The Theory of Reasoning

intended for the Appendix , in order to avoid interrupting the exposition of the subject by too great particularity, the simplest instance will here suffice: the lines A and B are respectively equal to c, and therefore they are equal to each other. Here the mind observing successively the equality of A to c and that of B to c, is thence led to discern the mutual equality of A and B, which is not self-evident or immediately discernible from the inspection of A and B alone. It is plain that in reasoning of this second species, which is with great propriety termed demonstrative, we intuitively discern, at each step, that one fact implies another, and discern too that a denial of the implied fact involves a contradiction. But demonstrative reasoning is not confined tothe science of quantity. It is to be found in all departments of human knowledge. See Appendix, Article 1. D Whenever the mind discerns one fact to be implied in another, or the exclusion of a fact to be implied in another fact, it reasons demonstratively, whether they are facts of quantity or otherwise. Examples of this truth might be multiplied without end, but the few which follow will be sufficient for illustration. That portrait is a striking likeness of two different persons; therefore they must resemble each other. The two litigants cannot both be the exclusive owners of the property in dispute; therefore one of them must be urging a wrong claim. The traveller who was a...