By : Dr. Marsigit, M.A
Reviewed by : Nurmanita Prima Rahmawati (Pendidika Matematika Subsidi ‘09/ 09301241014 http://nurmanitaprima.blogspot.com)
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 stated that what was accomplished Kant has given the depth and accuracy of the mathematical basis, and therefore the achievement can not be ignored.
According to Kant, mathematics should dipahamai and constructed using pure intuition, that intuition "space" and "time". Mathematical concepts and decisions that are "synthetic a priori" will cause the natural sciences had become dependent on mathematics in explaining and predicting natural phenomena. According to him, mathematics can be understood through intuition sensing, as long as the results can be adapted to our pure intuition.
Kant's view about the role of intuition in mathematics has provided a clear picture of the foundation, structure and mathematical truth. Moreover, if we learn more 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 intutionism philosophy and constructivism .
According to Kant, arithmetic and geometry is a discipline that is synthetic and independent from one another. In one of his works, he concluded that mathematical truths are synthetic a priori truths. Logic of truth and the truth is revealed only through the definition, then can the truth that is analytic. Truth is intuitive analytic a priori. But the truth of mathematics as synthetic truth is a construction of a concept or several concepts that generate new information. If the concept is derived purely from empirical data then the verdict was the verdict obtained a posteriori. Synthesis derived from pure intuition a priori decision produces.
According to Kant, intuition and decisions that are "synthetic a priori" applies to geometry and arithmetic. The concept of geometry is "intuitive spatial" and the concept of arithmetic are "intuitive time" and "numbers", and both are "innate intuitions". With the concept of intuition, he suggests that mathematics also requires empirical data is that the mathematical properties can be found through intuition sensing, but the human mind can not reveal the nature of mathematics as "noumena" but only revealed as a "phenomenon".
Kant gives a small contribution for a middle way that mathematics is synthetic a priori decision, the decision which first obtained a priori from the experience, but the concept is not obtained, but rather a purely empirical. Knowledge of geometry is synthetic a priori be possible if and only if understood in a transcendental concept of spatial and generate a priori intuition.
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