Metaphysics is nothing other than the philosophy of the fundamental principles of our cognition. Accordingly, what was established in the preceding reflection about mathematical cognition in comparison with philosophy will also apply to metaphysics. We have seen that the differences which are to be found between cognition in mathematics and cognition in philosophy are substantial and essential. And in this connection, one can say with Bishop Warburton that nothing has been more damaging to philosophy than mathematics, and in particular the imitation of its method in contexts where it cannot possibly be employed. The application of the mathematical method in those parts of philosophy involving cognition of magnitudes is something quite different, and its utility is immeasurable.

In mathematics I begin with the definition of my object, for example, of a triangle, or a circle, or whatever. In metaphysics I may never begin with a definition. Far from being the first thing I know about the object, the definition is nearly always the last thing I come to know. In mathematics, namely, I have no concept of my object at all until it is furnished by the definition. In metaphysics I have a concept which is already given to me, although it is a confused one. My task is to search for the distinct, complete and determinate concept. How then am I to begin? Augustine said: ‘I know perfectly well what time is, but if someone asks me what it is I do not know.’ In such a case as this, many operations have to be performed in unfolding obscure ideas, in comparing them with each other, in subordinating them to each other and in limiting them by each other. And I would go as far as to say that, although much that is true and much that is penetrating has been said about time, nonetheless no real definition has ever been given of time.