What is Kantian Philosophy of Mathematics? An Overview of Contemporary Studies
... Reappraisal. In: C. J. Posy and O. Rechter, ed. 2020. Kant’s Philosophy of Mathematics; Volume I: The Critical Philosophy and Its Roots. Cambridge: Cambridge University Press, pp. 103-125.
Carson, E., 1997. Kant on Intuition in Geometry. Canadian Journal of Philosophy, 27(4), pp. 489-512.
Carson, E., 2009. Hintikka on Kant’s mathematical method. Revue Internationale de Philosophie, 250(4), pp. 435-449.
Carson, E., 2020. Arithmetic and the Conditions of Possible Experience In: C. J. Posy, O. Rechter, ed. 2020. Kant’s Philosophy of Mathematics; Volume I: The Critical Philosophy and Its Roots. Cambridge: Cambridge University ...
Kant and new mathematics 100 years later
Cassirer’s critique of Russell’s philosophy of mathematics and the Neo-Kantian philosophy of science and mathematics as a whole is of special relevance in the context of modern mathematics and mathematical physics. The fact that the modern standard axiomatic architecture of mathematical theories does ...
A transcendental analysis of mathematics: The constructive nature of mathematics
Kant’s transcendental philosophy (transcendentalism) focuses on both the human method of cognition in general [CPR, B 25] and certain types of cognition aimed at justifying their objective significance. This article aims to explicate Kant’s understanding (resp. justification) of the abstract nature of mathematical knowledge (cognition) as the “construction of concepts in intuition” (see: “to construct a concept means to exhibit a priori the intuition corresponding to it”; [CPR, A 713/В 741], which is “thoroughly grounded on definitions, ...
A transcendental analysis of mathematics: The abstract nature of mathematical knowledge
.... Benacerraf, P. 1965, What Numbers Could not Be // The Philosophical Review, vol. 74, № 1.27. Beth, E. 1965, Mathematical Thought. Dordrecht.28. Burgess, J., Rosen, G. 1999, Subject with No Object.29. Field, H. 1980, Science without Numbers: a Defense of Nominalism. Oxford.30. Field, H. 1989, Realism, Mathematics and Modality. Oxford.31. Frege, G. 1892, Uber Sinn und Bedeutung // Zeitschrift fur Philosophie und philosophische Kritik, Leipzig.32. Hanna, R. 2001, Kant and the Foundations of Analytic Philosophy, Oxford.33. Hanna, R. 2001, Kant in the XX century. URL: http://spot.colorado.edu/~ rhanna/kant_in_the_twentieth_century_proofs_dec07.pdf34....
Kant, Gödel, and the problem of synthetic a priori judgements
Debates over Kant’s famous postulate about the existence of synthetic a priori judgements in mathematics, formulated in the Critique of Pure Reason, have been raging for over two centuries. On the one hand, it was fiercely criticised by neo-positivists in the early 20th century. On the other hand, Kant’s ideas on constructive nature of mathematics ...
Analytic philosophy: a historico-critical survey
1. Austin J. L. Ifs and Cans // Proceedings of the British Academy. 1956. Vol. 42.
2. Black M. Relations between Logical Positivism ... ... Logical Point of View. Cambridge (Mass.), 1953.
15. Ramsey F. P. The Foundations of Mathematics and Other Logical Essays. L., 1931.
16. Ramsey F. P. Notes on Philosophy... ...
23. Russell B. My Philosophical Development. L., 1959.
24. Schlick M. Die Wende der Philosophie // Erkenntnis. 1929. Vol. 1.
25. Schlick M. Philosophical Papers / ed....
Kant’s transcendentalism and concept of the thing in itself
... philosophy (transcendentalism) and its central concept — the thing in itself is the kind of concept without which it is impossible to enter Kant’s philosophy (a paraphrase... ... Themselves and Appearances: Intentionality and Reality, Archiv für Geschichte der Philosophie, vol. 61 (1979), p. 293—308.
5. Aquila, R. 1983, Representational Mind:... ... (matematicheskie) ob"ekty, konstrukcii i dokazatel'stva [Transcendental analysis of mathematical activity: abstract (mathematical) objects, structures and proofs], in:...
Transzendentalphilosophie als kritische Bestimmung des Standpunkts. Eine wissenschaftstheoretische Annäherung
Both the categories and principles of understanding as well as the ideas and principles of reason build transcendental ... ... Engelhard, Hg. 2004. Warum Kant heute? Systematische Bedeutung und Rezeption seiner Philosophie in der Gegenwart. Berlin: De Gruyter, S. 328-351.
Brandt, R., 2003. Universität... ... Science. Dordrecht: Reidel, pp. 201-235.
Kitcher, Ph., 1992. Kant’s Philosophy of Mathematics. In: C. J. Posy, Hg. 1992. Kant’s Philosophy of Mathematics. Modern Essays...
