On difficulties concerning intuition and intuitive knowledge - response to James Page, this issue, p. 223

Mind, April, 1993 by Charles Parsons

"Intuition" as understood in contemporary discourse (not only in philosophy) is primarily a source of belief or putative knowledge. It is natural to regiment the notion as a propositional attitude, so that one would speak of an agent as having the intuition that p, or perhaps as intuiting that p. There is, however, a notion of intuition of objects that has roots in the history of philosophy, particularly in Kant. Kant insists on the fundamental role of such intuition in mathematical knowledge, but he is not as explicit as one might expect in affirming the existence and role of intuition of mathematical objects, for want of a theory of such objects. In our time of greater explicitness about ontological commitments, a Kantian conception of intuition would naturally be developed so as to include intuition of mathematical objects. There is, however, much room for ambiguity both in the notion of intuition and in the concept of mathematical object.

A further problem would arise however the idea is further developed: how is intuition of objects related to propositional knowledge? In Kant, intuition is connected with knowledge of objects, but since such knowledge consists of judgments, it appears that intuition is a component of or at least gives rise to propositional knowledge. My own attempts to develop a conception of intuition are in the Kantian tradition, in particular in that it is primarily a notion of intuition of objects that I undertook to explicate. Then the question of the role of such intuition in propositional knowledge is a natural one.

It is on this point that James Page criticizes my views.(2) He concedes that there is intuition of abstract objects, at least of the kind on which I have focused most closely. The questions he raises concern the relation of this intuition to knowledge. I have used the term "intuitive knowledge" to describe knowledge that is based on intuition in an appropriate way.(3) Some of the objections Page makes were probably encouraged by the fact that I did not offer a definition or characterization of intuitive knowledge. I am not sure an exact characterization is even feasible. One might compare the related notion of perceptual knowledge, or knowledge by perception: the project of an "analysis" of knowledge in the sense of a philosopher's definition has run into formidable difficulties, and concerning the further problem just what the role of perception has to be for knowledge to count as perceptual, one would not expect very sharp boundaries.

It should, however, be possible to explain the general idea and to state some of the general properties one would expect a notion of intuitive knowledge to have. One condition is surely that intuition should play an essential role in it. I stated as a necessary condition for intuitive knowledge that it should "rest on" the intuition of objects (1986, p. 215). Page, citing this remark, writes

Our knowledge that a statement is true is intuitive knowledge if it involves the intuition of those objects which make that statement true (p. 224).(4)

As we shall see, Page questions whether the necessary condition is satisfied in some relevant cases.

Another underlying idea of a conception of intuitive knowledge is that intuition should be in some way sufficient for the knowledge in question. By looking at the analogous perceptual case we can see that this is going to give rise to difficulties. Propositional knowledge requires something more than perceptual capacity or even actual perception; to know that a rabbit is there it is not enough to see a rabbit (which usually means simply seeing something that is in fact a rabbit), but something further of a nature that is naturally called conceptual: one must recognize what one sees as a rabbit (and as being there, whatever counts as that). I shall try, in responding to Page's claims, to bring out how far I understand intuition in my sense as being sufficient for intuitive knowledge.

I

Before I reply to Page's criticism, however, I shall mention another prior difficulty for my conception of intuition (and that of Hilbert which was its model) suggested by some published or forthcoming discussions.(5)

The difficulty touches most directly the "modal nominalist" construal of types in my first systematic presentation (1971, [section] III) of my conception of intuition of such objects. But let us consider, to simplify things, a purely nominalist approach to the stroke language.(6) The nominalist approach has certain difficulties. It presupposes that there is a relation of concrete (let us suppose physical) objects which we can call "being of the same type". But this relation will have to be an equivalence relation. In practice, however, it is to a certain degree vague what counts as a token of a given type. But then it is not clear that such a relation can be defined that will be transitive. For example it might be vague with regard to strings of strokes what the distance between them might be. Consider the examples

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