DESARROLLO MECANICO

In this chapter I have taken various objections originally advanced against Kant by Philip Kitcher in relation, not to Kant himself, but to the neo-Kantian view. In this Postscript I argue that in fact Kitcher seriously misreads Kant, and specifically that the Irrelevance Objection is ill-founded as a result.

As a summary reading o f Kant, Kitcher claims that:

Kant proposes that we construct figures in thought, inspect them with the mind’s eye, and thus arrive at a priori knowledge o f the axioms from which our proofs begin ... Kant’s own proposal is tied to a sensuous notion of pure intuition—we draw mental pictures and look at them.^"^^

But I suggest that this is misleading, and perhaps mistaken, in three respects. First, as far as I am aware, Kant does not discuss the specific question o f how we know the axioms o f Euclid’s geometry in any detail in the first Critique, and it is certainly not at the forefront o f the discussion in the Doctrine of Method, on which Kitcher’s

reconstruction is based. As I argued at the end of the last chapter, the focus there is on the epistemology of the reasoning involved in following Euclid’s argument, and this does not concern as such—though it does logically presuppose— an account of how the reasoner knows Euclid’s axioms. Secondly, Kant’s notion of pure intuition is not, I think, sensuous, at least if this term is taken in the normal way as relating to

sensations. On the contrary, Kant explicitly dissociates pure intuition from sensation, which he takes as arising in empirical intuition. Pure intuitions are pure in being sensation-free, and they are intuitions in being immediate singular representations. Thirdly, Kant’s view is not—as Kitcher later a c k n o w le d g e s—that the reasoner merely draws diagrams and then looks at them. This would be, or would be close to, a reading-off view of the kind rejected (both on its own merits and as an interpretation o f Kant) in the previous chapter. Rather, the reasoner follows the argument in relation to the triangles represented by the diagram; and it is this overall process— and not any tacit appeal to specific features of the diagram as such—that ultimately confers

justification.

Does Kant’s own position succumb to the Irrelevance Objection? I suggested above that it does not, and that there is a strategy available to him that is broadly analogous to that of the neo-Kantian. But there is also a question as to whether the objection, which derives from Kitcher’s misreading, ever really gets going against Kant’s position. Recall that the Irrelevance Objection presents a dilemma: either the generalisation to Euclid’s conclusion is conceptual or it is not. If it is conceptual, then— supposedly—it does not depend on intuition, and the figure is redundant. But if it is not conceptual, then the figure must have intuitive properties as well as merely accidental properties, and a non-circular account is required o f how a reasoner may differentiate between them.

If Kant is to face this dilemma, then on his account it must be an either/or matter whether the generalisation is conceptual or involves intuition. But is this in fact his view? O f course, the disjunction between intuition and concept is fimdamental to Kant. But recall that, in relation to the kind(s) of reasoning discussed in the Doctrine o f Method, Kant’s claim is that the scope of the generalisation is determined not by the concept o f a triangle as such but by the schema o f the concept o f a triangle; that is, by the reasoner’s grasp o f what objects are generated by the relevant construction procedure. This grasp has a spatial or intuitive component, and schemata are, precisely, for Kant what unite the conceptual and the intuitive.

Kitcher 1984, p. 52, Kitcher 1975 recognises, if only briefly, the epistemic role of construction procedures in Kant’s account (p. 43); but this recognition is not carried forward to Kitcher 1984,

Kitcher tries to cut off this line of response as follows;

Geometrical truths must either be about some particular feature o f the world— that feature in virtue o f which they are true—or they must state some

particular property o f our concepts. Since they are not analytic, the latter cannot be the case. So geometric truths are true in virtue of some facet of the world.

Call this the “No-Property” argument. However, in reply Kant can simply deny the move from non-analyticity to the claim that geometrical claims do not state properties of concepts; he can claim that such claims might state properties o f concepts

understood in relation to their schemata—properties not “contained in” the

concepts— and still be synthetic. And this seems to be Kant’s p o s itio n :c o m p a r e his remarks in the Schematism,^"^* and also (and explicitly) in the Doctrine of Method. In a telling passage from the latter, Kant remarks:

[In geometrical reasoning] I am not to see what I actually think in my concept o f a triangle (this is nothing further than its mere definition), rather I am to go beyond it to properties that do not lie in this concept but still belong to i t ... I put together in a pure intuition the manifold that belongs to the schema o f a triangle in general and thus to its concept, through which general synthetic propositions must be constructed.

For Kant, this aptly brings out (1) the connection between geometrical concepts and geometrical definitions here, (2) the important contrast between a concept and the schema of a concept, and (3) the explanatory value o f the latter. Since geometrical claims rely on schemata for their generality, it does seem that Kant’s view is that they are both synthetic and state properties o f concepts.

So the “No-Property” argument fails, and Kitcher’s overall argument by dilemma cannot really be formulated fairly against Kant. O f course, I am not suggesting that Kant’s view of concepts is not problematic, and there are serious difficulties relating to his conception of a schema, as noted. But this would not affect the point being

Kitcher 1975, p. 29. Cf. Friedman 1992, p. 90.

made here, which is that— at least as formulated—the Irrelevance Objection does not properly arise for Kant, once his position is better understood.