.

This formidable objection is refuted, with beautiful clearness and
simplicity, by these three Diagrams, which show us that, in each of the
three Figures, the Conclusion is really involved in the _two_ Premisses
taken together, each contributing its share.

Thus, in Fig. I., the Premiss xm_{0} empties the _Inner_ Cell of the
N.W. Quarter, while the Premiss ym_{0} empties its _Outer_ Cell. Hence
it needs the _two_ Premisses to empty the _whole_ of the N.W. Quarter,
and thus to prove the Conclusion xy_{0}.

Again, in Fig. II., the Premiss xm_{0} empties the Inner Cell of the
N.W. Quarter. The Premiss ym_{1} merely tells us that the Inner Portion
of the W. Half is _occupied_, so that we may place a 'I' in it,
_somewhere_; but, if this were the _whole_ of our information, we should
not know in _which_ Cell to place it, so that it would have to 'sit on
the fence': it is only when we learn, from the other Premiss, that the
_upper_ of these two Cells is _empty_, that we feel authorised to place
the 'I' in the _lower_ Cell, and thus to prove the Conclusion x'y_{1}.

Lastly, in Fig. III., the information, that m _exists_, merely
authorises us to place a 'I' _somewhere_ in the Inner Square----but it
has large choice of fences to sit upon! It needs the Premiss xm_{0} to
drive it out of the N. Half of that Square; and it needs the Premiss
ym_{0} to drive it out of the W. Half. Hence it needs the _two_
Premisses to drive it into the Inner Portion of the S.E. Quarter, and
thus to prove the Conclusion x'y'_{1}.

pg165

APPENDIX,

ADDRESSED TO TEACHERS.

Sec. 1.

_Introductory._

There are several matters, too hard to discuss with _Learners_, which
nevertheless need to be explained to any _Teachers_, into whose hands
this book may fall, in order that they may thoroughly understand what my
Symbolic Method _is_, and in what respects it differs from the many
other Methods already published.

These matters are as follows:--

The "Existential Import" of Propositions.
The use of "is-not" (or "are-not") as a Copula.
The theory "two Negative Premisses prove nothing."
Euler's Method of Diagrams.
Venn's Method of Diagrams.
My Method of Diagrams.
The Solution of a Syllogism by various Methods.
My Method of treating Syllogisms and Sorites.
Some account of Parts II, III.

Sec. 2.

_The "Existential Import" of Propos