1 References to the Critique of Pure Reason will be given in the text using the standard ‘A’ and ‘B’ notation. ‘A’ refers to the pagination of the first edition (1781) and ‘B’ to that of the second edition (1787). (Of the numerous editions of the Critique, Kant prepared only these two himself.) I will use Norman Kemp Smith’s 1927 translation, Immanuel Kant’s Critique of Pure Reason (London: MacMillan 1963), sometimes with minor changes. Except in one part of the paper noted later, a reference only to one edition means that the passage in question does not appear in the other one.

2 Kant’s attack on rational psychology in the chapter on the paralogism is, to my mind, the most successful discussion in the whole of the Critique of Pure Reason. Kant’s attempt to ‘deny knowledge’ in various domains ‘in order to make room for faith’ (Bxxx) was at the heart of his reasons for writing the Critique of Pure Reason, though this has sometimes been overlooked.

3 This of course was the general view at the time. Descartes took geometry as his exemplar of certain knowledge. As a very different example, we might recall that in 1763 the Berlin Academy proposed as a topic, ‘Are the Metaphysical Sciences Amenable to the Same Certainty as the Mathematical?’

4 This is how Patricia Kitcher sees Kant, ’s central task, too (Kant’s Transcendental Psychology [New York: Oxford University Press 1990], 15).Google Scholar

5 Paul Guyer says that Feder was the villain. Apparently the passages that upset Kant were mostly added by Feder to Garve, ’s original draft (Kant and the Claims of Knowledge [New York: Cambridge University Press 1987], 434).Google Scholar

6 Hume uses the denial of a priori knowledge argument in the Enquiry Concerning Human Understanding (1748), Hendel, Charles W. ed. (Indianapolis: Library of the Liberal Arts 1955), 42.Google Scholar In A Treatise on Human Nature (1736), Selby-Bigge, L.A. ed. (Oxford: Clarendon Press 1888)Google Scholar he does not refer to a prioricity in the relevant section at all (cf. 78-84).

7 Kant made the same assumption about the necessity of the propositions of mathematics and physics in Prolegomena to Any Future Metaphysics (1783), revision of Carus trans. by Lewis White Beck (Indianapolis: Library of Liberal Arts 1950).

8 Kripke, Saul ‘Naming and Necessity,’ in Harman, G. and Davidson, D. eds., Semantics of Natural Languages (Dordrecht: D. Reidel 1972)CrossRefGoogle Scholar

9 Two secondary issues arise in connection with this discussion of the analytic a priori. The first is that we should acknowledge that Kant accepted that we have and use analytic propositions linking concepts derived from experience, too (83). I do not need to consider this kind of analytic proposition here. The second concerns his view of the relationship between analyticity and definition.

It would be natural to think that when Kant talks about ‘breaking [a concept] up into those constituent concepts that have always been thought in it, though confusedly’ (A7=B11), he is talking about defining the concept. However, in the only section of the first Critique devoted explicitly and single-mindedly to definition, Kant raises very Putnam-like objections to the very possibility of defining concepts:

… an empirical concept cannot be defined at all, but only made explicit [perhaps something like being explicated in Carnap’s sense]. For since we find in it only a few characteristics of a certain species of sensible object, it is never certain that we are not using the word, in denoting one and the same object, sometimes so as to stand for more, and sometimes so as to stand for fewer characteristics (1. Definitions, A727=B755-A733=B760).

Kant then illustrates the problem, as did Putnam two hundred years later, by the example of gold.

The relation of this skepticism about definition, which comes very late in the Critique, to Kant’s ready acceptance of analyticity in the Introduction, deserves more exploration than I can give it here. Unlike our contemporaries, Kant did not base analyticity upon definitions (cf. Beck, L.W. ‘Kant’s Theory of Definition’ [Studies in The Philosophy of Kant (Indianapolis: Bobbs-Merrill 1963), 61-73]Google Scholar, and Dryer, D.P.Kant’s Solution for Verification in Metaphysics [London: George Allen & Unwin 1966], 324).Google Scholar

10 See, for example, his ‘There is at least One A Priori Truth,’ reprinted in Philosophical Papers, Vol. 3: Realism and Reason (Cambridge: Cambridge University Press 1983). The truth he has in mind is not every statement is both true and false. He means that this statement is necessary truth, and could not be false, not that we know its truth independent of experience (though he might believe that, too).

11 Kemp Smith translates ‘merkmale’ and ‘merkmalen’ as ‘characters.’ I think that term misses both the simplicity and the special technical sense of ‘merkmal,’ a term whose literal means is ‘mark,’ ‘sign,’ ‘indication,’ etc., but which often means something like ‘differentiating feature’ (differentiae) in Kant’s work. (What exactly the term means, however, is controversial.)

