Page:An Investigation of the Laws of Thought (1854, Boole, investigationofl00boolrich).djvu/201

CHAP. XIII.] CHAPTER XIII. ANALYSIS OF A PORTION OF DR. SAMUEL CLARKE'S "DEMONSTRATION OF THE BEING AND ATTRIBUTES OF GOD," AND OF A PORTION OF THE "ETHICA ORDINE GEOMETRICO DEMONSTRATA" OF SPINOZA. HE general order which, in the investigations of the following chapter, I design to pursue, is the following. I shall examine what are the actual premises involved in the demonstrations of some of the general propositions of the above treatises, whether those premises be expressed or implied. By the actual premises I mean whatever propositions are assumed in the course of the argument, without being proved, and are employed as parts of the foundation upon which the final conclusion is built. The premises thus determined, I shall express in the language of symbols, and I shall then deduce from them by the methods developed in the previous chapters of this work, the most important inferences which they involve, in addition to the particular inferences actually drawn by the authors. I shall in some instances modify the premises by the omission of some fact or principle which is contained in them, or by the addition or substitution of some new proposition, and shall determine how by such change the ultimate conclusions are affected. In the pursuit of these objects it will not devolve upon me to inquire, except incidentally, how far the metaphysical principles laid down in these celebrated productions are worthy of confidence, but only to ascertain what conclusions may justly be drawn from given premises; and in doing this, to exemplify the perfect liberty which we possess as concerns both the choice and the order of the elements of the final or concluding propositions, viz., as to determining what elementary propositions are true or false, and what are true or false under given restrictions, or in given combinations. The chief practical difficulty of this inquiry will consist,