PERAN INTUISI DALAM MATEMATIKA MENURUT IMMANUEL KANT

PERAN INTUISI DALAM MATEMATIKA

MENURUT IMMANUEL KANT

 by Marsigit

Reviewed by Khilmi Nur Ma’rifah

Immanuel Kant said that mathematics was not developed only with the concept of a posteriori empirical. But the empirical data obtained from sensing experience necessary to explore mathematical concepts that a priori the intuition-based construction of mathematical concepts of space and time. This is what makes mathematics as a science. Because if the mathematics developed just analytic methods will not be generated (constructed) a new concept, and thus will cause the math is just as science fiction.

With his theory, Kant tried to give a solution (compromise) of extreme conflict between rationalists and empiricists in building the foundation of mathematics. Intuition into the core and key to the understanding and construction of mathematics.

Michael Friedman (Shabel, L., 1998) mention that what Kant accomplished has given the depth and accuracy of the mathematical basis, and therefore its achievement can not be ignored. In the ontology and epistemology, after the era of Kant, mathematics has been developed with these approaches more or less influenced by Kant's view.
Kant argues that mathematics is built on pure intuition is intuition of space and time in which mathematical concepts can be constructed synthetically. Pure intuition (Kant, I, 1783) is the foundation of all reasoning and decision mathematics. If not then the reasoning is based on pure intuition is not possible.

Pure mathematics (ibid.), in particular the geometry can be objective reality when it comes to sensing objects. Concepts of geometry are not produced only by pure intuition, but also related to the concept of space in which objects are represented geometry. The concept of space (ibid.) is itself a form of intuition in which the ontological essence of representation can not be tracked.
Intuition sensing itself is a representation which depends on the existence of the object. So it seems impossible to find such a priori intuition, because intusi a priori not rely on the existence of the object.

Intuition in Arithmetic

Kant (Kant, I., 1787) argues that the propositions of arithmetic should be synthetic in order to obtain new concepts. If you rely solely on the analytical method, 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 obtain a new concept apart from the already mentioned it, and it certainly 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 5; and thus it must be synthetic.
Intuition in Geometry

While Kant (Kant, I, 1783), argues that the geometry should be based on pure spatial intuition. If the concepts of geometry get rid of our empirical concepts or sensing, the concept of the concept of space and time would still remain; namely that the concepts of geometry are a priori. But Kant (ibid.) emphasizes that, as in mathematics in general, the concepts of geometry will only 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.

Intuition in Decision Mathematics

According to Kant, the ability to take a decision to be "innate" 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 menentukn types of decisions.