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1/ THE STANDARD FORMS 15



When this thing (say, X) is P, it is more R than when it is Q,
and when it is Q, it is enough R to be S;
therefore, when it is P, it is enough R to be S.

More R is required for this thing (say, X) to be P than for it to be Q,
and when it is S, it is R enough to be P;
therefore, when it is S, is R enough to be Q.

We can construct similar negative moods, of course. Notice that I have specified the subject as ‘this
thing’ (or X) in both major premises, but these could equally be generalities, i.e. have ‘something,
anything’ as their subject. Such single-subject a fortiori arguments are not mere theoretical
possibilities, but often occur in practice. Note the conditional form the sentences take; these are really,
therefore, cases of implicational argument (see next section). The conditioning may obviously be
based on any type of modality – extensional, natural, temporal or spatial.


2. Implicational a fortiori arguments
In addition to the above four valid copulative moods, I identified in Judaic Logic four comparable
‘implicational’ moods. The first two I called antecedental (instead of subjectal) and the last two I
called consequental (instead of predicatal). These four moods have the same figures as the preceding
four; but they differ in involving the relation of implication instead of the copulative one, and therefore
theses instead of terms as the items under consideration. I list them for you anyway, just to make sure
there is no misunderstanding:

e. The positive antecedental (+a) mood:

P implies more R than (or as much R as) Q (implies R),
and, Q implies enough R to imply S;
therefore, all the more (or equally), P implies enough R to imply S.

f. The negative antecedental (–a) mood:

P implies more R than (or as much R as) Q (implies R),
yet, P does not imply enough R to imply S;
therefore, all the more (or equally), Q does not imply enough R to imply S.

g. The positive consequental (+c) mood:

More (or as much) R is required to imply P than to imply Q,
and, S implies enough R to imply P;
therefore, all the more (or equally), S implies enough R to imply Q.

h. The negative consequental (–c) mood:

More (as much) R is required to imply P than to imply Q,
yet, S does not imply enough R to imply Q;
therefore, all the more (or equally), S does not imply enough R to imply P.

Clearly, mostly similar comments can be made regarding the structures of these additional four valid
moods (or eight, if we distinguish between superior and egalitarian moods) as for those preceding
them.
In particular note well the fact that the middle thesis (R) is always a consequent (or non-consequent),
whereas the other three theses (P, Q and S) have varied roles as antecedents (or non-antecedents) or
consequents (or non-consequents) depending on the figure concerned. In antecedental argument, R is
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