PERAN INTUISI DALAM MATEMATIKA MENURUT IMMANUEL KANT

By: Dr. Marsigit, M.A.

Reviewed by: Fikri Hermawan

Kant's view of mathematics can contribute significantly in terms of the philosophy of mathematics, especially regarding the role of intuition and the construction of mathematical concepts. Michael Friedman (Shabel, L., 1998) mention that what Kant accomplished has given the depth and accuracy on the basis of mathematics achievement and therefore can not be ignored. In the ontology and epistemology, after the era of Kant, mathematics has been developed with the approach that is heavily influenced by Kant's view.

When seen further, Kant thought more bases to the role of intuition for the concepts of mathematics and only rely on the concept of construction as was the case in Euclidean geometry. Kant's view about the role of intuition in mathematics has provided a clear picture of the foundation, structure and mathematical truth. Moreover, if we learn more knowledge of Kant's theory, in which dominated discussion about the role and position of intuition, then we will also get an overview of the development of mathematical foundation of the philosophy of Plato to contemporary mathematics.

According to Kant (Kant, I., 1781), and the construction of mathematical understanding is obtained first discovered by pure intuition in the sense or mind. And mathematics is built on pure intuition is intuition of space and time where the concept of mathematics can be constructed synthetically. Intuition by kind and type, plays a very important to construct a mathematical as well as investigate and explain how mathematics is understood in the form of geometry or arithmatika.

Kant (Kant, I., 1787) argues that the propositions of arithmetic should be synthetic in order to obtain new concepts. If you just rely on the analytical method, then it will not be obtained for new concepts. Kant (Wilder, RL, 1952) connecting arithmetic with the intuition of time as a form of inner intuition to show that awareness of the concept of numbers includes the constituent aspects of consciousness such that the structure can be shown in order of time. So the intuition of time causes the concept of numbers became concrete in accordance with empirical experience.

While Kant (Kant, I, 1783), argues that the geometry should be based on pure spatial intuition. If the geometry of the concepts we remove the concepts of empirical or sensing, the concept of the concept of space and time would be left is that the concepts of geometry are a priori. But Kant stressed that, as in mathematics in general, the concepts of geometry is likely to be synthetic a priori if the concepts that refer only to objects that diinderanya. So in the empirical intuition of space and time are intuitions a priori.

According to Kant, is innate ability to take decisions and have intrinsic characteristics, structured and systematic. The structure of mathematical decision in accordance with the structure of mathematical propositions are linguistic expressions. Like the others, the propositions of mathematics connects subject and predicate with a copula. Relations subject, predicate and copula type is what will find types of decisions.