PERAN INTUISI DALAM MATEMATIKA
MENURUT IMMANUEL KANT
Marsigit
Fakultas Matematika dan Ilmu Pengethuan Alam,
Universitas Negeri Yogyakarta
Reviewed by: Felisitas Sayekti Purnama U (09301241007)
Student of Mathematics Education 2009 in Yogyakarta State University
(http://felisitassayekti.blogspot.com)
Student of Mathematics Education 2009 in Yogyakarta State University
(http://felisitassayekti.blogspot.com)
Immanuel Kant is well-known mathematical figure. He expressed his views about mathematics from the philosophy of mathematics. Kant's view about the role of intuition and the construction of mathematical concepts. According to Kant, mathematics should be conceived and constructed using pure intuition, that intuition "space" and "time". Mathematical concepts and decisions that are synthetic a priori will lead to natural science was dependent on mathematics to explain and predict natural phenomena. According to Kant, 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.
Kant also argues that the foundations of mathematics is intuition. Understanding and mathematical construction is obtained by first finding "pure intuition" in the sense or mind. Mathematical intuition is constructed through three stages of "intuition sensing", "intuitive sense", and "intuition mind". Sensing intuition associated with the object of mathematics. Intuition reason (Verstand) sensing intuition into the results of intuition "space" and "time". With the intuitive mind "Vernuft", the ratio we are faced with decisions of mathematical argumentation. Obtained a priori mathematical concepts from experience with intuitive sensing, but the concept is pure. Next is a synthetic process in the sense of intuition "Verstand" which allows constructing mathematical concepts that are "synthetic" in space and time. Prior to the decisions taken by intuition mind "Vernuft" advance the objects of mathematics in the form of "Form" synthesized into "categories" as an innate ideas, the "quantity", "quality", "relation" and "modalities". Thus it becomes the foundation for the intuition of pure mathematics and mathematical truths that are "apodiktik".
In arithmetic, Kant argued that the propositions of arithmetic are synthetic in order to obtain a new concept. The concept of numbers in arithmetic obtained by the intuition of time. On the sum 2 + 3, the representation 2 3 precedes representation, and representation of 2 +3 precedes representation 5. Kant's intuition connecting arithmetic with time as a form of "inner intuition" to show that awareness of the concept of numbers covering aspects of its formation so that the structure of consciousness can be shown in order of time. So, the intuition of time causes the concept of numbers became concrete in accordance with empirical experience.
In geometry, Kant argues that the spatial geometry is based on pure intuition. Geometry is the science which determines the spatial properties of a synthetic but a priori. Synthetic means that concepts of geometry can not be constructed only from pure concepts alone, but must be based on pure intuition that occurred prior to perceive an object, so it is a pure intuition and not empirical.
In making any mathematical intuition plays a large. The ratio of the mind held intuition argument (mathematics) and combine the decisions (mathematics). Decision mathematical cognition is the awareness that are complex traits that have a) related to mathematical objects, either directly (through intuition) or indirect (via draft), b) include math concepts both concepts in the predicate as well as on the subject, c) is a pure reason in accordance with pure logic principal, d) involve the laws of mathematics are constructed by intuition, and e) declare the value of the truth of a mathematical proposition.
In arithmetic, Kant argued that the propositions of arithmetic are synthetic in order to obtain a new concept. The concept of numbers in arithmetic obtained by the intuition of time. On the sum 2 + 3, the representation 2 3 precedes representation, and representation of 2 +3 precedes representation 5. Kant's intuition connecting arithmetic with time as a form of "inner intuition" to show that awareness of the concept of numbers covering aspects of its formation so that the structure of consciousness can be shown in order of time. So, the intuition of time causes the concept of numbers became concrete in accordance with empirical experience.
In geometry, Kant argues that the spatial geometry is based on pure intuition. Geometry is the science which determines the spatial properties of a synthetic but a priori. Synthetic means that concepts of geometry can not be constructed only from pure concepts alone, but must be based on pure intuition that occurred prior to perceive an object, so it is a pure intuition and not empirical.
In making any mathematical intuition plays a large. The ratio of the mind held intuition argument (mathematics) and combine the decisions (mathematics). Decision mathematical cognition is the awareness that are complex traits that have a) related to mathematical objects, either directly (through intuition) or indirect (via draft), b) include math concepts both concepts in the predicate as well as on the subject, c) is a pure reason in accordance with pure logic principal, d) involve the laws of mathematics are constructed by intuition, and e) declare the value of the truth of a mathematical proposition.
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