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==== Politics ====
Kant argued that in order to maintain human freedom, we must all seek a society in which it is possible to live free and rational lives. He called this state a ''Rechtsstaat,'' or a Republic governed by law. The sole purpose of this state was to maximize the possibility of human autonomy.
==== Mathematics ====
According to Kant, mathematics possesses objective validity because it expresses the necessary conditions of possible experience. Arithmetic, as an example, is grounded in the necessary conditions of possible experience and provides a priori cognition of objects with regard to their form. Kant believes that mathematics is a suitable tool for describing nature, but it encounters certain philosophical challenges. One such challenge arises from the notion that if something is composite, there must also exist something simple. This contradicts the concept of infinite divisibility of space, as it suggests that there are indivisible elements (atoms or monads) that constitute the universe. Kant addresses this issue by proposing that appearances are not things in themselves and that philosophical reasoning based solely on concepts would not be valid for appearances.
Another issue Kant discusses is the question of infinitely small magnitudes in mathematics. While some philosophers argue for the existence of atoms or monads, Kant separates the concepts of infinite divisibility and infinitely small magnitudes. He considers infinitely small magnitudes as necessary ideas to express changes caused by fundamental forces and the construction of intuition. Regarding the method of mathematics, Kant argues that it differs from the method of philosophy. Mathematics is capable of producing definitions in a strict sense and is considered a paradigm of synthetic cognition a priori. It uses concepts in concreto, starting with definitions and containing few unprovable propositions. Philosophy, on the other hand, analyzes data and deals with concepts in abstracto.
Kant illustrates the distinction between mathematics and philosophy through the discussion of the definition of a circle. The standard definition, which states that a circle is a figure with each point equidistant from a given center, does not prove its possibility. Kant proposes a genetic definition that demonstrates the constructability of a circle. According to Kant, mastering a mathematical concept means understanding the rule of construction of the object of the concept.
===[[File:Descartes.png]] {{PHB|Cartesianism}}===
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