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Summary Immanuel Kant's theoretical philosophy constitutes a philosophical system, a theory about the conditions for objective knowledge. Kant's approach to theoretical philosophy, in his pre-Critical and Critical works, is influenced heavily by his engagement with science, with mathematics, and with logic. Kant's views on these subjects have been widely influential, though they have been criticized widely as well. Appreciation of Kant's work in science, mathematics, and logic is philosophically productive at least two ways: (1) A contextual history of Kant's own work, emphasizing his responses to his predecessors and contemporaries, and (2) A systematic understanding of how the Kantian approach has been employed in these fields.
Key works One locus classicus for Kant's epistemological positions on reason, mathematics,  judgment, and objectivity is The Critique of Pure Reason. A recent translation and edition of Kant's work on science, including the Universal Natural History, can be found in Natural Science. Among the most significant of Kant's texts for his philosophy of science specifically are The Metaphysical Foundations of Natural Science and Prolegomena to any Future Metaphysics. This category also encompasses elements of Kant's theory of judgment, key texts for which include The Critique of Judgment and Lectures on Logic.
Introductions A general introduction to Kant's philosophy of science, with references to other texts, is found at Watkins & Stan 2014. A similar article for Kant's theory of judgment is Hanna 2008.
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  1. Wilson Harris (1999). The Psyche of Space and Intuition of Otherness. Clr James Journal 7 (1):3-13.
  2. Peter Plaass, Alfred E. Miller & Carl Friedrich Weizsäcker (1994). Kant's Theory of Natural Science.
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  3. Konstantin Pollok (2014). From the Clarity of Ideas to the Validity of Judgments: Kant's Farewell to Epistemic Perfectionism. Canadian Journal of Philosophy 44 (1):18-35.
  4. Irving Polonoff (1994). Michael Friedman., Kant and the Exact Sciences. International Studies in Philosophy 26 (4):129-130.
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  5. Carl J. Posy (1992). Kant's Philosophy of Mathematics Modern Essays.
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  6. Joelle Proust (1989). Questions of Form: Logic and Analytic Proposition From Kant to Carnap. Univ of Minnesota Press.
    Hence, this book's provocative claim: today's so-called logical empiricism owes much more to Kant's notion of science than to Hume's.
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  7. H. K. R. (1969). Geometry and Chronometry in Philosophical Perspective. [REVIEW] Review of Metaphysics 23 (1):130-130.
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  8. K. R. (1972). The Notion of Form in Kant’s Critique of Aesthetic Judgment. [REVIEW] Review of Metaphysics 26 (2):369-370.
  9. Sebastian Rand (2014). Review: Friedman, Michael, Kant’s Construction of Nature: A Reading of the Metaphysical Foundations of Natural Science. [REVIEW] Review of Metaphysics 67 (3):635-637.
  10. Ofra Rechter (2013). On Kant on Arithmetic, Time, and Irrationals. In Margit Ruffing, Claudio La Rocca, Alfredo Ferrarin & Stefano Bacin (eds.), Kant Und Die Philosophie in Weltbürgerlicher Absicht: Akten des Xi. Kant-Kongresses 2010. De Gruyter 209-222.
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  11. Ofra Rechter (2006). The View From 1763: Kant on the Arithmetical Method Before Intuition. In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer 21--46.
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  12. Klaus Reich, Jane Kneller & Michael Losonsky (1994). The Completeness of Kant's Table of Judgments. Philosophical Review 103 (2):373-375.
  13. Dale Riepe (1964). K. H. Potter's "Presuppositions of India's Philosophies". [REVIEW] Philosophy and Phenomenological Research 24 (3):443.
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  14. Kenneth Rogerson (2013). Kant on Negative Judgments of Taste. In Margit Ruffing, Claudio La Rocca, Alfredo Ferrarin & Stefano Bacin (eds.), Kant Und Die Philosophie in Weltbürgerlicher Absicht: Akten des Xi. Kant-Kongresses 2010. De Gruyter 215-224.
