s "Either (1) or (3) or (4) is true."
Now the assertion "Either (1) or (3) is true" is equivalent to "Some xy
are not-z"; and the assertion "(4) is true" is equivalent to "No xy
exist." Hence the Contradictory to "All xy are z" may be expressed as
the Alternative Proposition "Either some xy are not-z, or no xy exist,"
but _not_ as the Categorical Proposition "Some y are not-z."

pg196
(B) [See p. 171, at end of Section 2.]

There are yet _other_ views current among "The Logicians", as to the
"Existential Import" of Propositions, which have not been mentioned in
this Section.

One is, that the Proposition "some x are y" is to be interpreted,
neither as "Some x _exist_ and are y", nor yet as "If there _were_ any x
in existence, some of them _would_ be y", but merely as "Some x _can be_
y; i.e. the Attributes x and y are _compatible_". On _this_ theory,
there would be nothing offensive in my telling my friend Jones "Some of
your brothers are swindlers"; since, if he indignantly retorted "What do
you _mean_ by such insulting language, you scoundrel?", I should calmly
reply "I merely mean that the thing is _conceivable_----that some of
your brothers _might possibly_ be swindlers". But it may well be doubted
whether such an explanation would _entirely_ appease the wrath of Jones!

Another view is, that the Proposition "All x are y" _sometimes_ implies
the actual _existence_ of x, and _sometimes_ does _not_ imply it; and
that we cannot tell, without having it in _concrete_ form, _which_
interpretation we are to give to it. _This_ view is, I think, strongly
supported by common usage; and it will be fully discussed in Part II:
but the difficulties, which it introduces, seem to me too formidable to
be even alluded to in Part I, which I am trying to make, as far as
possible, easily intelligible to mere _beginners_.

(C) [See p. 173, Sec. 4.]

The three Conclusions are

"No conceited child of mine is greedy";
"None of my boys could solve this problem";
"Some unlearned boys are not choristers."

pg197

INDEX.

Sec. 1.

_Tables._

I. Biliteral Diagram. Attributes of Classes, and
Compartments, or Cells, assigned to them 25

II. do. Representation of Uniliteral Propositions of
Existence 34