THE PHILOSOPHY OF SPINOZA AND LEIBNIZ. 351 (as we have already seen) the figures or determinations of extension are reducible to directions of motion (leaving out of account mass, or moving body, and velocity). All real motion, then, has direction ; it is given, not independently, but in relation to extension. And consequently the motion whose quantity in the universe is fixed must be motion having direction : the direction is conserved as well as the quantity of abstract motion. But the direction of a motion is not something actual in the sense that it can be seen or pictured as a whole. It is a quality, a potentiality or partly hidden tendency in the motion, an infinitesimal, out of which the finite motion develops. This potentiality or tendency, which is presupposed by all actual motion when we take into consideration its direction, is what Leibniz means by Force. And thus for Leibniz Force, as qualitative, as a potency passing into actuality, an identity in difference, is the sub- stance or reality from which actual visible or picturable motion and extension are abstractions. 1 An infinitely little line is a direction of motion and an infinitely little motion (or direction of motion) is a force. Thus the positive interpretation of the infinitely little means a passing from superficial ideas of sense and imagination to deeper and more comprehensive notions of thought, from the abstract to the concrete. But the attitude of sense or imagination is not absolutely cut off from the attitude of thought or understanding. Comprehen- sion by the understanding is a thinking out of what appears imperfectly in sense. (2) This leads naturally to a brief consideration of the difference between Spinoza's theory of knowledge and that of Leibniz. Spinoza draws a sharp line between opinio or imaginatio, on the one hand, and ratio and scientia intuitiva, on the other. Opinio or imaginatio is the cause of falsity, while the knowledge given by ratio and scientia intuitiva is necessarily true.' 2 Thus in the Tractatus de Intellectus Emenda- tione we find Spinoza insisting mainly on the distinction 1 Thus Spinoza and Leibniz are both opposed to Descartes's theory that extension is the essence of corporeal substance, on the ground that divisible extension presupposes something omni parte carens. But this indivisible basis of extension is conceived by Spinoza negatively, as being entirely without parts in any sense, as being one in opposition to many, while Leibniz conceives it positively, as something which has degrees or varieties and thus as one in many. The difference is so considerable and so closely connected with Leibniz's mathematics that I think it ought to weigh heavily against the suggestion of Stein (p. 64 sqq.) that Leibniz was probably influenced by Spinoza in his criticism of Descartes's view of " extended substance ".
- Eth., ii, 40, 41.