  15. Waldemar Rohloff (2012). From Ordinary Language to Definition in Kant and Bolzano. Grazer Philosophische Studien 85 (1):131-149.
    In this paper I discuss Kant's and Bolzano's differing perspectives on ordinary natural language. I argue that Kant does not see ordinary language as providing semantically organized content and that, as a result, Kant does not believe that ordinary language is sufficiently well-developed to support philosophical analysis and definition. By contrast, for Bolzano, the content given in ordinary language are richly structured entities he calls 'propositions in themselves'. This contrast in views is used to explain Bolzano's criticism of Kant's belief (...)
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  16. Paul Rusnock (2003). Qu'est-ce que la représentation ? Bolzano et la philosophie autrichienne. Philosophiques 30 (1):67-81.
    Largement inconnu en Allemagne au XIXe siècle, Bolzano connut un meilleur sort en Autriche, surtout auprès des étudiants de Brentano, qui étudièrent avidement sa Théorie de la science. Cependant, un examen attentif de la réception des idées de Bolzano chez les brentaniens nous montrent qu’il fut souvent mal compris. Cet article discute d’un cas particulier de ce phénomène, la réaction de K. Twardowski à la théorie de la représentation de Bolzano.Largely ignored in Germany during the nineteenth century, Bolzano was certainly (...)
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  17. Paul Rusnock (ed.) (2000). Bolzano's Philosophy and the Emergence of Modern Mathematics. Rodopi.
    Contents: Acknowledgements. Conventions. Preface. Biographical sketch. 1 Introduction. 2 The Contributions. 3 Early work in analysis. 4 The Theory of Science . 5. Later mathematical studies. A On Kantian Intuitions. B The Bolzano-Cauchy Theorem.
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  18. Paul Herbert Rusnock (1996). A Critical Introduction to Bolzano's Philosophy. Dissertation, University of Waterloo (Canada)
    Received accounts of nineteenth-century thought make little or no room for the substantial contributions of the Bohemian philosopher Bernard Bolzano . This thesis constitutes a sustained attempt to show that this omission is a serious mistake, that Bolzano is more rightly treated as one of the major figures of western philosophy. To his contemporaries, Bolzano was known primarily as a teacher, religious leader, and social reformer. Outside of central Europe, though, he became known primarily through his logical and mathematical writings. (...)
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  19. Paul Rusnock & Rolf George (eds.) (2014). Bernard Bolzano: Theory of Science. OUP Oxford.
    This is the first full English translation of Bernard Bolzano's masterwork, the Theory of Science (1837)--a monumental and revolutionary study in logic, epistemology, heuristics, and scientific methodology. Each volume includes an introduction which illuminates the historical context of Bolzano's work and its continuing relevance.
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  20. Bertrand Russell (1996). Foundations of Geometry. Routledge.
    The Foundations of Geometry was first published in 1897, and is based on Russell's Cambridge dissertation as well as lectures given during a journey through the USA. This is the first reprint, complete with a new introduction by John Slater. It provides both an insight into the foundations of Russell's philosophical thinking and an introduction to the philosophy of mathematics and logic. As such it will be an invaluable resource not only for students of philosophy, but also for those interested (...)
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  21. Frank Schalow (2009). Reinscribing the «Λογωσ» in Transcendental Logic: Kant’s Highest Principle of Synthetic Judgments Revisited. Existentia 19 (3-4):205-224.
  22. Eva Schaper (1971). SWING, Thomas Kaehao.-"Kant's Transcendental Logic". [REVIEW] Philosophy 46:75.
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  23. Irmgard Braier Scherer (1991). The Crisis of Judgment in Kant's Three "Critiques", the Aesthetic Factor and Kant's Architectonic Solution. Dissertation, The American University
    This dissertation will explore a unique problem in Kant's critical philosophy, thus far not dealt with in the larger perspective it deserves, namely the possibility of judgment, particularly aesthetic judgment in the shadow of reason and understanding. Kant tells us in the Critique of Pure Reason that in the course of human conduct the power of judgment is more important than knowledge and reason , but how this is so he only comes to fully articulate in his culminating critical work, (...)
