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  1. The First Draft of Spinoza's Ethics.Yitzhak Melamed - forthcoming - In Spinoza in 21st-Century French and American Philosophy. Bloomsbury.
    The two manuscripts of the Korte Verhanedling that were discovered in the mid-nineteenth century contain two appendices. These appendices are even more enigmatic than the KV itself, and it is the first appendix that is the subject of this study. Unfortunately, there are very few studies of this text, and its precise nature seems to be still in question after more than a century and a half of scholarship. It is commonly assumed that the appendices were written after the body (...)
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  2. On Tait on Kant and Finitism.W. Sieg - 2016 - Journal of Philosophy 113 (5/6):274-285.
    In his “Kant and Finitism” Tait attempts to connect his analysis of finitist arithmetic with Kant’s perspective on arithmetic. The examination of this attempt is the basis for a distinctive view on the dramatic methodological shift from Kant to Dedekind and Hilbert. Dedekind’s 1888 essay “Was sind und was sollen die Zahlen?” gives a logical analysis of arithmetic, whereas Hilbert’s 1899 book “Grundlagen der Geometrie” presents such an analysis of geometry or, as Hilbert puts it, of our spatial intuition. This (...)
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  3. David Hilbert’s ’Vorlesungen’ Logic and Foundations of Mathematics.Vito Michele Abrusci - 1989 - In G. Corsi, C. Mangione & M. Mugnai (eds.), Atti Del Convegno Internazionale di Storia Della Logica, San Gimignano, 1987. Editrice Cooperativa Libraria Universitaria Editrice, 1989. pp. 333-338..
  4. Husserl and Hilbert on Completeness, Still.Jairo Jose da Silva - 2016 - Synthese 193 (6):1925-1947.
    In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...)
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  5. Mathematics in Kant's Critical Philosophy: Reflections on Mathematical Practice.Lisa Shabel - 2002 - Routledge.
    This book provides a reading of Kant's theory of the construction of mathematical concepts through a fully contextualised analysis. In this work the author argues that it is only through an understanding of the relevant eighteenth century mathematics textbooks, and the related mathematical practice, that the material and context necessary for a successful interpretation of Kant's philosophy can be provided.
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  6. From Kant to Hilbert, Volume 2: A Source Book in the Foundations of Mathematics.William Bragg Ewald - 2005 - Oxford University Press UK.
    Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth cnetury ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics--algebra, geometry, number theory, analysis, logic and set theory--with narratives to show (...)
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  7. Intuition and Reasoning in Geometry.Otto Hölder - 2013 - Philosophia Scientae 17:15-52.
  8. On the Mathematical Method and Correspondence with Exner: Translated by Paul Rusnock and Rolf George.Bernard Bolzano (ed.) - 2004 - Rodopi.
    The Prague Philosopher Bernard Bolzano has long been admired for his groundbreaking work in mathematics: his rigorous proofs of fundamental theorems in analysis, his construction of a continuous, nowhere-differentiable function, his investigations of the infinite, and his anticipations of Cantor's set theory. He made equally outstanding contributions in philosophy, most notably in logic and methodology. One of the greatest mathematician-philosophers since Leibniz, Bolzano is now widely recognised as a major figure of nineteenth-century philosophy.Praised by Husserl as “one of the greatest (...)
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  9. Intuition and Reasoning in Geometry Inaugural Academic Lecture Held on July 22, 1899. With Supplements and Notes: Otto Hölder (1859-1937). [REVIEW]Paola Cantu & Oliver Schlaudt - 2013 - Philosophia Scientiae 17 (1):15-52.
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  10. Different Senses of Finitude: An Inquiry Into Hilbert's Finitism.Sören Stenlund - 2012 - Synthese 185 (3):335-363.
    This article develops a critical investigation of the epistemological core of Hilbert's foundational project, the so-called the finitary attitude. The investigation proceeds by distinguishing different senses of 'number' and 'finitude' that have been used in the philosophical arguments. The usual notion of modern pure mathematics, i.e. the sense of number which is implicit in the notion of an arbitrary finite sequence and iteration is one sense of number and finitude. Another sense, of older origin, is connected with practices of counting (...)
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  11. Spiritual Presence and Dimensional Space Beyond the Cosmos.Hylarie Kochiras - 2012 - Intellectual History Review 22 (1):41-68.
    This paper examines connections between concepts of space and extension on the one hand and immaterial spirits on the other, specifically the immanentist concept of spirits as present in rerum natura. Those holding an immanentist concept, such as Thomas Aquinas, typically understood spirits non-dimensionally as present by essence and power; and that concept was historically linked to holenmerism, the doctrine that the spirit is whole in every part. Yet as Aristotelian ideas about extension were challenged and an actual, infinite, dimensional (...)
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