II and OI are inadmissible by Canon VI.; which leaves AA, IA, AI, EA, OA, EI--DA_r_A_pt_I, DI_s_A_m_I_s_, DA_t_I_s_I, FE_l_A_pt_O_n_, BO_k_A_rd_O, FE_r_I_s_O--three affirmative moods and three negative. IV. The Fourth Figure is fenced by three special rules. (1) In negative moods, the Major Premiss is universal. (2) If the Minor is negative, both premisses are universal. (3) If the Major is affirmative, the Minor is universal. (1) Otherwise, the Figure being P in M M in S, there would be illicit process of the Major. (2) The Major must be universal by special rule (1), and if the Minor were not also universal, the Middle would be undisturbed. (3) Otherwise M would be undistributed. Rule (1) cuts off the right-hand column, OA, OE, OI, and OO; also IE and IO. Rule (2) cuts off AO, EO. Rule (3) cuts off AI, II. EE goes by general Canon IV.; and we are left with AA, AE, IA, EA, EI--B_r_A_m_A_nt_I_p_, CA_m_E_n_E_s_, DI_m_A_r_I_s_, FE_s_A_p_O, F_r_E_s_I_s_O_n_. CHAPTER IV. THE ANALYSIS OF ARGUMENTS INTO SYLLOGISTIC FORMS. Turning given arguments into syllogistic form is apt to seem as trivial and useless as it is easy and mechanical. In most cases the necessity of the conclusion is as apparent in the plain speech form as in the artificial logical form. The justification of such exercises is that they give familiarity with the instrument, serving at the same time as simple exercises in ratiocination: what further uses may be made of the instrument once it is mastered, we shall consider as we proceed. I.--FIRST FIGURE. Given the following argument to be put into Syllogistic form: "No war is long popular: for every war increases taxation; and the popularity of anything that touches the pocket is short-lived". The simplest method is to begin with the conclusion--"No war is long popular"--No S is P--then to examine the argument to see whether it yields premisses of the necessary form. Keeping the form in mind, Celarent of Fig. I.-- No M is P All S is M No S is P-- we see at once that "Every war increases taxation" is of the form All S is M. Does the other sentence yield the Major Premiss No M is P, when M represents the increasing of taxation, _i.e._, a class bounded by that attribute? We see that the last sentence of the argument is equivalent to saying that "Nothing that increases taxation is long popular"; and this with the Minor yields the conclusion in Celarent. Nothing that increases taxation is long popular. Every war increases taxation. No war is long popular.