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The thesis that the necessary and the a priori are extensionally equivalent consists of two independent claims: 1) All a priori truths are necessary and 2) all necessary truths are a priori. In Naming and Necessity1 Saul A. Kripke gives examples of necessary but a posteriori truths, so he disagrees with the second leg of the thesis.2 His examples are of two types; on the one hand statements involving essential properties and on the other hand true identity statements. My concern will be with examples of the second type and whether they refute (2). (2), however, is ambiguous and can mean one of three things.

The thesis that the necessary and the a priori are extensionally equivalent consists of two independent claims: 1) All a priori truths are necessary and 2) all necessary truths are a priori. In Naming and Necessity1 Saul A. Kripke gives examples of necessary but a posteriori truths, so he disagrees with the second leg of the thesis.2 His examples are of two types; on the one hand statements involving essential properties and on the other hand true identity statements. My concern will be with examples of the second type and whether they refute (2). (2), however, is ambiguous and can mean one of three things: a) If p is a necessary truth, then one can know a priori that p is necessary. b) If p is a necessary truth, then one can know a priori that p. c) If p is a necessary truth, then one can know a priori that p and that p is necessary. Kripke maintains that we know a priori that if an identity statement is true, then it is necessarily true. Consequently, the issue at hand is how we come to know the truth of such identity statements, so it is clearly (b) that we should be concerned with.3 In order to refute (b), and thus (2), we apparently need to show that..

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 ?

I argue that you can have a priori knowledge of propositions that neither are nor appear necessarily true. You can know a priori contingent propositions that you recognize as such. This overturns a standard view in contemporary epistemology and the traditional view of the a priori, which restrict a priori knowledge to necessary truths, or at least to truths that appear necessary.

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.

If I understand him correctly, Derek Parfit’s views place us, philosophically speaking, in a very small box. According to Parfit, normativity is an irreducible non-natural property that is independent of the human mind. That is to say, there are normative truths - truths about what we ought to do and to want, or about reasons for doing and wanting things. The truths in question are synthetic a priori truths, and accessible to us only by some sort of rational intuition. Parfit supposes that if we are to preserve the irreducibility of the normative, this is just about all we can say, at least until we bring in some actual intuitions to supply the story with some content.