The metaphysics of science
A reflection on the meaning of Kant’s manuscript where he uses the expression ‘metaphysics of science’. 20th century philosophy of science acknowledged ... ... science, which can be only of metaphysical nature. The experience of building a system of transcendental metaphysics combined with mathematics and physics shows that philosophy of science is necessary for solving the most important problems of the humanity ...
Analytic Philosophy: a Historico-Critical Survey
1. Austin, 1956: Austin J. L. Ifs and C ans // Proceedings of the British Academy. 1956. Vol. 42.
2. Black, 1940: Black M. Relations between Logical ... ... : Harvard University Press, 1953.
15. Ramsey,1931: Ramsey F. P. The Foundations of Mathematics and Other Logical Essays. L. : Kegal Paul, Trench, Trübner & Co., 1931... ... Development. L. : Allen & Unwin, 1959.
24. Schlick, 1929: Schlick M. Die Wende der philosophie // Erkenntnis. 1929. Vol. 1.
25. Schlick, 1979: Schlick M. Philosophical...
Condorcet interpretation of probability’s theory: the use of a mathematical construct to the field of social action
Probability theory, which emerged as early as the 17th century thanks to the works of Pascal and Fermat, served for a long time as a tool of professional mathematicians.... ... basis for the theory of social choice. However, Condorcet’s ideas on the limits of mathematical constructs’ application in social and moral sciences opened up opportunities... ... Ch., Oeuvres complètes, Oxford, Voltaire Foundation.
18. Picavet, Fr. 1888, La philosophie de Kant en France de 1773 à 1814, Paris, Alcan.
19. Rashed, R. 1974...
Kant’s transcendentalism as a transcendental paradigm of philo¬so¬phiz¬ing
This paper considers Kant’s transcendental philosophy as a special transcendental paradigm (a special type of philosophical research) differing from both the "objective" metaphysics of Antiquity and the "subjective" ... ... matematicheskoy deiatel'nosti: abstraktnye (matematicheskie) ob'ekty, konstrukcii i dokazatel'stva [Transcendental analysisof mathematics: abstract (mathematical) objects, constructions and proofs], Dokazatel'stvo: ochevidnost', dostovernost' i ubeditel'nost' ...
... Marburger Neukantianismus in Quellen. Basel; Stuttgart, 1986.
28. Jegelka N. Paul Natorp: Philosophie, Pädagogik, Politik. Würzburg, 1992. (Epistemata: Reihe Philosophie; Bd... ... Verlagsgeselschaft,1912. S. 143—146.
70. Saltzman J. D. Paul Natorp’s Philosophy of Religion within the Marburg Neokantian Tradition / Preface by W. H. Capps. Hildesheim;... ... estestvoznanija. (Szhatoje posobije k lekcijam) [Logic. Substantiation and logicalconstruction of mathematics and mathematical natural science]. Translated by V. A. Radzievskij with...
J. N. Tetens’s ‘transcendental philosophy’ as a basic science¬ and criti¬cal propaedeutics to metaphysics
... Speculative Philosophy, J. N. Tetens sets out to justify the possibility and necessity of metaphysics as a general speculative science. His primary objective is to defend... ... of the corporeal’ dealing with the things corporealand their properties (physics, mathematics, etc.). Both branches of metaphysics require a common basic science, which... ... Philosophietradition // Ernst Platner (1744—1818): Konstellationen der Aufklärung zwischen Philosophie, Medizin und Anthropologie/ Naschert G., Stiening G. (Hrsg.). Hamburg, 2007...
The central philosophical conception of the creator of logical algebra: On the bicentenary of George Boole
The article considers the history of George Boole’s main philosophical conception consisting in using his logical-algebraic and theoretical-probabilistic methods ... ... обращения: 15.10.2015).
2. Boole M. E. Collected works : in 4 vols. / ed. by E. M. Cobham. L., 1931. Vol. 2.
3. Boole G. The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning. Cambridge ; L., 1847.
4. Boole G. An ...
I. Kant and J. Jungius: on the development of critical tradition in the 17th century German philosophy
This article presents a comparative analysis of the “critical programmes” of Joachim Jungius and I. Kant. J. Jungius’s “criticism” is characterised as methodological,... ... is aimed against the critique of reasoning and is of logical nature. However, according to Jungius, it is not traditional but mathematical logic — which he interprets inthe manner of constructivism — that should be the instrument of critique. Traditional ...
Dilemmas of logical hylomorphism
Logical hylomorphism considers logic as a theory of formal relations. However, it is difficult to give a precise definition of these relations due to a multitude of interpretations ... ... interpretations. Dordrecht, Boston, 1974. Р. 85—132.
16. Dragalina-Chernaya E. Logical hylomorphism revisited // Philosophy, Mathematics, Linguistics: Aspects of Interaction 2014 (PhML-2014). St. Petersburg, 2014. P. 6—11.
