write the whole Sorites thus:--

"No a are b';
All b are c;
All c are d;
No e' are a';
All h are e'.
.'. All h are d".

In the above Sorites, the 3 Partial Conclusions are the
Positions "No a are e'", "No a are d'", "No d' are e'"; but, if
the Premisses were arranged in other ways, other Partial
Conclusions might be obtained. Thus, the order 41523 yields the
Partial Conclusions "No c' are b'", "All h are b", "All h are
c". There are altogether _nine_ Partial Conclusions to this
Sorites, which the Reader will find it an interesting task to
make out for himself.]

pg087

CHAPTER II.

_PROBLEMS IN SORITESES._

Sec. 1.

_Introductory._

The Problems we shall have to solve are of the following form:--

"Given three or more Propositions of Relation, which are proposed as
Premisses: to ascertain what Conclusion, if any, is consequent from
them."

We will limit ourselves, at present, to Problems which can be worked by
the Formulae of Fig. I. (See p. 75.) Those, that require _other_ Formulae,
are rather too hard for beginners.

Such Problems may be solved by either of two Methods, viz.

(1) The Method of Separate Syllogisms;
(2) The Method of Underscoring.

These shall be discussed separately.

pg088
Sec. 2.

_Solution by Method of Separate Syllogisms._

The Rules, for doing this, are as follows:--

(1) Name the 'Universe of Discourse'.

(2) Construct a Dictionary, making a, b, c, &c. represent
the Terms.

(3) Put the Proposed Premisses into subscript form.

(4) Select two which, containing between them a pair of
codivisional Classes, can be used as the Premisses of a
Syllogism.

(5) Find their Conclusion by Formula.

(6) Find a third Premiss which, along with this Conclusion,
can be used as the Premisses of a second Syllogism.

(7) Find a second Conclusion by Formula.

(8) Proceed thus, until all the proposed Premisses have
been used.

(9) Put the last Conclusion, which is the Complete
Conclusion of the Sorites, into concrete form.

[As an example of this process, let us take, as the proposed Set
of Premisses,

(1) "All the policemen on this beat sup with our cook;
(2) No m