PERAN INTUISI DALAM MATEMATIKA MENURUT IMANUEL KANT
By : Dr.Marsigit
By : Dr.Marsigit
Reviewed By : Eka Sulistyawati
1. Preface
Kant's view of mathematics can contribute significantly in terms from the philosophy of mathematics, especially regarding the role of intuition and construction concept mathematics. Michael Friedman (Shabel, L., 1998) mention that what was achieved. Kant has given the depth and accuracy of the mathematical foundation, and by because it's achievements can not be ignored. In the ontology and epistemology, after the era of Kant, mathematics has been developed with nearly more or less influenced by Kant's view. Some authors argue that Kant's depart from philosophy of geometry from bridge to the philosophy of arithmetic and algebra philosophy. But moreover, the views of Kant's more based on the role of intuition for all mathematical concepts and just rely on the concept of construction as occurs in Euclidean geometry (ibid.). According to Kant (Wilder, RL, 1952), mathematics must understand and constructed using pure intuition, that intuition "space" and "time".
Kant's view of mathematics can contribute significantly in terms from the philosophy of mathematics, especially regarding the role of intuition and construction concept mathematics. Michael Friedman (Shabel, L., 1998) mention that what was achieved. Kant has given the depth and accuracy of the mathematical foundation, and by because it's achievements can not be ignored. In the ontology and epistemology, after the era of Kant, mathematics has been developed with nearly more or less influenced by Kant's view. Some authors argue that Kant's depart from philosophy of geometry from bridge to the philosophy of arithmetic and algebra philosophy. But moreover, the views of Kant's more based on the role of intuition for all mathematical concepts and just rely on the concept of construction as occurs in Euclidean geometry (ibid.). According to Kant (Wilder, RL, 1952), mathematics must understand and constructed using pure intuition, that intuition "space" and "time".
2. Intuition For Basic Mathematics
According to Kant (Kant, I., 1781), and the construction of mathematical understanding is obtained by first finding "pure intuition" in the sense or mind. Mathematics that are "synthetic a priori 'can be constructed through the three stages of intuition there are "sensing intuition ", "resonable intuition", and "mind intuition". Sensing intuition related to mathematical objects that can be perceived as an element of a posteriori. Reason intuition(Verstand) synthetic results intuition sense into "Space" and "time" intuition. With the mind intuition "Vernuft", the ratio we are faced with verdicts mathematical arguments.
According to Kant (Kant, I., 1781) is a mathematical reasoning characterised by construct concepts are synthetic a priori in concepts of space and time. Pure mathematics (ibid.), in particular the geometry can be true if the objective related to sensing objects. The concepts of geometry not only produced by pure intuition, but also related to the concept of space in which geometry objects are represented. The concept of space (ibid.) is itself a form of intuition in which the ontological essence of representation can not be tracked. Kant (Wikipedia) and then ask the question whether the reasoning mathematics should be based on experience? Or how is it possible to find intuition a priori from empirical data? Kant (Kant, I, 1783) gives a solution that mathematical concepts first obtained a priori from the experience of sensing intuitive, but the concept obtained is not empirical, but rather pure.
Intuition, plays a very important to construct a mathematical as well investigate and explain how mathematics is understood in the form geometry or arithmetic. A transcendent understanding of mathematics through intuition purely in space and time is what causes the mathematic is possible as a science (ibid.).
According to Kant (Kant, I., 1781), and the construction of mathematical understanding is obtained by first finding "pure intuition" in the sense or mind. Mathematics that are "synthetic a priori 'can be constructed through the three stages of intuition there are "sensing intuition ", "resonable intuition", and "mind intuition". Sensing intuition related to mathematical objects that can be perceived as an element of a posteriori. Reason intuition(Verstand) synthetic results intuition sense into "Space" and "time" intuition. With the mind intuition "Vernuft", the ratio we are faced with verdicts mathematical arguments.
According to Kant (Kant, I., 1781) is a mathematical reasoning characterised by construct concepts are synthetic a priori in concepts of space and time. Pure mathematics (ibid.), in particular the geometry can be true if the objective related to sensing objects. The concepts of geometry not only produced by pure intuition, but also related to the concept of space in which geometry objects are represented. The concept of space (ibid.) is itself a form of intuition in which the ontological essence of representation can not be tracked. Kant (Wikipedia) and then ask the question whether the reasoning mathematics should be based on experience? Or how is it possible to find intuition a priori from empirical data? Kant (Kant, I, 1783) gives a solution that mathematical concepts first obtained a priori from the experience of sensing intuitive, but the concept obtained is not empirical, but rather pure.
Intuition, plays a very important to construct a mathematical as well investigate and explain how mathematics is understood in the form geometry or arithmetic. A transcendent understanding of mathematics through intuition purely in space and time is what causes the mathematic is possible as a science (ibid.).
