PERAN
INTUISI DALAM MATEMATIKA MENURUT IMMANUEL KANT
By: Dr. Marsigit, M.A
By: Dr. Marsigit, M.A
Reviewed by: Seto
Marsudi (09301241009)
Mathematics
Education Regular 2009
(http://rasamalaempat.blogspot.com/)
(http://rasamalaempat.blogspot.com/)
Kant's view of
mathematics can contribute significantly in terms of the philosophy of
mathematics, especially about the role of intuition and the construction of
mathematical concepts. Kant
concludes that mathematics that arithmetic and geometry is a discipline that is
synthetic and independent from one another. According
to Kant (Wilder, RL, 1952), mathematics should be conceived and constructed
using pure intuition, that intuition "space" and "time".
Kant concluded that mathematical truths are synthetic a priori truths. Truths of logic and truths which are revealed only through the definition is the truth which is analytic. Analytic truth is a priori intuitive. But, the truth of mathematics as synthetic truth is a construction of a concept or several concepts that generate new information. If the pure concept is derived from empirical data then the verdict obtained is the verdict of a posteriori. Synthesis which is derived from pure intuition results decision. a priori.
According to Kant (Kant, I, 1783), a concept of numbers in arithmetic obtained by the intuition of time. On the sum of 2 + 3, representation of 2 must precede the representation of 3, and 2 +3 precedes representation of 5. To prove that 2 + 3 = 5, according to Kant, we must pay attention to what happened. Currently, given 2, as then given 3 and the next moment again proved the result is 5. Thus the concept of arithmetic found in the sequence of steps in the intuition of time.
Kant (ibid.), argues that the geometry should be based on pure spatial intuition. In his Prolegomena, Kant describes the inference of geometry in everyday life that the left hand is not congruent with right hand. According to Kant, the concept of "hand" here is not adequately understood only by empirical intuition, but in an empirical intuition contained abstract concept of "hand" and the concept of "no congruent" synthetically derived. According to Kant, this process can be applied to understand the concepts of geometry.
Kant concluded that intuition and decisions that are "synthetic a priori” applies to both 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 wants to show that mathematics also requires empirical data that the mathematical properties can be found through intuitive sensing, but human reason can not reveal the nature of mathematics as "noumena" but only revealed as a "phenomenon".
Kant contributed for giving a middle way that mathematics is synthetic a priori, the decision which first obtained a priori from the experience, but the concept is not obtained, but a purely empirical. Knowledge of geometry which is synthetic a priori be possible if and only if understood in a transcendental concept of spatial and generate a priori intuition.
Kant concluded that mathematical truths are synthetic a priori truths. Truths of logic and truths which are revealed only through the definition is the truth which is analytic. Analytic truth is a priori intuitive. But, the truth of mathematics as synthetic truth is a construction of a concept or several concepts that generate new information. If the pure concept is derived from empirical data then the verdict obtained is the verdict of a posteriori. Synthesis which is derived from pure intuition results decision. a priori.
According to Kant (Kant, I, 1783), a concept of numbers in arithmetic obtained by the intuition of time. On the sum of 2 + 3, representation of 2 must precede the representation of 3, and 2 +3 precedes representation of 5. To prove that 2 + 3 = 5, according to Kant, we must pay attention to what happened. Currently, given 2, as then given 3 and the next moment again proved the result is 5. Thus the concept of arithmetic found in the sequence of steps in the intuition of time.
Kant (ibid.), argues that the geometry should be based on pure spatial intuition. In his Prolegomena, Kant describes the inference of geometry in everyday life that the left hand is not congruent with right hand. According to Kant, the concept of "hand" here is not adequately understood only by empirical intuition, but in an empirical intuition contained abstract concept of "hand" and the concept of "no congruent" synthetically derived. According to Kant, this process can be applied to understand the concepts of geometry.
Kant concluded that intuition and decisions that are "synthetic a priori” applies to both 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 wants to show that mathematics also requires empirical data that the mathematical properties can be found through intuitive sensing, but human reason can not reveal the nature of mathematics as "noumena" but only revealed as a "phenomenon".
Kant contributed for giving a middle way that mathematics is synthetic a priori, the decision which first obtained a priori from the experience, but the concept is not obtained, but a purely empirical. Knowledge of geometry which 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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