Some Considerations Regarding the Critical Concept of Demonstration

This article examines the Kantian notion of mathematical demonstration. This notion is developed in the section entitled "Discipline of pure reason in its dogmatic use" of the Critique of Pure Reason. In this text, Kant explains why successful procedures in mathematical knowledge are impracticable in metaphysics. First, two passages are studied in which the philosopher describes two demonstrations: the demonstration of the congruence of the angles of the base of an isosceles triangle, and the demonstration that the sum of the internal angles of any triangle is equal to two right angles. Afterwards, the description of the mathematical demonstration as an (ii) apodictic (iii) intuitive (i) proof is examined. This analysis shows that mathematical demonstration does not constitute the same kind of procedure presented as demonstration in 57 and 59 of the Critique of Judgement.