17. Dutilh Novaes С. The ...
Kant’s Asynchronicity Concerning Newtonian Space and Gravity in his Pre-Critical Writings
... that takes place in Kant’s struggle with the central Newtonian concepts. Newtonian space and gravity, in revised form, are of central concern to Kant’s critical philosophy. But Kant adapted and re-evaluated these two concepts in an asynchronous way.... ... III. Edited by H. Turnbull, J. Scott, A. Hall [a.o.]. Cambridge: Cambridge University Press.
Newton, I., 1999. The Principia. Mathematical Principles of Natural Philosophy. Translated by I. B. Cohen and A. Whitman. Berkeley: University of California Press....
Kantian motives in logic and philosophy of science. Idea of Unity of a priory and empirical knowledge
Kant insisted on the inherent unity of a priori and empirical elements of cognition. To what extent further progress of philosophy and exact sciences confirmed (or ... ... inclined to judge that apriorism in its modest version do not contradict to modest type of empiricism. Real practice of logical and mathematical reasoning provides pry conjunctions of a priori and empirical elements of cognitive processes. We can find their ...
The transcendental theory of experience and modern philoso¬phy of science
This article sets out to develop a transcendental theory of science based on the original interpretation and modern development of Kant’s transcendentalism (theory of experience). The ... ..., Kant’s theory of experience, philosophy of science, indirect phenomenon, Copernican revolution, transcendental theory of mathematics and physics.
Katrechko S. L.
Kantian motives in logic and philosophy of science. The idea of unity of a priory and empirical elements of cognition
Kant insisted on the inherent unity of a priori and empirical elements of cognition. To what extent further progress of philosophy and exact sciences confirmed (or ... ... to judge that apriorism in its modest version does not contradict a modest type of empiricism. Real practice of logical and mathematical reasoning provides pry conjunctions of a priori and empirical elements of cognitive processes. We can find the harmonic ...
Events as a semantic framework for the construction of reality: the prospects of a transition to a dynamic ontology
Events are the main element in the formation and presentation of a worldview across all the research disciplines in the humanities and other sciences. Cognising and understanding reality requires ... ... into account the temporal factor in the development of reality. The second problem concerns the development of theoretical (mathematical) tools to describe such dynamics. In this connection, we identify the mathematical semantics of event processes. ...
Problems of analytic and synthetic propositions in the history of logic
Certain historical facts relating to the history of discussions on the nature of analytic and synthetic propositions in logic are used to demonstrates that the interpretation ... ... системы, 172). Новосибирск, 2002.
15. Blake Ch. N. O. Lossky. Analytic and synthetic propositions and mathematical logic. N. Y. : International Universities Press, Inc., 1953, 16 p. // The Journal of Symbolic Logic. 1954. Vol. 19,...
Similarities and differences in curricula of a bachelor’s degree in oceanology at the universities in St Petersburg, Klaipeda, and Kaliningrad
Conducting a multi-aspect comparative analysis of curricula of bachelor’s degree programmes in oceanology offered at universities in St Petersburg, Klaipeda and Kaliningrad,... ... practices. The clustering of competence modules and disciplines at each university within generalised academic areas — physics and mathematics, philosophy, informatics and computers, geoecology, measurement disciplines, etc. — made a more detailed comparison ...
Kant, Radical Agnosticism, and Methodological Eliminativism about Things-in-Themselves
... recent paper, “Things in Themselves: An Interim Report,” Robert Howell says that a philosophically satisfactory resolution of all-too-familiar problems about Kant’s views on the object of knowledge and the nature of things-in-themselves should meet ... ... 1872—1921. Volume 1. N. Y.
10. Russell, B. 1959, My Philosophical Development. London.
11. Russell, B. 1996, Principles of Mathematics. 2nd ed. N. Y.
Kant, metaphysics, epistemology, transcendental idealism, things in themselves, radical agnosticism,...
The Pythagorean-mathematical component of P. A. Florensky’s social philosophy
This article considers the amalgamation of N. Bugaev’s arrythmology and G. Leibnitz’s monadology supplemented by G. Cantor’s set theory as the methodological basis ... ... “social engineer” who develops the concept of a good state, whereas the human being serves as material for this social and mathematical structure.
1. Андроник (Трубачев), иеродиакон. К 100-летию со дня рождения ...
Theoretical analysis of fuzzy logic and Q. E. method in economics
This paper analyzes the key elements of fuzzy logic and showes that through rational, behavioral economics and neo-classical economics it is possible to develop ... ... Systems. 2015. Vol. 281. P. 32—43. doi:
19. Verdegay J. L. Progress on Fuzzy Mathematical Programming: A personal perspective // Fuzzy Sets and Systems. 2015. Vol. 281. P. 219—226. doi: https:// doi....
OPOIAZ and Bakhtin: the Decision Science’s perspective
Decision science is a relatively new discipline: the product of a cross-pollination among mathematics, psychology, economy and a few other branches of knowledge. It studies how humans make their choices and purports to provide a “rational framework for choosing between alternative courses of action when the consequences resulting from ...