Oct 10, 2012

Elegi Menggapai 'Kant's Philosophy of Mathematics'


By Marsigit


Kant’s philosophy of mathematics plays a crucial role in his critical philosophy, and a clear understanding of his notion of mathematical construction would do much to elucidate his general epistemology. Friedman M. in Shabel L. insists that Kant’s philosophical achievement consists precisely in the depth and acuity of his insight into the state of the mathematical exact sciences as he found them, and, although these sciences have radically changed in ways, this circumstance in no way diminishes Kant’s achievements. Friedman M further indicates that the highly motivation to uncover Kant’s philosophy of mathematics comes from the fact that Kant was deeply immersed in the textbook mathematics of the eighteenth century. Since Kant’s philosophy of mathematics was developed relative to a specific body of mathematical practice quite distinct from that which currently obtains, our reading of Kant must not ignore the dissonance between the ontology and methodology of eighteenth- and twentieth-century mathematics. The description of Kant’s philosophy of mathematics involves the discussion of Kant’s perception on the basis validity of mathematical knowledge which consists of arithmetical knowledge and geometrical knowledge. It also needs to elaborate Kant perception on mathematical judgment and on the construction of mathematical concepts and cognition as well as on mathematical method.
Some writers may perceive that Kant’s philosophy of mathematics consists of philosophy of geometry, bridging from his theory of space to his doctrine of transcendental idealism, which is parallel with the philosophy of arithmetic and algebra. However, it was suggested that Kant’s philosophy of mathematics would account for the construction in intuition of all mathematical concepts, not just the obviously constructible concepts of Euclidean geometry. Attention to his back ground will provide facilitates a strong reading of Kant’s philosophy of mathematics which is historically accurate and well motivated by Kant’s own text. The argument from geometry exemplifies a synthetic argument that reasons progressively from a theory of space as pure intuition. Palmquist S.P. (2004) denotes that in the light of Kant’s philosophy of mathematics, there is a new trend in the philosophy of mathematics i.e. the trend away from any attempt to give definitive statements as to what mathematics is.

References:
Shabel, L., 1998, “ Kant on the ‘Symbolic Construction’ of Mathematical Concepts”, Pergamon Studies in History and Philosophy of Science , Vol. 29, No. 4, p. 592
2In Shabel, L., 1998, “ Kant on the ‘Symbolic Construction’ of Mathematical Concepts”, Pergamon Studies in History and Philosophy of Science , Vol. 29, No. 4, p. 595
3 Shabel, L., 1998, “ Kant on the ‘Symbolic Construction’ of Mathematical Concepts”, Pergamon Studies in History and Philosophy of Science , Vol. 29, No. 4, p. 617

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