(12) c'e'_{0}
(3) a_{1}c_{0}
.'. a_{1}e'_{0}

This Complete Conclusion, translated into _abstract_ form, is

"All a are e";

and this, translated into _concrete_ form, is

"Amos Judd loves cold mutton."

In actually _working_ this Problem, the above explanations
would, of course, be omitted, and all, that would appear on
paper, would be as follows:--

(1) k_{1}l'_{0}
(2) dh'_{0}
(3) a_{1}c_{0}
(4) b_{1}e'_{0}
(5) k'h_{0}
(6) b'l_{0}
(7) d'_{1}c'_{0}

(1) k_{1}l'_{0}
(5) k'h_{0}
.'. l'h_{0} ... (8)

(8) l'h_{0}
(2) dh'_{0}
.'. l'd_{0} ... (9)

(9) l'd_{0}
(6) b'l_{0}
.'. db'_{0} ... (10)

(10) db'_{0}
(4) b_{1}e'_{0}
.'. de'_{0} ... (11)

(11) de'_{0}
(7) d'_{1}c'_{0}
.'. c'e'_{0} ... (12)

(12) c'e'_{0}
(3) a_{1}c_{0}
.'. a_{1}e'_{0}

Note that, in working a Sorites by this Process, we may begin
with _any_ Premiss we choose.]

pg091
Sec. 3.

_Solution by Method of Underscoring._

Consider the Pair of Premisses

xm_{0} + ym'_{0}

which yield the Conclusion xy_{0}

We see that, in order to get this Conclusion, we must eliminate m and
m', and write x and y together in one expression.

Now, if we agree to _mark_ m and m' as eliminated, and to read the two
expressions together, as if they were written in one, the two Premisses
will then exactly represent the _Conclusion_, and we need not write it
out separately.

Let us agree to mark the eliminated letters by _underscoring_ them,
putting a _single_ score under the _first_, and a _double_ one under the
_second_.

The two Premisses now become

xm_{0} + ym'_{0}
- =

which we read as "xy_{0}".

In copying out the Premisses for underscoring, it will be convenient to
_omit all subscripts_. As to the "0's" we may always _suppose_ them
written, and, as to the "1's", we are not concerned to know _which_
Terms are asserted to _exist_, except those which appear in the
_Complete_ Conclusion; and for _them_ it will be easy enough to refer to
the original list.
pg092
[I will now go through the proc