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Kant maintains that his Critique of Pure Reason follows a “synthetic method” which he distinguishes from the analytic method of the Prolegomena by saying that the Critique “rests on no other science” and “takes nothing as given except reason itself”. The paper presents an account of the synthetic method of the Critique, showing how it is related to Kant’s conception of the Critique as the “science of an a priori judging reason”. Moreover, the author suggests, understanding its synthetic method sheds light on the structure of the Transcendental Deduction, and its function in the work as a whole.

The terms "a priori" and "a posteriori" refer primarily to how or on what basis a proposition might be known. A proposition is knowable a priori if it is knowable independently of experience. A proposition is knowable a posteriori if it is knowable on the basis of experience. The a priori/a posteriori distinction is epistemological and should not be confused with the metaphysical distinction between the necessary and the contingent or the semantical or logical distinction between the analytic and the synthetic. Two aspects of the a priori/a posteriori distinction require clarification: the conception of experience on which the distinction turns; and the sense in which a priori knowledge is independent of such experience. The latter gives rise to important questions regarding the positive basis of a priori knowledge.

In his Grundlagen , Frege held that geometrical truths.are synthetic a priori , and that they rest on intuition. From this it has been concluded that he thought, like Kant, that space and time are a priori intuitions and that physical objects are mere appearances. It is plausible that Frege always believed geometrical truths to be synthetic a priori ; the virtual disappearance of the word 'intuition' from his writings from after 1885 until 1924 suggests, on the other hand, that he became dissatisfied with the notion of intuition as he had employed it in Grundlagen . The belief that a priori intuition is a source of knowledge does not in itself entail idealism: that is a question about what it is that makes true the propositions known in this way. In Grundlagen , Frege expressly states that geometrical truths are objective in the sense of being independent of our intuition. This shows that, even at that period, Frege did not draw the idealist conclusion drawn by Kant.

(K1) All knowledge of necessary propositions is a priori. (K2) All propositions known a priori are necessary. (K3) All knowledge of analytic propositions is a priori; and (K4) Some propositions known a priori are synthetic.

On rationalist infallibilism, a wide range of both (i) analytic and (ii) synthetic a priori propositions can be infallibly justified (or absolutely warranted), i.e., justified to a degree that entails their truth and precludes their falsity. Though rationalist infallibilism is indisputably running its course, adherence to at least one of the two species of infallible a priori justification refuses to disappear from mainstream epistemology. Among others, Putnam (1978) still professes the a priori infallibility of some category (i) propositions, while Burge (1986, 1988, 1996) and Lewis (1996) have recently affirmed the a priori infallibility of some category (ii) propositions. In this paper, I take aim at rationalist infallibilism by calling into question the a priori infallibility of both analytic and synthetic propositions. The upshot will be twofold: first, rationalist infallibilism unsurprisingly emerges as a defective epistemological doctrine, and second, more importantly, the case for the a priori infallibility of one or both categories of propositions turns out to lack cogency.

There has been a significant shift in the discussion of a priori knowledge. The shift is due largely to the influence of Quine. The traditional debate focused on the epistemic status of mathematics and logic. Kant, for example, maintained that arithmetic and geometry provide clear examples of synthetic a priori knowledge and that principles of logic, such as the principle of contradiction, provide the basis for analytic a priori knowledge. Quine’s rejection of the analytic-synthetic distinction and his holistic empiricist account of mathematic and logical knowledge undercut the traditional defenses of the a priori in two ways. First, one could no longer defend the view that mathematical and logical knowledge is a priori solely by rejecting Mill’s inductive empiricism. Moreover, holistic empiricism proved to be a more challenging position to refute than inductive empiricism. Second, the rejection of the analytic-synthetic distinction blocked an alternative defense of the a priori status of mathematics and logic that appealed to their alleged analyticity.

Roderick Chisholm appears to agree with <span class='Hi'>Kant</span> on the question of the existence of synthetic a priori knowledge. But Chisholm’s conception of the a priori is a traditional Aristotelian conception and differs markedly from <span class='Hi'>Kant</span>’s. Closer scrutiny reveals that their agreement on the question of the synthetic a priori is merely verbal: what <span class='Hi'>Kant</span> meant to affirm, Chisholm denies. Curiously, it looks as if Chisholm agreed on all substantive issues with the empiricist rejection of <span class='Hi'>Kant</span>’s synthetic a priori. In the end, it turns out that Chisholm disagrees with empiricism and Kantianism over a fundamental question: whether mere understanding of the contents of our thoughts must always remain within the circle of our own ideas or can provide us with genuine knowledge of matters of fact.

In his essay “Logical Empiricism”, in the anthology Twentieth Century Philosophy, Professor Feigl writes: “All forms of empiricism agree in repudiating the existence of synthetic a priori knowledge.” Schlick makes the same point even more forcibly: “The empiricism which I represent believes itself to be clear on the point that, as a matter of principle, all propositions are either synthetic a posteriori or tautologous; synthetic a priori propositions seem to it to be a logical impossibility.” The denial of synthetic a prioris is a major thesis of the logical empiricist position, being found in the writings of most of the leaders of the movement. The reason for its importance is fairly clear. It provides a formula on which the empiricists can base their critique of traditional philosophy. To use Ayer's phrase, denial of the synthetic a priori results in “the elimination of metaphysics”. The philosophical tradition to which the empiricists are opposed and whose “metaphysics” they wish to eliminate can be called, somewhat loosely, rationalism.

In twentieth-century Kant scholarship, few have provided an account of the analytic-synthetic distinction and of the problem of the synthetic a priori that takes into consideration the views of Kant's idealist successors such as Maimon, Fichte, Schelling, and Hegel. I first explain how Kant formulates the analytic-synthetic distinction in terms of the determinate-indeterminate distinction, which, in turn, is based on the distinction between general and transcendental logic. Kant's problem of the synthetic a priori , then, is the problem of showing how the logical forms of judgment can be employed determinately (and not merely indeterminately). I then show that Maimon also formulates the distinction and the problem in the same way, and that his interpretation will shape how Fichte, Schelling, and Hegel each construe and address Kant's question, How are synthetic judgments possible a priori ?