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An important concept in The Philosophy Of Freedom is the existence of a universal world of ideals. Mathematics shows that there is a universal conceptual world of ideals we can perceive within and a particularized world that expresses those ideals without. Because we gain knowledge in two ways, thinking and observation, we face a duality. But thinking reconciles the separation when it adds the conceptual ideal, such as circle, to a particularized circle in the world. It is easy to see this in mathematics, but this also applies to everything else.