The Role of intuition in Mathematics by Immanuel Kant

By: Dr. Marsigit, M. A

Reviewed by: Hany Tri Wahyono

Kant view about mathematics so can give contribution that means in terms from the mathematics philosophy especially about the role of intuition and construction of mathematics concept. Some author argues that Kant start from geometry philosophy to bridge toward arithmetic philosophy and algebra philosophy. But if listened further, Kant views more based to intuition role for all mathematics concepts and just rely construction concept like which occurred to Euclides geometry. Kant view about the role intuition in mathematics has give image about base, structure and mathematics rightness.

From some description Kant argue that mathematics built above pure intuition that is intuition of space and time where mathematics concepts can constructed in synthesis. Sensing intuition itself is representation depend from presence object. We just can find intuition in form sensuous intuition that is based phenomena object and not based from the noumena. According to Kant intuition with the kind and variety have important role to construct mathematics at once investigate and describe how mathematics be understood in the form geometry or arithmetic.

Ability to decide is innate and has intrinsic characteristic, structured and systematic. Decision structure of mathematics appropriate with the structure of mathematics propositions linguistic expression. As other, mathematics propositions connecting the subject and predicate with copula. The relationship of subject, predicate and kind of copula that will determine the type of decision. Kant argues that all mathematics decision is synthetic and apodictic. Then through contradiction the synthetic decision obtained.

Kant (Randall, A., 1998) conclude that mathematics arithmetic and geometry is science discipline that synthetic and independent each other. Mathematics rightness is logical right and the right that derived that just through definition then to analytic. Analytic right is construction from a concept or some concept that produce new information. If pure concept derived from empiric data then conclusion that can be obtained is a posteriori. Synthesis that derived from pure intuition has result a priori. Intuition and decision synthetic a priori apply for geometry or arithmetic. Geometry concept is intuitive spatial and arithmetic concept is intuitive time, number, and that two is innate intuitions. With that intuitions concept mathematics also need empirical data that is mathematics can find through sensing intuitions, but human reason can not reveal the nature of mathematics as noumena but just reveal as phenomena.