(3) the three Propositions are so related that, if the first
two were true, the third would be true,
the Trio is called a '=Syllogism='; the Genus, of which each of the six
Terms is a Species, is called its ='Universe of Discourse=', or, more
briefly, its '=Univ.='; the first two Propositions are called its
'=Premisses=', and the third its '=Conclusion='; also the Pair of
codivisional Terms in the Premisses are called its '=Eliminands=', and
the other two its '=Retinends='.
The Conclusion of a Syllogism is said to be '=consequent=' from its
Premisses: hence it is usual to prefix to it the word "Therefore" (or
the Symbol ".'.").
pg057
[Note that the 'Eliminands' are so called because they are
_eliminated_, and do not appear in the Conclusion; and that the
'Retinends' are so called because they are _retained_, and _do_
appear in the Conclusion.
Note also 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 of the Trio, but depends entirely on
their _relationship to each other_.
As a specimen-Syllogism, let us take the Trio
"No x-Things are m-Things;
No y-Things are m'-Things.
No x-Things are y-Things."
which we may write, as explained at p. 26, thus:--
"No x are m;
No y are m'.
No x are y".
Here the first and second contain the Pair of codivisional
Classes m and m'; the first and third contain the Pair x and x;
and the second and third contain the Pair y and y.
Also the three Propositions are (as we shall see hereafter) so
related that, if the first two were true, the third would also
be true.
Hence the Trio is a _Syllogism_; the two Propositions, "No x are
m" and "No y are m'", are its _Premisses_; the Proposition "No x
are y" is its _Conclusion_; the Terms m and m' are its
_Eliminands_; and the Terms x and y are its _Retinends_.
Hence we may write it thus:--
"No x are m;
No y are m'.
.'. No x are y".
As a second specimen, let us take the Trio
"All cats understand French;
Some chickens are cats.
Some chickens understand French".
These, put into normal form, are
"All cats are creatures understanding French;
Some chickens are cats.
Some chickens are creatures understanding French".
Here all the six Terms are Species of the Genus "creatures."
Public-domain text, read in full here on John Shaqi.
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