Iycee Charles de Gaulle Summary Immanuel Kant and the role of non-Euclidean Geometry Essay

Immanuel Kant and the role of non-Euclidean Geometry Essay

Immanuel Kant and the role of non-Euclidean Geometry


            Immanuel Kant is one of the most influential philosophers in the history of Western philosophy. His contributions to metaphysics, epistemology, ethics, and aesthetics have had a profound impact on almost every philosophical movement that followed him.

            This essay will discuss about the Kant’s most original contribution to philosophy and the thought on non-Euclidean that deals with geometry on how physical space really works.

            Kant believed that human knowledge originates in our sensations and that the mind is a blank slate, or a tabula rasa, that becomes populated with ideas by its interactions with the world. Experience teaches us everything, including concepts of relationship, identity, causation, and so on. (Encyclopedia of Philosophy)

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            An example to illustrate this is a newly baby born is totally blank and as he grow up he acquire knowledge based on the people around him. He starts to talk mother because that is the first person who he usually see. What he learns from his parents it can be shown in his ways and decision, and cannot be forgotten.

            Kant always believed that the rational structure of the mind reflected the rational structure of the world, even of things-in-themselves that the operating system of the processor, by modern analogy, matched the operating system of reality. But Kant had no real argument for this the Ideas of reason just become postulates of morality and his system leaves it as something improvable. The paradoxes of Kant’s efforts to reconcile his conflicting approaches and requirements made it very difficult for later philosophers to take the overall system seriously. (Ross, 2002). The structure of knowledge gains and the experience that brought a person into the world would be the foundations of his moral in the outside world.

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Kant’s moral philosophy is developed in the Grounding for the Metaphysics of Morals (1785). From his analysis of the operation of the human will, Kant derived the necessity of a perfectly universality moral law, expressed in a categorical imperative that must be regarded as binding upon every agent. (Kemerling, 2006)

                        According to Kant, then, the ultimate principle of morality must be a moral law conceived so abstractly that it is capable of guiding us to the right action in application to every possible set of circumstances. So the only relevant feature of the moral law is its generality, the fact that it has the formal property of universality, by virtue of which it can be applied at all times to every moral agent. From this chain of reasoning about our ordinary moral concepts, Kant derived as a preliminary statement of moral obligation the notion that right actions are those that practical reason would will as universal law.

            Having mastered epistemology and metaphysics, Kant believed that a rigorous application of the same methods of reasoning would yield an equal success in dealing with the problems of moral philosophy. Thus, in the Critique of Practical Reason (1788), he proposed a Table of the Categories of Freedom in Relation to the Concepts of Good and Evil, using the familiar logical distinctions as the basis for a catalog of synthetic a priori judgments that have bearing on the evaluation of human action, and declared that only two things inspire genuine awe: the starry sky above and the moral law within.(Kamerling , 2001)


In relation to Science and Mathematics, he argues to that the space is largely a creation of our minds, and since we cannot imagine non-Euclidean space that Euclid’s fifth postulate must necessarily be true. The 5th postulate of Euclidean states that “If two straight lines lying in a plane are met by another line, and if the sum of he internal angles on one side is less than two right angles, then the straight lines will meet if the extended on the side on which the sum of the angles is less than two right angles.” The fifth axiom, also known as Euclid’s “parallel postulate” deals with parallel lines, and it is equivalent to this slightly more clear statement: “For a given line and point there is only one line parallel to the first line passing through the point” (This statement was first proved to be equivalent to Euclid’s fifth axiom by John Play fair in the 18th century

            His belief of geometry, however, the Euclidean distinction could be restored:  axioms would be analytic propositions, and postulates synthetic. His argument was supported by Euclid himself the founder of the non-Euclidean, were not comfortable with axiom five; it is quite a complicated statement and axioms are meant to be small, simple and straightforward. Kant suggests that the Euclidian space geometry was arbitrary. (Turner, 2003)


Kant’s final word here offers an explanation of our persistent desire to transcend from the phenomenal realm to the nominal. We must impose the forms of space and time on all we perceive, we must suppose that the world we experience functions according to natural laws, we must regulate our conduct by reference to a self-legislated categorical imperative, and we must postulate the nominal reality of ourselves, god, and free will all because a failure to do so would be an implicit confession that the world may be meaningless, and that would be utterly intolerable for us. Thus, Kant believed, the ultimate worth of his philosophy lay in his willingness to criticize reason in order to make room for faith.

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Immanuel Kant. Metaphysics. 25 November 2006, from <http://www.utm.edu/research/iep/k/kantmeta.htm>.

Kemerling, Garth. Emmanuel Kant (2001). 25 November 2006, from <http://www.philosophypages.com/hy/5i.htm#judgment>.

Kemerling, Garth. Emmanuel Kant (2006). 25 November 2006, from <http://www.philosophypages.com/ph/kant.htm>.

Ross, Kelley L. Emmanuel Kant. 25 November 2006, from <http://www.friesian.com/kant.htm>.

Turner, William. Emmanuel Kant. 25 November 2006, from <http://www.newadvent.org/cathen/08603a.htm>