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  1. 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 Roles of Kant’s Doctrines of Method.Gabriele Gava & Andrew Chignell - 2023 - Journal of Transcendental Philosophy 4 (2):73-79.
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  • Kant’s Doctrine of Definitions and the Semantic Background of the Transcendental Analytic.Bianca Ancillotti - 2023 - Journal of Transcendental Philosophy 4 (2):113-136.
    In this paper I argue that Kant’s doctrine of definitions, as it is developed in theTranscendental Doctrine of Method(TDM) and in the lectures on logic, lays down the semantic background of the problem of the objective reality of the categories and of the solution Kant provides for it in theTranscendental Analytic. The distinction between nominal and real definitions introduces a two-dimensional element in Kant’s theory of concepts, and this, I argue, provides a compelling explanation for the assumption Kant makes in (...)
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  • Kant’s Semiotics and Hermeneutics in the 1760s.Marco Costantini - 2023 - Kant Yearbook 15 (1):25-51.
    In this contribution, we first discuss the aspects of the analytic method conceived by Kant in the Deutlichkeit that differentiate it from the Wolffian method and relate it to the Newtonian method. Compared to the philosophical tradition, the task of analysing concepts appears profoundly changed. Since Kant aims philosophy towards the world, he considers concepts as something given and intends to discern their characteristic marks by observing their usual applications. Although Kant abandons any attempt to define concepts nominally, he still (...)
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  • Kant on the Givenness of Space and Time.Rosalind Chaplin - 2022 - European Journal of Philosophy 30 (3):877-898.
    Famously, Kant describes space and time as infinite “given” magnitudes. An influential interpretative tradition reads this as a claim about phenomenological presence to the mind: in claiming that space and time are given, this reading holds, Kant means to claim that we have phenomenological access to space and time in our original intuitions of them. In this paper, I argue that we should instead understand givenness as a metaphysical notion. For Kant, space and time are ‘given’ in virtue of three (...)
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  • Kantian Conceptualism/Nonconceptualism.Colin McLear - 2020 - Stanford Encyclopedia of Philosophy.
    Overview of the (non)conceptualism debate in Kant studies.
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  • The Kantian (Non)‐conceptualism Debate.Colin McLear - 2014 - Philosophy Compass 9 (11):769-790.
    One of the central debates in contemporary Kant scholarship concerns whether Kant endorses a “conceptualist” account of the nature of sensory experience. Understanding the debate is crucial for getting a full grasp of Kant's theory of mind, cognition, perception, and epistemology. This paper situates the debate in the context of Kant's broader theory of cognition and surveys some of the major arguments for conceptualist and non-conceptualist interpretations of his critical philosophy.
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  • Beauty in Proofs: Kant on Aesthetics in Mathematics.Angela Breitenbach - 2013 - European Journal of Philosophy 23 (4):955-977.
    It is a common thought that mathematics can be not only true but also beautiful, and many of the greatest mathematicians have attached central importance to the aesthetic merit of their theorems, proofs and theories. But how, exactly, should we conceive of the character of beauty in mathematics? In this paper I suggest that Kant's philosophy provides the resources for a compelling answer to this question. Focusing on §62 of the ‘Critique of Aesthetic Judgment’, I argue against the common view (...)
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  • Kant-Bibliographie 1999.M. Ruffing - 2001 - Kant Studien 92 (4):474-517.
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  • Kant on the imagination and geometrical certainty.Mary Domski - 2010 - Perspectives on Science 18 (4):409-431.
    My goal in this paper is to develop our understanding of the role the imagination plays in Kant’s Critical account of geometry, and I do so by attending to how the imagination factors into the method of reasoning Kant assigns the geometer in the First Critique. Such an approach is not unto itself novel. Recent commentators, such as Friedman (1992) and Young (1992), have taken a careful look at the constructions of the productive imagination in pure intuition and highlighted the (...)
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  • Kant’s Prize Essay and Nineteenth Century Formalism.Richard Lawrence - 2024 - Kant Yearbook 16 (1):31-52.
    Kant’s Prize Essay of 1764 emphasizes the importance for mathematical cognition of manipulating signs according to rules, which has led some recent commentators to ask whether Kant’s position there is a species of mathematical formalism. While most have hesitated to find formalism in the Prize Essay, this hesitation derives from misconceptions about what formalists actually believe. I therefore examine some nineteenth century formalists who were in dialogue with Kant, using their views as a model against which to compare the Prize (...)
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  • After Non-Euclidean Geometry: Intuition, Truth and the Autonomy of Mathematics.Janet Folina - 2018 - Journal for the History of Analytical Philosophy 6 (3).