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  24. Martin Schonfeld (2003). Kant and the Sciences. Mind 112 (447):579-583.
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  25. Dennis Schulting (ed.) (2015). The Bloomsbury Companion to Kant. Bloomsbury.
  26. Centro Fiorentino di Storia E. Filisofia Della Scienza (1992). Bolzano's Wissenschaftslehre, 1837-1987 International Workshop.
  27. Phillip Scuderi (2011). On The Subject/Object Distinction In Kant's Aesthetics: A Response To Zuckert. Florida Philosophical Review 11 (1):17-25.
    Given the abundant secondary scholarship that has ensued from Kant's discussion of judgments of taste, it is surprising that the question of just what judgments of taste are supposed to be about has never been settled. Rachel Zuckert has recently argued that for Kant, judgments of taste are about objects in the world. I argue, however, that we would do better to read Kant as claiming that judgments of taste are not about determinate objects at all; rather, they are about (...)
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  28. Jan Šebestík (2013). Review of S. Lapointe: Bolzano's Theoretical Philosophy, An Introduction. [REVIEW] Journal for the History of Analytical Philosophy 2 (2).
    Review of S. Lapointe: Bolzano’s Theoretical Philosophy, An Introduction.
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  29. Jan Sebestik (2003). La dispute de Bolzano avec Kant : Fragment d'un dialogue sur la connaissance mathématique. Philosophiques 30 (1):47-66.
    Ce dialogue confronte deux conceptions qui dominent jusqu’à nos jours la philosophie des mathématiques : d’un côté la conception kantienne qui souligne l’irréductible apport de l’intuition dans la formulation des axiomes, ainsi que l’effectivité des procédés de construction ; de l’autre côté la conception bolzanienne qui s’efforce d’éliminer toute intervention de l’intuition au profit des démonstrations et des procédés purement conceptuels.In this dialogue, two opposed conceptions, which dominate the philosophy of mathematics till today, are confronted. Kant’s account of mathematics is (...)
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  30. Jan Sebestik (1999). Forme, Variation Et Déductïbilité Dans la Logique de Bolzano/Form, Variation and Deducibility in Bolzano's Logic. Revue d'Histoire des Sciences 52 (3):479-506.
  31. S. Shaida (1978). Ibn Miskawaih's Concept of Justice and its Metaphysical Foundations. Indian Philosophical Quarterly 5 (3):299-318.
  32. Shuford Shuford (1952). UCHLER'S Toward a General Theory of Human Judgment. [REVIEW] Philosophy and Phenomenological Research 13:264.
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  33. Mark Siebel (2011). It Falls Somewhat Short of Logical Precision. Bolzano on Kant's Definition of Analyticity. Grazer Philosophische Studien 82 (1):91-127.
  34. Peter Simons (2003). Bolzano sur les nombres. Philosophiques 30 (1):127-135.
    Dans cet article, l’auteur présente la théorie bolzanienne du nombre. Il établit, sur la base d’une comparaison avec Frege, que la conception bolzanienne rencontre toutes les exigences d’une telle théorie tout en présentant plusieurs traits originaux, comme par exemple le fait qu’elle s’articule sur la base d’une théorie des « collections » , qui lui confèrent un intérêt philosophique certain. Tout en indiquant au passage un problème inhérent à la notion bolzanienne de Reihe, l’auteur présente la conception bolzanienne des nombres (...)
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  35. Hendrikus Adrianus Marie Snelders (1973). De Invloed van Kant, de Romantiek En de Natuurphilosophie Op de Anorganische Natuurwetenschappen in Duitsland = the Influence of Kant, Romanticism, and Naturphilosophie on the Inorganic Natural Sciences in Germany. Snelders.