3. Intuition in Arithmetic
Kant (Kant, I., 1787) argues that the propositions of arithmetic should are synthetic in order to obtain new concepts. If you just rely on the analytic method, then it will not be obtained for new concepts. If we call the "1" as the original numbers and only at the mention of it, then we do not acquire new concepts apart from the already mentioned it, and this of course is analytic. But if we consider the sum of 2 + 3 = 5. Intuitively 2 and 3 are different concepts and 5 is the concept differently. So 2 + 3 has produced a new concept that 5; and so of course it is synthetic.
Kant (Kant, I., 1787) argues that the propositions of arithmetic should are synthetic in order to obtain new concepts. If you just rely on the analytic method, then it will not be obtained for new concepts. If we call the "1" as the original numbers and only at the mention of it, then we do not acquire new concepts apart from the already mentioned it, and this of course is analytic. But if we consider the sum of 2 + 3 = 5. Intuitively 2 and 3 are different concepts and 5 is the concept differently. So 2 + 3 has produced a new concept that 5; and so of course it is synthetic.
4. Intuition in Geometry
According to Kant, drawing a straight line whose length is not finite, only a row of changes that occur from the movement in space, so that only empirical. Therefore, Kant concluded that to obtain the concept of a straight line we have to use pure intuition a priori. Thus, according to Kant, geometry is the science knowledge which determines the spatial properties of a synthetic but a priori. Kant (Shabel, L., 1998) makes an example of proof of the theorem the number of angles a triangle as that of Euclid. In triangle ABC, the line segment BC extended to D. Then make line CE parallel to BA. Since the line AB // CE then angle 1 = angle 4 and angle 2 = angle 5. So the corner angle 3 + 4 + 5 = angle 1 + 3 + 2 = straight line angle.
According to Kant (ibid.), the object of proving the above process is the triangle ABC
obtained based on pure intuition and a priori. The process of proving the number of angles. The triangle is an example of pure construction of a geometrical concept are synthetic a priori and produces a universal truth that the number of large angles of a triangle is a straight angle.
According to Kant, drawing a straight line whose length is not finite, only a row of changes that occur from the movement in space, so that only empirical. Therefore, Kant concluded that to obtain the concept of a straight line we have to use pure intuition a priori. Thus, according to Kant, geometry is the science knowledge which determines the spatial properties of a synthetic but a priori. Kant (Shabel, L., 1998) makes an example of proof of the theorem the number of angles a triangle as that of Euclid. In triangle ABC, the line segment BC extended to D. Then make line CE parallel to BA. Since the line AB // CE then angle 1 = angle 4 and angle 2 = angle 5. So the corner angle 3 + 4 + 5 = angle 1 + 3 + 2 = straight line angle.
According to Kant (ibid.), the object of proving the above process is the triangle ABC
obtained based on pure intuition and a priori. The process of proving the number of angles. The triangle is an example of pure construction of a geometrical concept are synthetic a priori and produces a universal truth that the number of large angles of a triangle is a straight angle.
5. Intuition in Decision Mathematics
According to Kant, with the intuition of mind, we hold the ratio argument (mathematics) and combine the decisions (mathematics). Decision mathematics is awareness of the nature of complex cognition that has the characteristics: a) relates with mathematical objects, either directly (through intuition) as well as no directly (via draft), b) include math concepts both concepts entirely the predicate and the subject, c) is a pure reasoning
accordance with principle pure logic, d) involve the laws of mathematics constructed by intuition, and e) declare the value of truth of a mathematics proposition .
According to Kant, with the intuition of mind, we hold the ratio argument (mathematics) and combine the decisions (mathematics). Decision mathematics is awareness of the nature of complex cognition that has the characteristics: a) relates with mathematical objects, either directly (through intuition) as well as no directly (via draft), b) include math concepts both concepts entirely the predicate and the subject, c) is a pure reasoning
accordance with principle pure logic, d) involve the laws of mathematics constructed by intuition, and e) declare the value of truth of a mathematics proposition .
6. Conclusion
Kant (Randall, A., 1998) concluded that mathematics is arithmetic and geometry is a discipline science that is synthetic and independent one with others. Kant (ibid.) to contribute because it gives the middle ground that the decision mathematics is synthetic a priori, namely the decision which first obtained a priori of experience, but the concept is not obtained empirical (Kant, I, 1783), but rather pure.
Kant (Randall, A., 1998) concluded that mathematics is arithmetic and geometry is a discipline science that is synthetic and independent one with others. Kant (ibid.) to contribute because it gives the middle ground that the decision mathematics is synthetic a priori, namely the decision which first obtained a priori of experience, but the concept is not obtained empirical (Kant, I, 1783), but rather pure.
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