by Masigit
reviewed by Naafi Awwalunita (09301241024)
According to Kant, mathematics as a science is possible if the concept of mathematical intuition constructed based on spatial and time. Construction of mathematical concepts by intuition of space and time will come in result that mathematics as a science is "synthetic a priori". By Kant’s view, synthetic methods opposed to analytic methods and the concept of "a priori" opposed to "a posteriori". If the mathematics is developed only by the method of "analytic" it will not be generated (constructed) a new concept, and because of that, math is just as science fiction.
According to Kant, mathematics was not developed just by the concept of "a posteriori" because if so, math would be empirical. But the empirical data obtained from sensory experiences are needed to explore mathematical concepts that are "a priori". This is where the unique role of Kant's theory, which attempts to give a solution (middle) of extreme conflict between the rationalist and the empiricist in building the foundation of mathematics. According to Kant, intuition becomes the core and key to the understanding and construction of mathematics.
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 (Shabel, L., 1998) mentioned that what Kant accomplished has given the depth and accuracy of the mathematical basis, and therefore its achievement cannot be ignored. In the ontology and epistemology, after the era of Kant, mathematics has been developed with these approaches are somewhat influenced by Kant's view.
Some authors argue that Kant's philosophy of geometry to depart from the bridge to the philosophy of arithmetic and algebra philosophy. But if you listened further, the views of Kant's prefer to basic on the role of intuition for the concepts of mathematics and only rely on the concept of construction as in Euclidean geometry. There was the view that the construction of spatial concepts of Euclidean geometry is actually based on "pure intuition" but Kant gave a new trend on the view of mathematics a more constructive (Palmquist, SP, 2004).
According to Kant (Wilder, RL, 1952), mathematics must understood 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 to explain and predict natural phenomena. According to him, mathematics can be understood through "sensing intuition", as long as the results can be customized with 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 we will also get an overview of the development of mathematical foundation of the philosophy of Plato to contemporary mathematics, through the common thread of philosophy and constructivism intuitionism.
Kant (Randall, A., 1998) concluded that the mathematics of arithmetic and geometry is a discipline that is synthetic and independent from one another. In his work The Critique of Pure Reason and the Prolegomena to Any Future Metaphysics, Kant (ibid.) concluded that mathematical truths are synthetic a priori truths. Truths of logic and truth are revealed only through the definition of the truth of which is analytic.
Truth can be 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 obtained then the verdict was the verdict of a posteriori. Synthesis derived from pure intuition a priori result in a decision. Kant (Wegner, P.) concluded that intuition and decisions that are "synthetic a priori 'applies to geometry and arithmetic. The concept of geometry is "intuitive spatial" and arithmetic concepts are "intuitive time" and "numbers", and both are "innate intuitions". With the concept of intuition, Kant (Posy, C., 1992) wanted to show that mathematics also requires empirical data is that the mathematical properties can be found through
sensing intuition, but human reason can not reveal the nature of mathematics as "noumena" but only revealed as a "phenomenon".
Kant has an important contribution because his theory gives 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 by empirical (Kant, I, 1783), but rather pure. 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.
Tidak ada komentar:
Posting Komentar