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  36. David Lee Sobers (1967). Kant's Justification of the Possibility of Judgments of Taste. Dissertation, The University of Rochester
  37. Thomas Solly (1839). A Syllabus of Logic in Which the Views of Kant Are Generally Adopted, and the Laws of Syllogism Symbolically Expressed. Deighton Parker Parker.
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  38. Grapotte Sophie, Lequan Mai & Ruffing Margit (eds.) (2011). Kant et les sciences. Un dialogue philosophique avec la pluralité des savoirs. Vrin.
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  39. Prokop SouSedík (2006). Rigorisace Infinitesimálního Počtu a Obrat K Jazyku (Kant–Bolzano–Frege). Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 13 (1):32-54.
    Mathematics in the 19th century underwent explosive development. The discussion among philosophers was motivated by new results which conflicted with Kant’s very influential conception. One of the most important areas which lead to the meeting of philosophy and mathematics was a rigorous account of the infinitesimal calculus. In his article the author shows that considerations of this type found in Bolzano and Frege are important not only for the overcoming of the Kantian conception, but as for what we today call (...)
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  40. Nicholas Stang (2011). A Kantian Reply To Bolzano's Critique Of Kant's Analytic-Synthetic Distinction. Grazer Philosophische Studien 85 (1):33-61.
    One of Bolzano's objections to Kant's way of drawing the analytic-synthetic distinction is that it only applies to judgments within a narrow range of syntactic forms, namely, universal affirmative judgments. According to Bolzano, Kant cannot account for judgments of other syntactic forms that, intuitively, are analytic. A recent paper by Ian Proops also attributes to Kant the view that analytic judgments beyond a limited range of syntactic forms are impossible. I argue that, correctly understood, Kant's conception of analyticity allows for (...)
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  41. W. Stegmaier (1980). Kant Theory of Natural-Science. Philosophisches Jahrbuch 87 (2):363-377.
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  42. S. G. Sterrett (2003). POTTER, M.-Reason's Nearest Kin. Philosophical Books 44 (3):294-294.
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  43. Tuomo Suntola (2001). New Cosmology Model Shows Relativity in Universal Time and Distant Observations in Euclidean Geometry. Apeiron 8 (3):97.
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  44. Daniel Sutherland (2014). Kant on the Construction and Composition of Motion in the Phoronomy. Canadian Journal of Philosophy 44 (5-6):686-718.
    This paper examines the role of Kant's theory of mathematical cognition in his phoronomy, his pure doctrine of motion. I argue that Kant's account of how we can construct the composition of motion rests on the construction of extended intervals of space and time, and the representation of the identity of the part–whole relations the construction of these intervals allow. Furthermore, the construction of instantaneous velocities and their composition also rests on the representation of extended intervals of space and time, (...)
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  45. Daniel Ludwig Sutherland (1998). The Role of Intuition in Kant's Philosophy of Mathematics and Theory of Magnitudes. Dissertation, University of California, Los Angeles
    The way in which mathematics relates to experience has deeply engaged philosophers from the scientific revolution to the present. It has strongly influenced their views on epistemology, mathematics, science, and the nature of reality. Kant's views on the nature of mathematics and its relation to experience both influence and are influenced by his epistemology, and in particular the distinction Kant draws between concepts and intuitions. My dissertation contributes to clarifying the role of intuition in Kant's theory of mathematical cognition. It (...)
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  46. Karel Svoboda (1954). Bolzanova Estetika = Bolzanos Ästhetik / Karel Svoboda. Nakl. Csav.
  47. Thomas Kaehao Swing (1971). Kant's Transcendental Logic. Philosophical Review 80 (3):403-407.
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  48. Robert Theis (1983). Science et métaphysique. Une relecture de Kant (II). Filosofia Oggi 6 (3):331-356.
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  49. Robert Theis (1982). Science et métaphysique. Une relecture de Kant (I). Filosofia Oggi 5 (3):343-352.
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  50. Claude Therien (2010). Aesthetic Judgment Under the Pressure of Modern Life Following Simmel and Valery. Revue Philosophique De Louvain 108 (4):639-661.
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