By :Marsigit, M.A
Reviewed by :SitiNuruniyah/09301241023
According to Kant, the construction and understanding of mathematic is obtained by first finding "pure intuition" in the mind. Mathematics that are "synthetic a priori" can be constructed through the three stages of intuition, that" intuition sensing "," intuitive sense ", and" intuition mind ". Mathematics is a reasoning that is constructed concepts synthetic a priori in concepts of space and time. Pure intuition is the foundation of all reasoning and decision mathematics. Pure mathematics, especially geometry can be objective reality when it comes to sensing objects. 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 a priori intuition not rely on the existence of the object.
Kant also argues that the propositions of arithmetic should be synthetic in order to obtain new concepts. If only rely on the analytical method, then it will not be obtained for new concepts. For example, if seen from the structure of the sentence, the statement "2 + 3 = 5" has "2 +3" as the subject and "5" as a predicate. Concepts contained in the predicate of the concept of five, not contained in the concept of "2 +3", namely that the subject does not contain predicate. This is according to Kant as synthetic principle in arithmetic. According to Kant, the concept of numbers in arithmetic obtained by the intuition of time. On the sum 2 + 3, 2 must precede the representation of representation 3, and 2 +3 precedes representation 5. To prove that 2 + 3 = 5, according to Kant, we must pay attention to what happened. Currently, given 2, as then administered 3 and the next moment again proved the result 5. Thus the concept of arithmetic found in the construction sequence of steps in the intuition of time. Kant's intuition connecting arithmetic with time as a form of "inner intuition", in order to obtain that intuition of time causes the concept of numbers became concrete in accordance with the empirical experience.
Intuition in Geometry, according to Kant, on the steps to prove that 2 is konkruen geometry, then the intuition that there must be a priori, and the steps are synthetic. If not, then acquired the concept and not merely empirical certainty apodiktik be obtained, namely that the procedure of proof is not clear. geometry is the science which determines the spatial properties of a synthetic but a priori.
Intuition in Decision Mathematics. According to Kant, the mind and intuition, the ratio held argument (mathematics) and combine the decisions (mathematics), namely awareness of the nature of complex cognition that have characteristics associated with the objects of mathematics, either through intuition or through the concept, encompassing both the concept of mathematical concepts on the subject and predicate, is a pure reason in accordance with pure logical principle, involving the laws of mathematics are constructed by intuition, and declare the truth value of a mathematical proposition. According to Kant, all decisions are a function of representation. "All Fs are Gs" is a decision that is universal. "F is G" is a singular decision. "Fs are Gs" is an affirmative decision. "There are no Fs are Gs", is a negative verdict. "Fs are non-Gs" was the verdict of infinite. According to Kant, all synthetic and the decision shall be based on intuition. So the truth of mathematics is not a truth of logic or truth or truth-based analytic concepts of truth but that is synthetic or truth based on intuition.