273. We may now appreciate at its just value, the opinion of Dugald Stewart, who, in his _Elements of the Philosophy of the Human Mind_, says: "It may be fairly questioned, too, whether it can, with strict correctness, be said of the simple arithmetical equation, 2 plus 2 = 4, that it may be represented by the formula A = A. The one is a proposition asserting the equivalence of two different expressions; to ascertain which equivalence may, in numberless cases, be an object of the highest importance. The other is altogether unmeaning and nugatory, and cannot, by any possible supposition, admit of the slightest application of a practical nature. What opinion then shall we form of the proposition A = A, when considered as the representative of such a formula as the binomial theorem of Sir Isaac Newton? When applied to the equation 2 plus 2 = 4, (which in its extreme simplicity and familiarity is apt to be regarded in the light of an axiom:) the paradox does not appear to be so manifestly extravagant; but, in the other case, it seems quite impossible to annex to it any meaning whatever."[22] This philosopher does not observe that the pretended extravagance arises from his wrong interpretation of his adversaries' opinion. No one ever thought of denying the importance of the discoveries which prove different expressions equivalent: no one doubts that Newton's formula of the binomial is a great advance upon the formula A = A: but the question consists not in this, but in seeing whether Newton's formula of the binomial is any thing more than the expression of identical things; and whether even the merit of the expression is or is not the fruit of a series of perceptions of identity. Were the question presented under Dugald Stewart's point of view, it would be unworthy of discussion: for philosophy should not dispute upon things that are ridiculous as well as absurd. [22] Part II., Chap. II., Sect. 3, § 2, pages 436-7. CHAPTER XXVIII. CONTINUATION OF THE SAME SUBJECT. 274. We will now explain how the doctrine of identity is applied in general to all reasoning, whether upon mathematical objects or not: with this view we will examine some of the dialectical forms in which the art of reasoning is taught. Every A is B; M is A: therefore M is B. In the major of this syllogism we find the identity of every A with B; and in the minor, the identity of M with B. In each of these propositions there is affirmation, and, consequently, perception of identity. Let us now see what takes place in the connection which constitutes the force of the argument.