Problems and Postulates: Kant on Reason and Understanding

the purpose of this paper is to think anew Kant’s conception of reason and understanding, the relation between these two faculties and the principles that govern them. I am chiefly interested in the contributions of reason and understanding to the advancement of knowledge. Hence the focus of my paper, so far as reason itself is concerned, is the theoretical rather than the practical employment of this faculty. On the other hand, I think it is useful and fair to say, on Kant’s account, that theoretical reason is itself practical—at least to the extent that we regard scientific enquiry as some kind of activity, namely a research activity, involving practices such as proof and experimentation, undertaken for the sake of a certain end, namely, the acquisition of knowledge. One of Kant’s concerns in the Critique of Pure Reason is to explain how this activity can be profitably pursued. To meet this concern, Kant must explain first of all how we set research goals for scientific enquiry. For without any such goals, we would have no cause to enquire into anything.¹ Kant must also explain where we can find, and how we can use, the means to advance these goals. For again, without any such means, the activity itself would be vain. As I shall argue, the ultimate goals of scientific enquiry spring from reason. The means for achieving these goals and their implementation is the task of our understanding.

We can see why Kant divides the tasks of reason and understanding in this way, if we follow Kant’s own example and reflect on the nature of geometrical demonstration. The difference between problems and postulates in geometry is important to Kant, precisely because he believed that it could help clarify the relation between our two higher faculties of cognition. Reason sets problems for us, just as the ancient geometers did: to that extent, it sets the goals of scientific enquiry. The understanding gives us the means to solve these problems (insofar as a solution is possible), because some of its principles have the character of geometrical postulates. Just as Euclid’s postulates tell us that we may construct circles and line segments to the end of solving problems (as, for example, the problem of constructing an equilaterial triangle), so the Postulates of Empirical Thought tell us what the understanding is licensed to do to the end of solving the special problems set by reason. If we overlook the difference between problems and postulates, says Kant, we shall confuse the separate spheres of reason and understanding. In that case, the activity of investigating nature will cease, on our own account, to be practically viable.

One thing that should emerge from this paper is the great significance of ancient Greek geometry for Kant—not just for his philosophy of mathematics properly speaking, but also for his conception of the way reason operates as a whole.² The evidence suggests that Kant used ancient Greek geometry as a clue or Leitfaden to unlock the workings of our higher cognitive faculties. To be sure, Kant says explicitly that Aristotelian logic plays the role of Leitfaden. But logic could do no more than indicate the formal constraints on our faculties. It could not help Kant see how reason and understanding cooperate to advance our knowledge of objects. Kant apparently believed that geometry could help him see this.³

My paper is divided into two sections. The first section is devoted to reason; the second is devoted to our understanding. In the last few pages, I shall sketch a picture of how the two faculties work together on Kant’s account.

1

Kant says that the distinctive feature of reason is its concern for what he sometimes calls “systematisation” or “systematic unity” (A645/B673; A694/B722–23). Reason takes a certain interest in the knowledge acquired by our understanding. This interest is expressed as an ideal to which such knowledge is expected to conform. As Kant himself puts it, reason seeks “a complete unity in the knowledge obtained by the understanding, by which this knowledge is...