All cognition, that is, all presentations consciously referred to an object, are either intuitions or concepts. Intuition is a singular presentation (repraesentatio singularis), the concept is a general (repraesentatio per notas communes) or reflected presentation (repraesentatio discursiva).(Jäsche Logic, §1)
In whatever manner and by whatever means a cognition may relate to objects, intuition is that through which it is in immediate relation to them, and to which all thought as a means is directed. But intuition takes place only in so far as the object is given to us.(Critique of Pure Reason, A19/B33)
Space is not a discursive or, as we say, general concept of relations of things in general, but a pure intuition.(A25/B39)
Charles Parsons has taught us that the Kantian conception of intuition is a multi-faceted notion and that this complexity affects Kant's philosophy of mathematics. In this essay, I focus on these two lessons, but also broaden them a bit. Specifically, I have three goals:
Parsons has taught us that the notion of immediacy – which he interprets phenomenologically – must be separately added to the traditional criterion of singularity that has been stressed by all commentators on Kant's definition of intuition. In this essay, however, I shall point out that Kant offers not two but three marks of human intuition: There is singularity; there is, as Parsons insists, immediacy; and there is also something I shall call “reference.” Kant calls it the “object givingness” of intuition. It is there quite clearly at A19.