logic, i.e. bivalence and the law of excluded middle. Consequently, an open futurist can straightforwardly retain classical logic without appeal to supervaluations, determinacy operators, or any further (...)
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  • "If-Then" as a Version of "Implies".Matheus Silva - manuscript
    Russell’s role in the controversy about the paradoxes of material implication is usually presented as a tale of how even the greatest minds can fall prey of basic conceptual confusions. Quine accused him of making a silly mistake in Principia Mathematica. He interpreted “if- then” as a version of “implies” and called it material implication. Quine’s accusation is that this decision involved a use-mention fallacy because the antecedent and consequent of “if- then” are used instead of being mentioned as the (...)
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