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The Principles of the Understanding set forth the main positive conclusions of Kants metaphysic of experience; that is to say, they are the ultimate synthetic a priori judgements which people are entitled to make about objects of experience. The Metaphysical Deduction has shown, according to Kant, that the categories are derived from the forms of judgement; and the Transcendental Deduction on its objective side has demonstrated the objective validity of categories so derived. It should be noted that Kant is assuming the subject-concept to refer to an object. Given a subject-concept, we can make analytic judgements by the principle of non-contradiction alone. Hence the principle of non-contradiction is a sufficient principle of all analytic judgements. Nevertheless Kant attempts to formulate the supreme principle of all synthetic judgements, and people must suppose that this principle is meant to cover a posteriori, as well as a priori, synthetic judgements.