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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. Stephan Kramer (2011). Bolzano on the Intransparency of Content. Grazer Philosophische Studien 82 (1):189-208.
  3. A. Krause (1999). Some Remarks to the" Natural Dogmatics" by Bernard Bolzano. Filosoficky Casopis 47 (6):915-934.
  4. Manfred Kühn (2001). Kant's Teachers in the Exact Sciences. In Eric Watkins (ed.), Kant and the Sciences. Oxford University Press. 11--30.
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  5. Wolfgang Künne (1997). Propositions in Bolzano and Frege. Grazer Philosophische Studien 53:203-240.
    Bolzano's Sätze an sich and Frege's Gedanken are obviously close relatives. The paper underlines both similarities and dissimilarities between the psychological and semantical roles assigned to structured truth-evaluable contents in Bolzano's and Frege's theories. In particular, their different accounts of propositional identity are compared, and it is argued that Dummett's recent criticism of Frege's account is grist to Bolzano's mill.
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  6. Wolfgang Künne (1997). Propositions in Bolzano and Frege. Grazer Philosophische Studien 53:203-240.
    Bolzano's Sätze an sich and Frege's Gedanken are obviously close relatives. The paper underlines both similarities and dissimilarities between the psychological and semantical roles assigned to structured truth-evaluable contents in Bolzano's and Frege's theories. In particular, their different accounts of propositional identity are compared, and it is argued that Dummett's recent criticism of Frege's account is grist to Bolzano's mill.
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  7. Wolfgang Künne (1997). Propositions in Bolzano and Frege. Grazer Philosophische Studien 53:203-240.
    Bolzano's Sätze an sich and Frege's Gedanken are obviously close relatives. The paper underlines both similarities and dissimilarities between the psychological and semantical roles assigned to structured truth-evaluable contents in Bolzano's and Frege's theories. In particular, their different accounts of propositional identity are compared, and it is argued that Dummett's recent criticism of Frege's account is grist to Bolzano's mill.
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  8. Wolfgang Künne, Mark Siebel & Markus Textor (eds.) (1997). Bolzano and Analytic Philosophy. Monograph Collection (Matt - Pseudo).
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  9. L. Kvasz (2000). Epistemological Aspects of Modern Painting. Filozofia 55 (8):601-619.
    The aim of the paper is to analyse the geometrical aspects of a series of modern paintings and to show the parallel between them and the development of modern geometry. It starts with El Greco, offering a geometrical explanation of his painting the figures in a prolonged manner. Further the analogy between the impressionist way of creating space and the geometrical idea of Cayley to use projective space as a basis for non-Euclidean geometry is reconstructed. Next the paper describes the (...)
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  10. Ladislav Kvasz (1999). Prolegomena K Formálnej Epistemológii. Organon F 6 (1999):223-239.
    The aim of this paper is a philosophical generalisation of the results, which we obtained through the analysis of the development of synthetic geometry. I our papers Náčrt analytickej teórie subjektu and Topológia versus teória množín we proposed a method of analysis of the development of geometry based on Wittgensteinś Picture theory of meaning from the Tractatus. It turned out, that the concept of the form of language can be effectively used to characterise the changes, which occured in the course (...)
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  11. Sandra Lapointe (2006). Bolzano Contre Kant. Le Nouvel Anti-Kant. Vrin.
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  12. Michael P. T. Leahy (1963). Kant and the Aesthetic Judgment.
  13. Michael Levin (2005). Non-Euclidean Sex. Think 4 (10):7-20.
    Perhaps there is nothing morally wrong with homosexuality. But does that mean that those who find it abhorrent should be forced to tolerate, it? Michael Levin questions some common liberal preconceptions about homosexuality, and also responds to my own (which appeared in Issue 5 of Think).
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  14. J. Louzil (1998). Bernard Bolzano-Apologist or Heretic? Filosoficky Casopis 46 (6):895-914.
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  15. J. Louzil (1981). Ethical and Sociopolitical Views of Bolzano, B. Filosoficky Casopis 29 (6):918-932.
  16. Maja Lovrenov (2006). The Role of Invariance in Cassirer's Interpretation of the Theory of Relativity. Synthesis Philosophica 21 (2):233-241.
    The paper considers Cassirer’s account of the philosophical problems raised by the theory of relativity. The main question the paper addresses is how Cassirer, as a Neokantian, responds to the discoveries made by Einstein. The problem here is especially the presupposition of the a priori nature of Euclidean geometry. Cassirer’s answer lies in showing that Kant’s philosophy is broad enough to include also non-Euclidean geometries in the determination of the physical world. He does this by showing that though Kant conceived (...)
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  17. Andrzej Lubomirski (1988). Frege i Kant. Archiwum Historii Filozofii I Myśli Społecznej 33.
