ied, is regarded as the _Predicate_, instead of the _Subject_, of the
Proposition, thus evading a very subtle difficulty which besets the
other form. These subtle difficulties seem to lie at the root of every
Tree of Knowledge, and they are _far_ more hopeless to grapple with than
any that occur in its higher branches. For example, the difficulties of
the Forty-Seventh Proposition of Euclid are mere child's play compared
with the mental torture endured in the effort to think out the essential
nature of a straight Line. And, in the present work, the difficulties of
the "5 Liars" Problem, at p. 192, are "trifles, light as air," compared
with the bewildering question "What is a Thing?"

In the Chapter on 'Propositions of Relation' I have inserted a new
Section, containing the proof that a Proposition, beginning with "All,"
is a _Double_ Proposition (a fact that is quite independent of the
arbitrary rule, laid down in the next Section, that such a Proposition
is to be understood as implying the actual _existence_ of its Subject).
This proof was given, in the earlier editions, incidentally, in the
course of the discussion of the Biliteral Diagram: but its _proper_
place, in this treatise, is where I have now introduced it.
pg-ix
In the Sorites-Examples, I have made a good many verbal alterations, in
order to evade a difficulty, which I fear will have perplexed some of
the Readers of the first three Editions. Some of the Premisses were so
worded that their Terms were not Specieses of the Univ. named in the
Dictionary, but of a larger Class, of which the Univ. was only a
portion. In all such cases, it was intended that the Reader should
perceive that what was asserted of the larger Class was thereby asserted
of the Univ., and should ignore, as superfluous, all that it asserted of
its _other_ portion. Thus, in Ex. 15, the Univ. was stated to be "ducks
in this village," and the third Premiss was "Mrs. Bond has no gray
ducks," i.e. "No gray ducks are ducks belonging to Mrs. Bond." Here the
Terms are _not_ Specieses of the Univ., but of the larger Class "ducks,"
of which the Univ. is only a portion: and it was intended that the
Reader should perceive that what is here asserted of "ducks" is thereby
asserted of "ducks in this village." and should treat this Premiss as if
it were "Mrs. Bond has no gray ducks in this village," and should
ignore, as superfluous, what it