By : Drs. Marsigit MA
Reviewed by: Fifi Yuniarti
Intuition is very important in making a decision. Intuition is the human ability to acquire knowledge or insight without going through the reasoning first. So it is necessary to reinforce the reasons to be more accurate intuition in making decision. Intuition has a role in many sciences, including mathematics.
According to Immanuel Kant, mathematics is built on pure intuition is intuition of space and time in which mathematical concepts can be constructed synthetically. Kant's view about the role of intuition in mathematics has provided a clear picture of the foundation, structure and mathematical truth. The role of intuition in mathematics includes, as basic mathematical intuition, intuition in arithmetic, intuition in geometric, intuition in decision mathematics.
Intuition as the basis of mathematics. According to Immanuel Kant mathematics as the science might happen if we were able to find a pure intuition as its foundation. For example the concept of geometry. Concepts of geometry are not only generated by pure intuition, but also includes the concept of space in which objects are represented geometry. Understanding of mathematics as a pure intuition which includes space and time to mention that this is what mathematics might be called science.
Intuition in arithmetic. Kant argued that the propositions of arithmetic should be synthetic in order to obtain new concepts. If you rely solely on the analytical method, then it will not be obtained for new concepts. Kant's intuition connecting arithmetic with time as a form of "inner intuition" to show that awareness of the concept of numbers formation include aspects such that the structure of consciousness can be shown in order of time. So the intuition of time led to the concept of real numbers into line with empirical experience.
Intuition in geometry. Kant argues that the geometry should be based on the concept of pure spatial intuition. Concepts of geometry are not only constructed with pure concepts, but also based on pure intuition so as to produce pure results. For example in proving the 2 pieces of geometry are mutually congruent. Concept used in proving the need to use a synthetic steps. Because if you do not use synthetic steps that it will produce evidence that is not clear.
Intuition in decision mathematics. Decision of discrete mathematics, among others, related to mathematical objects directly or indirectly, is a pure reasoning which correspond to pure logic, involving mathematical law associated with intuition, and declare the value of truth in a mathematical proposition. According to Kant, the ability to take decisions are "innate" as well as having intrinsic characteristics, structured, and systematic.
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