    The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Mathematics seemed increasingly detached from experience as well as its form; moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. This paper considers various philosophical responses to (...)
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  • Kant: Philosophy of Mind.Colin McLear - 2015 - Internet Encyclopedia of Philosophy.
    Kant: Philosophy of Mind Immanuel Kant was one of the most important philosophers of the Enlightenment Period in Western European history. This encyclopedia article focuses on Kant’s views in the philosophy of mind, which undergird much of his epistemology and metaphysics. In particular, it focuses on metaphysical and epistemological doctrines forming the … Continue reading Kant: Philosophy of Mind →.
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  • Locke and Kant on mathematical knowledge.Emily Carson - 2006 - In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 3--19.
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  • A Cognitive Approach to Benacerraf's Dilemma.Luke Jerzykiewicz - 2009 - Dissertation, University of Western Ontario
    One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...)
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  • Conceptual Analysis and the Analytic Method in Kant’s Prize Essay.Gabriele Gava - 2024 - Hopos: The Journal of the International Society for the History of Philosophy of Science 14 (1):164-184.
    Famously, in the essay Inquiry Concerning the Distinctness of the Principles of Natural Theology and Morality (Prize Essay), Kant attempts to distance himself from the Wolffian model of philosophical inquiry. In this respect, Kant scholars have pointed out Kant’s claim that philosophy should not imitate the method of mathematics and his appeal to Newton’s “analytic method.” In this article, I argue that there is an aspect of Kant’s critique of the Wolffian model that has been neglected. Kant presents a powerful (...)
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  • The Dissatisfied Skeptic in Kant's Discipline of Pure Reason.Charles Goldhaber - 2023 - Journal of Transcendental Philosophy 4 (2):157-177.
    Why does Kant say that a “skeptical satisfaction of pure reason” is “impossible” (A758/B786)? I answer this question by giving a reading of “The Discipline of Pure Reason in Respect of Its Polemic Employment.” I explain that Kant must address skepticism in this context because his warning against developing counterarguments to dogmatic attacks encourages a comparison between the critical and the skeptical methods. I then argue that skepticism fails to “satisfy” [befriedigen] reason insofar as it cannot “pacify” reason’s tendency to (...)
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  • The Method of Kant’s Groundwork of the Metaphysics of Morals: Establishing Moral Metaphysics as a Science.Susan V. H. Castro - 2006 - Dissertation, University of California, Los Angeles
    This dissertation concerns the methodology Kant employs in the first two sections of the Groundwork of the Metaphysics of Morals (Groundwork I-II) with particular attention to how the execution of the method of analysis in these sections contributes to the establishment of moral metaphysics as a science. My thesis is that Kant had a detailed strategy for the Groundwork, that this strategy and Kant’s reasons for adopting it can be ascertained from the Critique of Pure Reason (first Critique) and his (...)
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  • Kant's Conception of Number.Daniel Sutherland - 2017 - Philosophical Review Current Issue 126 (2):147-190.
    Despite the importance of Kant's claims about mathematical cognition for his philosophy as a whole and for subsequent philosophy of mathematics, there is still no consensus on his philosophy of arithmetic, and in particular the role he assigns intuition in it. This inquiry sets aside the role of intuition for the nonce to investigate Kant's conception of natural number. Although Kant himself doesn't distinguish between a cardinal and an ordinal conception of number, some of the properties Kant attributes to number (...)
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  • Kant’s Theory of Arithmetic: A Constructive Approach?Kristina Engelhard & Peter Mittelstaedt - 2008 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 (2):245-271.
    Kant's theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant's theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant's theory of arithmetic can (...)
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  • Kant on the Acquisition of Geometrical Concepts.John J. Callanan - 2014 - Canadian Journal of Philosophy 44 (5-6):580-604.
    It is often maintained that one insight of Kant's Critical philosophy is its recognition of the need to distinguish accounts of knowledge acquisition from knowledge justification. In particular, it is claimed that Kant held that the detailing of a concept's acquisition conditions is insufficient to determine its legitimacy. I argue that this is not the case at least with regard to geometrical concepts. Considered in the light of his pre-Critical writings on the mathematical method, construction in the Critique can be (...)
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  • Arbitrary combination and the use of signs in mathematics: Kant’s 1763 Prize Essay and its Wolffian background.Katherine Dunlop - 2014 - Canadian Journal of Philosophy 44 (5-6):658-685.
