ropositions are such that all
their Terms are Species of the same Genus, and are also so related that
two of them, taken together, yield a Conclusion, which, taken with
another of them, yields another Conclusion, and so on, until all have
been taken, it is evident that, if the original Set were true, the last
Conclusion would _also_ be true.
Such a Set, with the last Conclusion tacked on, is called a '=Sorites=';
the original Set of Propositions is called its '=Premisses='; each of
the intermediate Conclusions is called a '=Partial Conclusion=' of the
Sorites; the last Conclusion is called its '=Complete Conclusion=,' or,
more briefly, its '=Conclusion='; the Genus, of which all the Terms are
Species, is called its '=Universe of Discourse=', or, more briefly, its
'=Univ.='; the Terms, used as Eliminands in the Syllogisms, are called
its '=Eliminands='; and the two Terms, which are retained, and therefore
appear in the Conclusion, are called its '=Retinends='.
[Note that each _Partial_ Conclusion contains one or two
_Eliminands_; but that the _Complete_ Conclusion contains
_Retinends_ only.]
The Conclusion is said to be '=consequent=' from the Premisses; for
which reason it is usual to prefix to it the word "Therefore" (or the
symbol ".'.").
[Note that the question, whether the Conclusion is or is not
_consequent_ from the Premisses, is not affected by the _actual_
truth or falsity of any one of the Propositions which make up
the Sorites, by depends entirely on their _relationship to one
another_.
pg086
As a specimen-Sorites, let us take the following Set of 5
Propositions:--
(1) "No a are b';
(2) All b are c;
(3) All c are d;
(4) No e' are a';
(5) All h are e'".
Here the first and second, taken together, yield "No a are c'".
This, taken along with the third, yields "No a are d'".
This, taken along with the fourth, yields "No d' are e'".
And this, taken along with the fifth, yields "All h are d".
Hence, if the original Set were true, this would _also_ be true.
Hence the original Set, with this tacked on, is a _Sorites_; the
original Set is its _Premisses_; the Proposition "All h are d"
is its _Conclusion_; the Terms a, b, c, e are its _Eliminands_;
and the Terms d and h are its _Retinends_.
Hence we may
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