12 Allison, Henry gives a good account of them (Kant’s Transcendental Idealism [New Haven, CT: Yale University Press 1983]Google Scholar, ch. 4) and they have been explored by many other commentators. Because Jonathan Bennett argues that, in the end, so-called synthetic a priori propositions are really just unobviously analytic ones, he in particular devotes a lot of attention to the problems in Kant, ’s account of analyticity (Kant’s Analytic [Cambridge: Cambridge University Press 1966]Google Scholar, ch. 1 and 3). Kitcher makes some interesting remarks about the resemblances between Kant’s remarks on analytic connections and Quine’s attack on the very idea (27).

13 That Kant had this question in mind in the first edition, too, is indicated by way we end up with a parallel question if we change the equivalent part of the deleted first-edition passage into a question: ‘What … is … the ground of the possibility of a priori synthetic judgments[?]’ (AlO)

14 One commentator who gets the direction of Kant’s argument right is Harper, William (’Kant on the A Priori and Material Necessity,’ in Butts, Robert E. ed., Kant’s Philosophy of Physical Science [Dordrecht: D. Reidel 1986] 239-72).CrossRefGoogle Scholar Though he does not make the point explicitly, the whole structure of his paper presents Kant as arguing from necessity to a prioricity.

15 A further complication is that Kant also had a notion of necessary existence.Indeed it is in terms of this notion that he first explicates the schematized form of category of necessity, strangely enough (A145=B184), even though he explicates the category itself in other terms, in the second edition at least (B111).

16 In a criticism that has attained some notoriety, P.F. Strawson charges that Kant’s argument for the necessity of causal propositions (the Second Analogy) runs the two together (The Bounds of Sense [London: Methuen 1967], Part Two: III).

17 99ff. and many other references to necessity. Both Dryer’s distinction and my recasting of it smack of psychologism- a problem for another paper.

18 In an important paper on what Kant really had in mind by construction in geometry, Friedman convincingly argues that the important thing we construct in pure intuition is not an image, an imagined instance, of the object of a mathematical proposition but a procedure for demonstrating it: a sequence of Euclidean constructions, or a: sequence of calculations, that is to say, symbolic manipulations (‘Kant, ’s Theory of Geometry,’ The Philosophical Review 94 [1985] 455-506).Google Scholar

19 D.P. Dryer is one commentator who does not neglect these sections of the Doctrine of Method (see esp. ch. 7). My view of Kant’s theory of a priorik proof owes a lot to his work, though I disagree with him on a fundamental point, as we will see. Among recent English-speaking commentators, Patricia Kitcher makes some references to these passages (14-17), as does Michael Friedman, in an important article on the method of construction. There is also a brief but interesting footnote on the method of construction in Humphrey, Ted B. ‘The Historical and Conceptual Relations between Kant’s Metaphysics of Space and Philosophy of Geometry,’ journal of the History of Philosophy 11 (1973) 483-512CrossRefGoogle Scholar and L. W. Beck discusses various parts of the Methodenlehre in a number of works. As a rule, however, it is hardly mentioned; Strawson, Bennett, Allison, and Guyer are among the well known examples. An exception to this general rule is found in students of Kant’s philosophy of mathematics. They tend to pay a Jot of attention to the remarks in the Methodenlehre about construction in geometry at least, and, to a Jesser extent, those about what Kant calls ‘symbolic construction’ in algebra; cf. Thompson, M. ’Singular Terms and Intuitions in Kant’s Epistemology,’ Review of Metaphysics 26 (1972-73) 314-43;Google ScholarParsons, C. ‘Infinity and Kant’s Conception of the “Possibility of Experience“’ and ‘Kant’s Philosophy of Arithmetic,’ both collected in Mathematics in Philosophy (Ithaca, NY: Comell 1983);Google Scholar and Friedman.

20 Since the pages are exactly the same except for the page-numbers in the two editions in the Method, I will cite only the page numbers in B from now on.

21 The most interesting study of the role of the imagination in Kant’s model in general is Waxman’s, WayneKant’s Model of the Mind (Oxford: Oxford University Press 1991).Google Scholar Waxman argues that for Kant the imagination plays a large role, not just in the sort of imaginative exercise I am exploring, but also in ordinary sensible representation. Dryer emphasizes the role it plays, too.

22 That Kant does not make this point explicitly is remarkable. Yet he never distinguishes physics from philosophy nor treats the former separately anywhere in the chapter. We come to realize that if his method justifies the state- ments in philosophy that Kant credits to it, it also justifies his conviction that some of the propositions of physics are also necessary and universal only from the examples he uses. I have in mind in particular the example of causality that figures so centrally in the definitive statement of the method in Section IV (B816), but the way he discusses the other categories in Section I points in the same direction (B752). I should note, if only to say that I will not discuss, the complicated question of the relation of a priorik and a posteriori pursuits in physics. That Kant clearly recognized the central role of the latter comes through more clearly in the Prolegomena and The Metaphysical Foundations of Natural Science than in the first Critique. Very roughly, I think a posteriori investigations give us grounds for thinking that propositions of physics are true, while a priorik investigations establish that what they assert could not be otherwise.

