-CE_s_A_r_E, CA_m_E_str_E_s_,
FE_st_I_n_O BA_r_O_k_O.

III. In the Third Figure, the Minor Premiss must be affirmative.

Otherwise, the conclusion would be negative, and the Major Premiss
affirmative, and there would be illicit process of the Major, P being
the predicate term in the Major Premiss.

M in P
M in S.

This cuts off AE, EE, IE, OE, AO, EO, IO, OO,--the second and fourth
rows in the above list.

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