"Kant argued that that old division between a priori
truths and a posteriori
truths employed by both camps was insufficient to describe the sort of metaphysical claims that were under dispute. An analysis of knowledge also requires a distinction between synthetic
truths. In an analytic claim,
the predicate is contained within the subject. In the claim, "Every body occupies space," the property of occupying space is revealed in an analysis of what it means to be a body. The subject of a synthetic claim, however, does not contain the predicate. In, "This tree is 120 feet tall," the concepts are synthesized or brought together to form a new claim that is not contained in any of the individual concepts. The Empiricists had not been able to prove synthetic a priori
claims like "Every event must have a cause," because they had conflated "synthetic" and "a posteriori" as well as "analytic" and "a priori." Then they had assumed that the two resulting categories were exhaustive. A synthetic a priori claim, Kant argues, is one that must be true without appealing to experience, yet the predicate is not logically contained within the subject, so it is no surprise that the Empiricists failed to produce the sought after justification. The Rationalists had similarly conflated the four terms and mistakenly proceeded as if claims like, "The self is a simple substance," could be proven analytically and a priori.
Synthetic a priori claims, Kant argues, demand an entirely different kind of proof than those required for analytic, a priori claims or synthetic, a posteriori claims. Indications for how to proceed, Kant says, can be found in the examples of synthetic a priori claims in natural science and mathematics, specifically geometry. Claims like Newton's, "the quantity of matter is always preserved," and the geometer's claim, "the angles of a triangle always add up to 180 degrees" are known a priori, but they cannot be known merely from an analysis of the concepts of matter or triangle. We must "go outside and beyond the concept. . . joining to it a priori in thought something which I have not thought in it." (B 18) A synthetic a priori claim constructs upon and adds to what is contained analytically in a concept without appealing to experience. So if we are to solve the problems generated by Empiricism and Rationalism, the central question of metaphysics in the Critique of Pure Reason
reduces to "How are synthetic a priori judgments possible?" (19) If we can answer that question, then we can determine the possibility, legitimacy, and range of all metaphysical claims."
Immanuel Kant -- Metaphysics [Internet Encyclopedia of Philosophy]
The key question here is how are synthetic a priori judgments possible? :eek: