i.e. "No son of mine ever fails to be treated with respect."
"All cats understand French; Some chickens are cats".
Univ. "creatures"; m = cats; x = understanding French; y = chickens.
·---------------· ·-------· "All m are x; | | | |(I)| | Some y are m." | ·---|---· | |---|---| | |(I)| | | | | | |---|---|---|---| ·-------· | |(O)|(O)| | | ·---|---· | .'. "Some y are x." | | | ·---------------·
"All diligent students are successful; All ignorant students are unsuccessful".
Univ. "students"; m = successful; x = diligent; y = ignorant.
·---------------· ·-------· "All x are m; |(O) | (O)| |(O)|(I)| All y are m'." | ·---|---· | |---|---| | |(O)|(I)| | |(I)| | |---|---|---|---| ·-------· | |(O)| | | | ·---|---· | .'. "All x are y'; |(I) | | All y are x'." ·---------------·
i.e. "All diligent students are learned; and all ignorant students are idle". pg065 (4) [see p. 63]
"Of the prisoners who were put on their trial at the last Assizes, all, against whom the verdict 'guilty' was returned, were sentenced to imprisonment;
Some, who were sentenced to imprisonment, were also sentenced to hard labour".
Univ. "prisoners who were put on their trial at the last Assizes", m = sentenced to imprisonment; x = against whom the verdict 'guilty' was returned; y = sentenced to hard labour.
·---------------· "All x are m; |(O) | (O)| Some m are y." | ·---|---· | | | (I) | | |---|(I)|---|---| | | | | | | ·---|---· | There is no | | | Conclusion. ·---------------·
[Review Tables VII, VIII (pp. 48, 49). Work Examples § =1=, 17-21 (p. 97); § =4=, 1-6 (p. 100); § =5=, 1-6 (p. 101).]
_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.
(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.