It will be convenient to remember that, in translating a Proposition, beginning with “All”, from abstract form into subscript form, or vice versâ, the Predicate changes sign (that is, changes from positive to negative, or else from negative to positive).
[Thus, the Proposition “All y are x′” becomes “y1x0”, where the Predicate changes from x′ to x.
Again, the expression “x′1y′0” becomes “All x′ are y”, where the Predicate changes for y′ to y.]
[pg073]CHAPTER III.
SYLLOGISMS.
§ 1.
Representation of Syllogisms.
We already know how to represent each of the three Propositions of a Syllogism in subscript form. When that is done, all we need, besides, is to write the three expressions in a row, with “†” between the Premisses, and “¶” before the Conclusion.
[Thus the Syllogism
“No x are m′;
All m are y.
∴ No x are y′.”may be represented thus:—
xm′0 † m1y′0 ¶ xy′0
When a Proposition has to be translated from concrete form into subscript form, the Reader will find it convenient, just at first, to translate it into abstract form, and thence into subscript form. But, after a little practice, he will find it quite easy to go straight from concrete form to subscript form.]