  18. L. Magnani (2001). Philosophy and Geometry. Kluwer Academic Publisher.
    The total irrelevance of absolute space to scientific observation and experiment led him early to a most radical conclusion: experience cannot teach us anything about the true structure of space; consequently, the choice of a geometry for the ...
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  19. Gottfried Martin (1985). Arithmetic and Combinatorics: Kant and His Contemporaries. Southern Illinois University Press.
    This is the only work to provide a histori­cal account of Kant’s theory of arith­metic, examining in detail the theories of both his predecessors and his successors.
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  20. Peter McLaughlin (2014). Mechanical Explanation in the “Critique of the Teleological Power of Judgment. In Eric Watkins & Ina Goy (eds.), Kant's Theory of Biology. De Gruyter. 149-166.
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  21. James A. McWilliams (1939). The Kantian Philosophy of Space. Modern Schoolman 17 (1):19-19.
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  22. Carlos Mendiola Mejía (2010). La Biología En Kant. Revista de Filosofia 42 (129):117-127.
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  23. M. Meyer (2002). From Kant to Bourdieu: An Aesthetic Renewal? Revue Internationale de Philosophie 56 (220):259-274.
  24. Nathaniel Miller (2007). Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry. Center for the Study of Language and Inf.
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  25. Graham Nerlich (1991). Hands, Knees, and Absolute Space. In James Van~Cleve & Robert E. Frederick (eds.), Journal of Philosophy. Kluwer. 151--172.
  26. Alexandra Mary Newton (2013). Kant on the Form of Aesthetic Judgment. 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. 169-180.
  27. Harry A. Nielsen (1961). Kant's Metaphysics and Theory of Science. Modern Schoolman 38 (2):164-165.
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  28. Lara Ostaric (2013). Aesthetic Judgment and the Completion of Kant’s Critical System. 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. 679-690.
  29. Stephen Palmquist (2011). The Kantian Grounding of Einstein’s Worldview: Simultaneity, Synthetic Apriority and the Mystical. Polish Journal of Philosophy 5 (1):97-116.
    Part I in this two-part series employed a perspectival interpretation to argue that Kant’s epistemology serves as the philosophical grounding for modern revolutions in science. Although Einstein read Kant at an early age and immersed himself in Kant’s philosophy throughout his early adulthood, he was reluctant to admit Kant’s influence, possibly due to personal factors relating to his cultural-political situation. This sequel argues that Einstein’s early Kant-studies would have brought to his attention the problem of simultaneity and the method of (...)
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  30. Victor Pambuccian (2000). Another Constructive Axiomatization of Euclidean Planes. Mathematical Logic Quarterly 46 (1):45-48.
    H. Tietze has proved algebraically that the geometry of uniquely determined ruler and compass constructions coincides with the geometry of ruler and set square constructions. We provide a new proof of this result via new universal axiom systems for Euclidean planes of characteristic ≠ 2 in languages containing only operation symbols.
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  31. Charles Parsons (1984). Remarks on Pure Natural Science'. In Allen W. Wood (ed.), Self and Nature in Kant's Philosophy. Cornell University Press. 216--27.
  32. Renato Pettoello (2010). Eternal Geometry: Nelson and Non-Euclidean Geometries. Rivista di Storia Della Filosofia 65 (3):483-506.
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  33. 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.
  34. Irving Polonoff (1994). Michael Friedman., Kant and the Exact Sciences. International Studies in Philosophy 26 (4):129-130.
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  35. Carl J. Posy (1992). Kant's Philosophy of Mathematics Modern Essays.
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  36. 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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  37. H. K. R. (1969). Geometry and Chronometry in Philosophical Perspective. [REVIEW] Review of Metaphysics 23 (1):130-130.
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  38. Sebastian Rand (2014). Friedman, Michael., Kant’s Construction of Nature: A Reading of the Metaphysical Foundations of Natural Science. Review of Metaphysics 67 (3):635-637.
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  39. 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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  40. 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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  41. Klaus Reich, Jane Kneller & Michael Losonsky (1994). The Completeness of Kant's Table of Judgments. Philosophical Review 103 (2):373-375.
  42. Dale Riepe (1964). K. H. Potter's "Presuppositions of India's Philosophies". [REVIEW] Philosophy and Phenomenological Research 24 (3):443.
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  43. 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.
  44. 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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  45. 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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  46. 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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  47. 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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  48. 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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  49. Frank Schalow (2009). Reinscribing the «Λογωσ» in Transcendental Logic: Kant’s Highest Principle of Synthetic Judgments Revisited. Existentia 19 (3-4):205-224.
  50. Eva Schaper (1971). SWING, Thomas Kaehao.-"Kant's Transcendental Logic". [REVIEW] Philosophy 46:75.
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