_____
_/ + \_
_/___ ___\_
_/|##+#\_/ |\_
/ \###/#\ _/ \
| + \|_#_|/ |
\_ m \_/ y _/
\_____/ \_____/

The Major declares that all xm must be destroyed; erase it.

Then, as some my' is to be saved, it must clearly be my'x'. That is,
there must exist my'x'; or eliminating m, y'x'. In common phraseology,

'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."

Sec. 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!

As to _Syllogisms_, I find that their nineteen forms, with about a score
of others which they have ignored, can all be arranged under _three_
forms, each with a very simple Rule of its own; and the only question
the Reader has to settle, in working any one of t