By Marsigit
Reviewed by Siti Subekti
According to Kant, mathematics should be understood and constructed using pure intuition, intuition "space" and "time". Mathematical concepts and decision is "synthetic a priori" will cause the natural sciences into depends on mathematics in explaining and predicting phenomena. His mathematics can be understood through "intuition sensing", as long as the results can be customized with pure intuition. While understanding or construction with how to find the "pure intuition" in any sense or our mind.
Mathematics is "synthetic a priori" can be constructed through a 3 stage of intuition, intuition sensory perception, intuition advice, and intuition character. intuition sensory perception is associated with object in mathematics that can be absorbed as a posteriori elements. Sense intuition (Verstand) synthesis the result of intuition sensory perception into the intuition of "space" and "time". With intuition character (Vernuft), the ratio we are faced on the rulings of mathematical arguments.
Kant argued that propositions arithmetic should be analytic, so that instead of synthetic obtained new concepts. If we simply call the "1" as the natural numbers, then it is analytic. But if 2+3 = 5, then it is synthetic. By intuition 2 and 3 are different concepts and 5 is another concept anyway. So 2+3 has produced a new concept that is 5. Moreover, in addition 2+3, representation 2 precede representation 3, and representation 2+3 precede representation 5 so that in the preceding representation in arithmetic there is also the intuition of time.
Meanwhile, the geometry should be based on pure intuition is spatially. If empirical concepts or sensing removed from geometric concepts, the concept of space and time remaining so that the concepts of geometry are a priori. However, the concepts of geometry would only be "synthetic a priori" If the concepts it only refers to objects that are in its sense. Therefore, the geometry is a science that determines the properties of spatially synthetically but a priori. Synthetic means that the concepts of geometry cannot be constructed only of pure concepts, but it should be pure intuition rests on that occurs before percept the object, so that its intuition is indeed is pure and not empirical.
According to Kant, by intuition character, ratio held argumentations (mathematics) and incorporates rulings (mathematics). The verdict of mathematics cognition is consciousness that is complex with regard to mathematical objects, including the concepts of mathematics, is a pure reasoning in accordance with the establisheds pure logic, involve the laws of mathematics are constructed with intuition, and declared value of the truth of a mathematical proposition.
Kant held that all mathematical verdict is synthetic and apodiktik. Such a ruling can only be obtained with the "contradiction". If it says that 1 = 1 then this is a legal identity and are analytic. But if the "2 + 1 = 3", then it is a contradiction that the verdict of the synthetic retrieved from contradiction, namely by intuition "2+1" differs from "3".
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