Mathematical cognition

Presupposition, I define as something derived from Notion itself and determined by Notion. What is the notion of a circle? A round figure made up of constant radii in all directions. So I presuppose the radius of a circle is based upon being equidistant from the centre of the circle. So any proposition having a circle would determine its relationship to any other notion as being equidistant at a constant radius. So I accept the notion of a circle as the proof of circle itself but there is a need for a proof of a circle. So this is inherently a limitation of Mathematics that the proof of basic notions is desirable otherwise it is reduced to a presupposition for other notions.

The principle of magnitude as determining the radius of the circle and the principle of equality as all circles adhering to the same notion of circle reduce the self-moving idea of becoming a circle to mere material that constitutes the circle.

Mathematical cognition thus has to do with unessential determinations, the determinations that make up the notions itself. So transcendence in Mathematics become really difficult unless some help is sought from Philosophy of Mathematics.


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