_Given a Trio of Propositions of Relation, of which every two contain a Pair of codivisional Classes, and which are proposed as a Syllogism; to ascertain whether the proposed Conclusion is consequent from the proposed Premisses, and, if so, whether it is complete._ The Rules, for doing this, are as follows:-- (1) Take the proposed Premisses, and ascertain, by the process described at p. 60, what Conclusion, if any, is consequent from them. (2) If there be _no_ Conclusion, say so. (3) If there _be_ a Conclusion, compare it with the proposed Conclusion, and pronounce accordingly. I will now work out, in their briefest form, as models for the Reader to imitate in working examples, six Problems. (1) "All soldiers are strong; All soldiers are brave. Some strong men are brave." Univ. "men"; m = soldiers; x = strong; y = brave. pg067 ·---------------· ·-------· "All m are x; | | | |(I)| | All m are y. | ·---|---· | |---|---| Some x are y." | |(I)|(O)| | | | | |---|---|---|---| ·-------· | |(O)|(O)| | | ·---|---· | .'. "Some x are y." | | | ·---------------· Hence proposed Conclusion is right. (2) "I admire these pictures; When I admire anything I wish to examine it thoroughly. I wish to examine some of these pictures thoroughly." Univ. "things"; m = admired by me; x = these pictures; y = things which I wish to examine thoroughly. ·---------------· ·-------· "All x are m; |(O) | (O)| |(I)|(O)| All m are y. | ·---|---· | |---|---| Some x are y." | |(I)|(O)| | | | | |---|---|---|---| ·-------· | | |(O)| | | ·---|---· | .'. "All x are y." | | | ·---------------· Hence proposed Conclusion is _incomplete_, the _complete_ one being "I wish to examine _all_ these pictures thoroughly". (3) "None but the brave deserve the fair; Some braggarts are cowards. Some braggarts do not deserve the fair." Univ. "persons"; m = brave; x = deserving of the fair; y = braggarts. ·---------------· ·-------· "No m' are x; |(O) | (O)| | | | Some y are m'. | ·---|---· | |---|---| Some y are x'." | | | | | |(I)| | |---|---|---|---| ·-------· | | | | | | ·---|---· | .'. "Some y are x'." |(I) | | ·---------------·