23 ‘Prove’ (beweise) is the word Kant uses (B811ff.). Though the method cannot demonstrate the propositions of philosophy, neither construction nor demonstration being available in philosophy (B754-5), it can prove them. I will leave the sorting out of this distinction to another occasion.

24 Dryer, ch. 7; Allison, 78-80. Thus there had to be something wrong with both accounts. I will not inquire into what. To be fair, Dryer does recognize that Kant says what I just quoted him as saying (285). He just thinks Kant did not mean quite what he says there. In favor of both commentators, I should also acknowledge that, in later works, Kant himself says on occasion that pure intuition is required to prove synthetic a priori propositions (e.g., What Real Progress Has Metaphysics Made in Germany Since the Time of Leibniz and Wolff? Humphrey, Ted ed. and trans. [New York: Abaris Books 1983], Ak. XX, 266Google Scholar, quoted by Allison on 78, and the passages quoted by Dryer on 284-5.) However, there is some question as to whether the works in question are a reliable indication of Kant’s views. They are certainly completely inconsistent with the view expressed in the first Critique. It should additionally be noted that this issue may be smaller than it looks. Virtually anyone looking at what Kant says about the object in general would arrive at the view that it is some kind of singular representation, therefore something like a representation in pure intuition. I return to this issue briefly below. It seems to be a little unclear when What Real Progress … was written. Humphrey suggests 1793 as the probable date; a competition on the same topic was being held by the physics class (!) of the Academy of Berlin (see the translator’s introduction, 13). De Vleeschauwer says that Kant mailed three manuscripts subsequently edited into this work to a friend in 1800, apparently viewing them as ready for publication. See The Development of Kant’s Thought (1939), trans. Duncan, A.R.C. (London: Thomas Nelson and Sons 1962).Google Scholar Whatever, it is a late work (Kant died in 1804, just short of his 80th birthday), not even published during Kant’s lifetime, and it is flatly inconsistent with the first Critique on the point in question.

25 It is over this distinction that Dryer and I part company. Dryer does not give the kind of weight I give to the distinction between conditions of having experience and conditions of being an object (ch. 7). He also thinks that one can somehow establish that propositions are necessarily true by finding out that having and using them is a necessary condition of experiencing. Thus he does not see that the direction of proof in the method of proof in philosophy of the Discipline chapter is from the conditions of being an object to the conditions of experiencing an object, not the reverse. That is to say, he does not see the method of proof Kant describes in this chapter as anything more than a repetition of the central strategy.

26 Lectures on Logic, §1, Ak. IX, 91. As Allison points out (80), we need a representation of an instance of some sort to prove synthetic propositions, and this sort of singular representation does not suffer from the limitations of inductive generalization.

27 That is why I said earlier that the issue between Dryer and Allison and me on the issue of pure intuition may be smaller than it looks.

28 The lack of enthusiasm Wittgensteinians might feel for this latter idea can easily be imagined.

29 Kitcher provides a fine account of this strain of a priorio constructivism in Kant’s thought (ch. 3 and 4, particularly 72, 77, and 80). As she also notes, it allows us to answer the charge that Kant’s whole doctrine of synthesis is built upon an archaic, atomistic theory of sensible stimulation. Her kind of account also captures a lot of what is living in transcendental idealism. In recent cognitive science, the general idea behind it has really taken off, indeed in a number of different directions and under a number of different names.

30 Letter of July 1, 1797 (Ak. XI, 514)

31 The view I am developing here would fit very naturally with Friedman’s view that the job of construction in mathematics is to invent and work through a demonstration or calculation in the imagination (496ff.). The virtues of causalmechanism explanations have been explored recently by Salmon, Wesley in Scientific Explanation and the Causal Structure of the World (Princeton: Princeton University Press 1984) and Miller, Richard in Fact and Method: Explanation, Confirmation, and Reality in the Natural and Social Sciences (Princeton: Princeton University Press 1987).Google Scholar

32 Asking for a mechanism comes pretty close to begging the question in this case, but I will let that difficulty pass.

33 Intentional objects in ‘Two Aspects of Mental Images,’ in Brainstorms (Montgomery, VT: Bradford Books 1978), notional worlds in ‘Beyond Belief; in The Intentional Stance (Cambridge, MA: Bradford Books/MIT Press 1987).

34 ‘Naming and Necessity’