By Dr.Marsigit,MA
According to Immanuel Kant, mathematics as a science is possible if the mathematical concept of spatial and constructed based on the intuition of time. 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 mention that what Kant achieved has given depth and accuracy of the mathematical basic, and therefore the achievement can’t be ignored.
Kant's view about the role of intuition in mathematics has provided a clear picture of the foundation, structure and mathematical truth. If we learn more about knowledge of Kant's theory, in which dominated the discussion about the role and position of intuition, then we will also get an overview of the development of mathematical foundation from Plato to the contemporary philosophy of mathematics, through the common thread intuitionism philosophy and constructivism .
According to Kant, mathematics is a logical construct adjective as concepts are synthetic a priori in concepts of space and time. Therefore, Kant argues that mathematics is built on the intuition of pure intuition of space and time in which mathematical concepts can be constructed synthetically. Pure intuition is the foundation of all reasoning and decision mathematics.
Kant 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. While Kant, argues that the geometry should be based on pure spatial intuition. If the concepts of geometry was to eliminate the concepts of empirical or sensing, the concept of space and time would still remain; namely that the concepts of geometry are a priori.
Decision mathematics is the awareness that complex cognition that have the characteristics: a) relating to the objects of mathematics, either directly (through intuition) or indirectly (through concepts), b) include both mathematical concepts and the concepts entirely on predicate subjects, c) is a pure reasoning in accordance with pure logic, d) involve the laws of mathematics are constructed by intuition, and e) state the truth value of a mathematical proposition. Kant concluded that the mathematics of arithmetic and geometry is a discipline that is synthetic and independent from one another.
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