PERAN INTUISI DALAM MATEMATIKA MENURUT IMMANUEL KANT

Concluding Remark

Kant contributes significantly in terms from the philosophy of mathematics, especially for the role of intuition and concept construction mathematics. 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. Kant tried to give a solution of extreme conflict between rationalists and empiricists in building the foundation of mathematics.
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’t 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 intuity a priori not rely on the existence of the object.
1. 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.
2. Intuition in Geometry
Kant argues that the geometry should be based on the concept of pure spatial intuition. Concepts of geometry are not only constructed with pure concepts, but also based on pure intuition so as to produce pure results. For example in proving the 2 pieces of geometry are mutually congruent. Concept used in proving the need to use a synthetic step. Because if you do not use synthetic step that it will produce evidence that is not clear.
3. Intuition in Mathematics Decision
According to Kant, the ability to take a decision to be "innate" and have intrinsic characteristics, structured and systematic. The structures of mathematics decision according structure of mathematics proposition are linguistic expressions. Like the others, the propositions of mathematics connect subject and predicate with a copula. Relations subject, predicate and copula type is what will determine types of decisions.