[This is an extract from 'Hume and Kant on Reality', a chapter in The Sacred History of Being, published November 2, 2015]
Kant defines metaphysics very closely as something whose ‘fundamental propositions … and its fundamental concepts must never be taken from experience’, since metaphysical knowledge lies beyond experience. The ground of metaphysics will not be either ‘outer experience’, which he defines as the source of physics, nor ‘inner experience, which provides the basis for empirical psychology.’ In other words metaphysics is a priori knowledge, ‘out of pure understanding and pure reason’.
Kant recognizes the need to differentiate metaphysics from pure mathematics, and refers the reader to the Critique, where he says
‘Philosophical cognition is rational cognition from concepts. Mathematical cognition is rational cognition from the construction of concepts.’ [i]
He expands on this by saying that ‘to construct a concept means to exhibit a priori the intuition corresponding to it. Hence construction of a concept requires a non-empirical intuition. Consequently this intuition, as intuition, is an individual object; but as the construction of a concept, (a universal presentation), it must nonetheless express in the presentation its universal validity for all possible intuitions falling under the same concept.’
Kant uses the example of the construction of a triangle, arguing that this construction exhibits the object which corresponds to this concept ‘either through imagination alone, or in pure intuition.’ It can be drawn on paper of course, as a mathematical figure, but in such a case the representation is an empirical intuition, not a pure intuition, though both in the case of the pure intuition and the empirical intuition, Kant has exhibited the object a priori, without having used a model taken from experience (meaning that only the properties of a triangle have been used in its construction). Though the drawn figure is empirical, yet it serves to express the concept ‘without impairing the concept’s universality’. Only those properties which it is necessary to consider for the construction of the triangle are involved – the many inconsequential details of a physical triangle – the length of the sides, and the angles of the triangle, are not involved in the abstraction. All such irrelevant details are removed from the concept, and the result is therefore wholly abstracted from any particular instance of a triangle.
Kant’s argument is therefore that ‘philosophical cognition contemplates the particular only in the universal’. By contrast, he says that mathematical cognition ‘contemplates the universal in particular, and indeed even in the individual’. This might seem at first sight to be a strange distinction, however Kant explains himself clearly, saying that even in the case of this mathematical cognition, the contemplation of it is ‘a priori, and by means of reason.’ And so, ‘just as this individual is determined under certain universal conditions of construction, so the object of the concept – to which this individual corresponds only as its schema – must be thought of as determined universally. Thus the essential difference between these two kinds of rational cognition ‘consists in this difference of form, and does not rest on the difference of their matter or objects.’
[End of extract]