On the Architectonic Idea of Mathematics

Document Type : Research Paper

Author

Associate Professor of Philosophy Department, Saint Peter’s University, USA

Abstract

The architectonic is key for situating Kant’s understanding of science in the coming century. For Kant the faculty of reason turns to ideas to form a complete system. The coherence of the system rests on these ideas. In contrast to technical unity which can be abstracted a posteriori, architectonic ideas are the source of a priori unity for the system of reason because they connect our reasonable pursuit to essential human ends. Given Kant’s focus on mathematics, in the architectonic and his critical philosophy more generally, we must have some sense of the architectonic idea of mathematics. In this paper, I argue for the key principles of the architectonic idea of mathematics: 1) because mathematics is grounded in a priori intuition, it is a peculiarly human activity; 2) the method of mathematics is one of a priori construction, a method only mathematics can employ and: 3) the objects of mathematics are extensive magnitudes. Given these principles, we can use the architectonic idea to have some clarity about how mathematics has dealt with historical development.

Keywords

References

Gava, G. (2014). Kant’s Definition of Science in the Architectonic of Pure Reason and the Essential Ends of Reason, Kant-Studien, 105 (3), 372-393. http://dx.doi.org/10.1515/kant-2014-0016
 Guyer, P. (2005). Kant’s System of Nature and Freedom: Selected Essays, Oxford University Press.
 Kant, I. (1999). Correspondence, Edited by A. Zweig, Cambridge University Press.
 Kant, I. (1998). The Critique of Pure Reason, Edited by P. Guyer & A. Wood, Cambridge University Press.
 Kant, I. (2014). On Kästner’s Treatises,” translated by Ch. Onof & D. Schulting, Kantian Review. 19 (2), 305-313. https://doi.org/10.1017/S1369415414000077
 Manchester, P. (2008). Kant’s Conception of Architectonic in its Philosophical Context, KantStudien, 99 (2), 133-151. http://dx.doi.org/10.1515/KANT.2008.010
Oneill, O. (1992). Vindicating Reason in Cambridge Companion to Kant, Edited by P. Guyer, Cambridge University Press.
Onof, Ch. & Schulting, D. (2015). Space as Form of Intuition and as Formal Intuition: On the Note to B160 in Kant’s Critique of Pure Reason, Philosophical Review. 124 (1), 1-58. http://dx.doi.org/10.1215/00318108-2812650
Sutherland, D. (2006). Kant on Arithmetic, Algebra and the Theory of Proportions, Journal of the History of Philosophy. 44 (4), 533-558. http://dx.doi.org/10.1353/hph.2006.0072
Send comment about this article
CAPTCHA Image
Journal of Philosophical Investigations
Volume 18, Issue 47 - Serial Number 47
Special Issue: Kant's Philosophy in the 21st Century (Summer 2024)
2024
Pages 203-218

Files

Share

How to cite

Statistics