walk!_"

And _you_ will reply "But suppose there was a mad bull behind
you?"

And then your innocent friend will say "Hum! Ha! I must think
that over a bit!"

You may then explain to him, as a convenient _test_ of the
soundness of a Syllogism, that, if circumstances can be invented
which, without interfering with the truth of the _Premisses_,
would make the _Conclusion_ false, the Syllogism _must_ be
unsound.]

[Review Tables V-VIII (pp. 46-49). Work Examples Sec. =4=, 7-12 (p.
100); Sec. =5=, 7-12 (p. 101); Sec. =6=, 1-10 (p. 106); Sec. =7=, 1-6
(pp. 107, 108).]

pg070

BOOK VI.

THE METHOD OF SUBSCRIPTS.

CHAPTER I.

_INTRODUCTORY._

Let us agree that "x_{1}" shall mean "Some existing Things have the
Attribute x", i.e. (more briefly) "Some x exist"; also that "xy_{1}"
shall mean "Some xy exist", and so on. Such a Proposition may be called
an '=Entity=.'

[Note that, when there are _two_ letters in the expression, it
does not in the least matter which stands _first_: "xy_{1}" and
"yx_{1}" mean exactly the same.]

Also that "x_{0}" shall mean "No existing Things have the Attribute x",
i.e. (more briefly) "No x exist"; also that "xy_{0}" shall mean "No xy
exist", and so on. Such a Proposition may be called a '=Nullity='.

Also that "+" shall mean "and".

[Thus "ab_{1} + cd_{0}" means "Some ab exist and no cd exist".]

Also that ">" shall mean "would, if true, prove".

[Thus, "x_{0} > xy_{0}" means "The Proposition 'No x exist'
would, if true, prove the Proposition 'No xy exist'".]

When two Letters are both of them accented, or both _not_ accented, they
are said to have '=Like Signs=', or to be '=Like=': when one is
accented, and the other not, they are said to have '=Unlike Signs=', or
to be '=Unlike='.

pg071

CHAPTER II.

_REPRESENTATION OF PROPOSITIONS OF RELATION._

Let us take, first, the Proposition "Some x are y".

This, we know, is equivalent to the Proposition of Existence "Some xy
exist". (See p. 31.) Hence it may be represented by the expression
"xy_{1}".

The Converse Proposition "Some y are x" may of course be represented by
the _same_ expression, viz. "xy_{1}".

Similarly we may represent the three similar Pairs of Converse
Propositions, viz.--

"Some x