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Synthetic a priori judgments are possible from "summary" of Immanuel Kant: Prolegomena to Any Future Metaphysics by Immanuel Kant

Kant argues that synthetic a priori judgments are possible because they are not derived from experience, but rather from the pure concepts of the understanding. These judgments go beyond what is contained in the subject and predicate of a proposition, thereby adding something to our knowledge that is not simply a tautological truth. For Kant, synthetic judgments are those in which the predicate concept is not contained in the subject concept. This is in contrast to analytic judgments, where the predicate is already contained within the subject. A priori judgments, on the other hand, are those that are known independently of experience, through pure reason. Kant believes that synthetic a priori judgments are necessary for the possibility of experience itself. He argues that the categories of the understanding, such as causality and substa...
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    Immanuel Kant: Prolegomena to Any Future Metaphysics

    Immanuel Kant

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