'Some y' are x',' or, 'Some not-gamblers are not-philosophers.'" pg183 (5) _Solution by my Method of Diagrams._ The first Premiss asserts that no xm exist: so we mark the xm-Compartment as empty, by placing a 'O' in each of its Cells. The second asserts that some my' exist: so we mark the my'-Compartment as occupied, by placing a 'I' in its only available Cell. ·---------------· | | | | ·---|---· | | |(O)|(O)| | |---|---|---|---| | | |(I)| | | ·---|---· | | | | ·---------------· The only information, that this gives us as to x and y, is that the x'y'-Compartment is _occupied_, i.e. that some x'y' exist. Hence "Some x' are y'": i.e. "Some persons, who are not philosophers, are not gamblers". (6) _Solution by my Method of Subscripts._ xm_{0} + my'_{1} ¶ x'y'_{1} i.e. "Some persons, who are not philosophers, are not gamblers." § 9. _My Method of treating Syllogisms and Sorites._ Of all the strange things, that are to be met with in the ordinary text-books of Formal Logic, perhaps the strangest is the violent contrast one finds to exist between their ways of dealing with these two subjects. While they have elaborately discussed no less than _nineteen_ different forms of _Syllogisms_----each with its own special and exasperating Rules, while the whole constitute an almost useless machine, for practical purposes, many of the Conclusions being incomplete, and many quite legitimate forms being ignored----they have limited _Sorites_ to _two_ forms only, of childish simplicity; and these they have dignified with special _names_, apparently under the impression that no other possible forms existed!