Thus, Camestres is reduced to Celarent,—

All P is M,⟍ ⟋No M is S,
No S is M, ⟋ ⟍All P is M,
therefore, No S is P.therefore, No P is S,
therefore, No S is P.[ 342]

[342] The order of inference in this and in other reductions might be made clear by the use of arrows, representing inference, as follows:

All P is M,⟍ ↗No M is S,
No S is M, ⟋ ↘All P is M,
↓
No S is P.←No P is S,

s (in the middle of a word) indicates that in the process of reduction the preceding proposition is to be simply converted. 321 Thus, in reducing Camestres to Celarent, as shewn above, the minor premiss is simply converted.

s (at the end of a word) shews that the conclusion of the new syllogism has to be simply converted in order that the given conclusion may be obtained. This again is illustrated in the reduction of Camestres. The final s does not affect the conclusion of Camestres itself, but the conclusion of Celarent to which it is reduced.[343]

[343] This peculiarity in the signification of s and p when they are final letters is sometimes overlooked. The point to be noted is that the conclusion of the syllogism originally given is not, like the original premisses, a datum from which we set out, but a result that we have to reach. It follows that the conclusion to be manipulated, if any, must be the conclusion of the syllogism obtained by reduction, not the conclusion of the original syllogism. This is clearly shewn in the case of Camestres by the method adopted in the last preceding [note] to illustrate the reduction of Camestres to Celarent. The reduction of Disamis, Bramantip, Camenes, Dimaris to figure 1 might be illustrated similarly.

p (in the middle of a word) signifies that the preceding proposition is to be converted per accidens ; as, for example, in the reduction of Darapti to Darii,—

All M is P,All M is P,
All M is S, Some S is M,
therefore, Some S is P.therefore, Some S is P.

p (at the end of a word[344]) implies that the conclusion obtained by reduction is to be converted per accidens. Thus, in Bramantip, the p does not relate to the I conclusion of the mood itself;[345] it really relates to the A conclusion of the syllogism in Barbara which is given by reduction. Thus,—