    In his 1763 Prize Essay, Kant is thought to endorse a version of formalism on which mathematical concepts need not apply to extramental objects. Against this reading, I argue that the Prize Essay has sufficient resources to explain how the objective reference of mathematical concepts is secured. This account of mathematical concepts’ objective reference employs material from Wolffian philosophy. On my reading, Kant's 1763 view still falls short of his Critical view in that it does not explain the universal, unconditional (...)
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  • Univalent foundations as structuralist foundations.Dimitris Tsementzis - 2017 - Synthese 194 (9):3583-3617.
    The Univalent Foundations of Mathematics provide not only an entirely non-Cantorian conception of the basic objects of mathematics but also a novel account of how foundations ought to relate to mathematical practice. In this paper, I intend to answer the question: In what way is UF a new foundation of mathematics? I will begin by connecting UF to a pragmatist reading of the structuralist thesis in the philosophy of mathematics, which I will use to define a criterion that a formal (...)
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  • Mendelssohn and Kant on Mathematics and Metaphysics.John J. Callanan - 2014 - Kant Yearbook 6 (1):1-22.
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  • The point of Kant's axioms of intuition.Daniel Sutherland - 2005 - Pacific Philosophical Quarterly 86 (1):135–159.
    Kant's Critique of Pure Reason makes important claims about space, time and mathematics in both the Transcendental Aesthetic and the Axioms of Intuition, claims that appear to overlap in some ways and contradict in others. Various interpretations have been offered to resolve these tensions; I argue for an interpretation that accords the Axioms of Intuition a more important role in explaining mathematical cognition than it is usually given. Appreciation for this larger role reveals that magnitudes are central to Kant's philosophy (...)
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  • Definitions of Kant’s categories.Tyke Nunez - 2014 - Canadian Journal of Philosophy 44 (5-6):631-657.
    The consensus view in the literature is that, according to Kant, definitions in philosophy are impossible. While this is true prior to the advent of transcendental philosophy, I argue that with Kant's Copernican Turn definitions of some philosophical concepts, the categories, become possible. Along the way I discuss issues like why Kant introduces the ‘Analytic of Concepts’ as an analysis of the understanding, how this faculty, as the faculty for judging, provides the principle for the complete exhibition of the categories, (...)
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  • Kant on real definitions in geometry.Jeremy Heis - 2014 - Canadian Journal of Philosophy 44 (5-6):605-630.
    This paper gives a contextualized reading of Kant's theory of real definitions in geometry. Though Leibniz, Wolff, Lambert and Kant all believe that definitions in geometry must be ‘real’, they disagree about what a real definition is. These disagreements are made vivid by looking at two of Euclid's definitions. I argue that Kant accepted Euclid's definition of circle and rejected his definition of parallel lines because his conception of mathematics placed uniquely stringent requirements on real definitions in geometry. Leibniz, Wolff (...)
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  • Frank Pierobon. Kant et les mathématiques: La conception kantienne des mathématiques [Kant and mathematics: The Kantian conception of mathematics]. Bibliothèque d'Histoire de la Philosophie. Paris: J. Vrin. ISBN 2-7116-1645-2. Pp. 240. [REVIEW]Emily Carson - 2006 - Philosophia Mathematica 14 (3):370-378.
    This book is a welcome contribution to the literature on Kant's philosophy of mathematics in two particular respects. First, the author systematically traces the development of Kant's thought on mathematics from the very early pre-Critical writings through to the Critical philosophy. Secondly, it puts forward a challenge to contemporary Anglo-Saxon commentators on Kant's philosophy of mathematics which merits consideration.A central theme of the book is that an adequate understanding of Kant's pronouncements on mathematics must begin with the recognition that mathematics (...)
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  • The View from 1763: Kant on the Arithmetical Method before Intuition.Ofra Rechter - 2006 - In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 21--46.
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  • Looking for laws in all the wrong spaces: Kant on laws, the understanding, and space.James Anthony Messina - 2018 - European Journal of Philosophy 26 (1):589-613.
    Prolegomena §38 is intended to elucidate the claim that the understanding legislates a priori laws to nature. Kant cites various laws of geometry as examples and discusses a derivation of the inverse-square law from such laws. I address 4 key interpretive questions about this cryptic text that have not yet received satisfying answers: How exactly are Kant's examples of laws supposed to elucidate the Legislation Thesis? What is Kant's view of the epistemic status of the inverse-square law and, relatedly, of (...)
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  • Soft Axiomatisation: John von Neumann on Method and von Neumann's Method in the Physical Sciences.Miklós Rédei & Michael Stöltzner - 2006 - In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 235--249.
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