By : Dr. Marsigit, M.A.
Reviewed by Yustia Rahmawati (p.matswa 09 / 09301244005)
According to Kant, mathematics as a science is possible if the concept constructed based on mathematical and spatial intuition of time. According to Kant, mathematics was not developed only with the concept of a posteriori because if so math will be empirical. However, empirical data gained from experience isrequired for sensing explore the mathematical concepts that are a priori. This is where the uniquethe role of Kant's theory, which attempts to give solution (middle) of extreme conflict between the rationalist and the empiricist in build the foundation of mathematics. According to Kant, intuition becomes the core and key the understanding and construction of mathematics.
Preliminary. Kant's view of mathematics can contribute significantly in terms from the philosophy of mathematics, especially regarding the role of intuition and construction concepts of mathematics. Michael Friedman (Shabel, L., 1998) mention that what was achieved Kant has given the depth and accuracy of the mathematical foundation, and by because it's achievements can not be ignored.
Intuition as the Basis for Mathematics. According to Kant (Kant, I., 1781),, and the construction of mathematical understanding is obtained by first finding pure intuition in the sense or mind. The mathematics are synthetic a priori can be constructed through three stages of intuition ie intuition sensing, intuition is reasonable, and intuitive mind.
Intuition in Arithmetic. Kant (Kant, I., 1787) argues that the propositions of arithmetic should are synthetic in order to obtain new concepts. If you just rely on method analytic, then it will not be obtained for new concepts. If we call the "1" as the original numbers and only at the mention of it, then we do not acquire new concepts other than those referred to it, and this of course is analytic. But if we consider the sum of 2 + 3 = 5. Intuitively 2 and 3 are different concepts and 5 is the concept differently. So 2 + 3 has produced a new concept that is 5; and so of course it is synthetic.
Intuition in Geometry. While Kant (Kant, I, 1783), argues that the geometry should based on pure spatial intuition. If the geometry of the concepts we remove the empirical concepts or sensing, the concept of spatial concepts and time will still remain; namely that the concepts of geometry are a priori.
Intuition in Decision Mathematics. According to Kant, with the intuition of mind, we hold the ratio of the argument (mathematical) and combine the decisions (mathematics). Decision mathematics is awareness of the nature of complex cognition that have the characteristics: a) relating with mathematical objects, both directly (through intuition) and are not directly (through concepts), b) include both mathematical concepts and predicate concepts entirely on the subject, c) is a pure reasoning accordance with pinsip-pinsip pure logic, d) involve the laws of mathematics constructed by intuition, and e) state the value of the truth of a proposition of mathematics.
Knot. Kant (Randall, A., 1998) concluded that mathematics is arithmetic and geometry is a discipline that is synthetic and independent one with the others. In his work The Critique of Pure Reason and the Prolegomena to Any Future Metaphysics, Kant (ibid.) concludes that the truths of mathematics is a synthetic a priori truths. Truths of logic and truth are derived only through the definition of the truth of which is analytic.
Tidak ada komentar:
Posting Komentar