T 2.3.3.2

The understanding exerts itself after two different ways, as it judges from demonstration or probability; as it regards the abstract relations of our ideas, or those relations of objects, of which experience only gives us information. I believe it scarce will be asserted, that the first species of reasoning alone is ever the cause of any action. As it's proper province is the world of ideas, and as the will always places us in that of realities, demonstration and volition seem, upon that account, to be totally remov'd, from each other. Mathematics, indeed, are useful in all mechanical operations, and arithmetic in almost every art and profession: But 'tis not of themselves they have any influence. Mechanics are |the art of regulating the motions of bodies to some design'd end or purpose; and the reason why we employ arithmetic in fixing the proportions of numbers, is only that we may discover the proportions of their influence and operation. A merchant is desirous of knowing the sum total of his accounts with any person: Why? but that he may learn what sum will have the same effects in paying his debt, and going to market, as all the particular articles taken together. Abstract or demonstrative reasoning, therefore, never influences any of our actions, but only as it directs our judgment concerning causes and effects; which leads us to the second operation of the understanding.