--.

(3) _Fallacy of two Entity-Premisses._

Here the given Pair may be represented by either (xm_{1} + ym_{1}) or
(xm_{1} + ym'_{1}).

These, set out on Triliteral Diagrams, are

xm_{1} + ym_{1} xm_{1} + ym'_{1}
.---------------. .---------------.
| | | | | |
| .---|---. | | .---|---. |
| | (I) | | | | (I) | |
|---|(I)|---|---| |(I)|---|---|---|
| | | | | | | | | |
| .---|---. | | .---|---. |
| | | | | |
.---------------. .---------------.

pg084
Sec. 4.

_Method of proceeding with a given Pair of Propositions._

Let us suppose that we have before us a Pair of Propositions of
Relation, which contain between them a Pair of codivisional Classes, and
that we wish to ascertain what Conclusion, if any, is consequent from
them. We translate them, if necessary, into subscript-form, and then
proceed as follows:--

(1) We examine their Subscripts, in order to see whether they are

(a) a Pair of Nullities;
or (b) a Nullity and an Entity;
or (c) a Pair of Entities.

(2) If they are a Pair of Nullities, we examine their Eliminands, in
order to see whether they are Unlike or Like.

If their Eliminands are _Unlike_, it is a case of Fig. I. We then
examine their Retinends, to see whether one or both of them are asserted
to _exist_. If one Retinend is so asserted, it is a case of Fig. I (a);
if both, it is a case of Fig. I (b).

If their Eliminands are Like, we examine them, in order to see whether
either of them is asserted to exist. If so, it is a case of Fig. III.;
if not, it is a case of "Fallacy of Like Eliminands not asserted to
exist."

(3) If they are a Nullity and an Entity, we examine their Eliminands, in
order to see whether they are Like or Unlike.

If their Eliminands are Like, it is a case of Fig. II.; if _Unlike_, it
is a case of "Fallacy of Unlike Eliminands with an Entity-Premiss."

(4) If they are a Pair of Entities, it is a case of "Fallacy of two
Entity-Premisses."

[Work Examples Sec. =4=, 1-11 (p. 100); Sec. =5=, 1-12 (p. 101);
Sec. =6=, 7-12 (p. 106); Sec. =7=, 7-12 (p. 108).]

pg085

BOOK VII.

SORITESES.

CHAPTER I.

_INTRODUCTORY._

When a Set of three or more Biliteral P