Part 35 (1/2)

-- 694. It is convenient to represent the two syllogisms in juxtaposition thus--

Baroko. Barbara.

All A is B. All A is B.

Some C is not B. / All C is A.

.'. Some C is not A. / All C is B.

-- 695. The lines indicate the propositions which conflict with one another. The initial consonant of the names Baroko and Eokardo indicates that the indirect reduct will be Barbara. The k indicates that the O proposition, which it follows, is to be dropped out in the new syllogism, and its place supplied by the contradictory of the old conclusion.

-- 696. In Bokardo the two syllogisms will stand thus--

Bokardo. Barbara.

Some B is not A. / All C is A.

All B is C. X All B is C.

.'. Some C is not A./ .'. All B is A.

-- 697. The method of indirect reduction, though invented with a special view to Baroko and Bokardo, is applicable to all the moods of the imperfect figures. The following modification of the mnemonic lines contains directions for performing the process in every case:--Barbara, Celarent, Darii, Ferioque prioris; Felake, Dareke, Celiko, Baroko secundae; Tertia Cakaci, Cikari, Fakini, Bekaco, Bokardo, Dekilon habet; quarta insuper addit Cakapi, Daseke, Cikasi, Cepako, Ceskon.

-- 698. The c which appears in two moods of the third figure, Cakaci and Bekaco, signifies that the new conclusion is the contrary, instead of, as usual, the contradictory of the discarded premiss.

-- 699. The letters s and p, which appear only in the fourth figure, signify that the new conclusion does not conflict directly with the discarded premiss, but with its converse, either simple or per accidens, as the case may be.

-- 700. l, n and r are meaningless, as in the original lines.

CHAPTER XIX.

_Of Immediate Inference as applied to Complex Propositions._

-- 701. So far we have treated of inference, or reasoning, whether mediate or immediate, solely as applied to simple propositions. But it will be remembered that we divided propositions into simple and complex. I t becomes inc.u.mbent upon us therefore to consider the laws of inference as applied to complex propositions. Inasmuch however as every complex proposition is reducible to a simple one, it is evident that the same laws of inference must apply to both.

-- 702. We must first make good this initial statement as to the essential ident.i.ty underlying the difference of form between simple and complex propositions.

-- 703. Complex propositions are either Conjunctive or Disjunctive (-- 214).

-- 704. Conjunctive propositions may a.s.sume any of the four forms, A, E, I, O, as follows--

(A) If A is B, C is always D.

(E) If A is B, C is never D.

(I) If A is B, C is sometimes D.

(O) If A is B, C is sometimes not D.

-- 705. These admit of being read in the form of simple propositions, thus--

(A) If A is B, C is always D = All cases of A being B are cases of C being D. (Every AB is a CD.)

(E) If A is B, C is never D = No cases of A being B are cases of C being D. (No AB is a CD.)

(I) If A is B, C is sometimes D = Some cases of A being B are cases of C being D. (Some AB's are CD's.)