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1/ THE STANDARD FORMS 11

P is more R than (or as much R as) Q (is R),

and Q is R enough to be S;

therefore, all the more (or equally), P is R enough to be S.

Notice that the valid inference goes ‘from minor to major’; that is, from the minor term (Q) to the

major one (P); meaning: from the minor term as subject of ‘R enough to be S’ in the minor premise, to

the major term as subject of same in the conclusion. Any attempt to go from major to minor in the

same way (i.e. positively) would be invalid inference.

b. The negative subjectal {–s} mood:

P is more R than (or as much R as) Q (is R),

yet P is R not enough to be S;

therefore, all the more (or equally), Q is R not enough to be S.

Notice that the valid inference goes ‘from major to minor’; that is, from the major term (P) to the

minor one (Q); meaning: from the major term as subject of ‘R not enough to be S’ in the minor

premise, to the minor term as subject of same in the conclusion. Any attempt to go from minor to

major in the same way (i.e. negatively) would be invalid inference.

We can summarize all information about subjectal argument as follows: “Given that P is more R than

or as much R as Q is R, it follows that: if Q is R enough to be S, then P is R enough to be S; and if P is

R not enough to be S, then Q is R not enough to be S; on the other hand, if Q is R not enough to be S,

it does not follow that P is R not enough to be S; and if P is R enough to be S, it does not follow that Q

is R enough to be S.” In this summary format, we resort to nesting: the major premise serves as

primary antecedent, and the valid minor premises and conclusions appear as consequent conditions

and outcomes, while the invalid moods are expressed as non-sequiturs.

For example: granted Jack (P) can run faster (R) than Jill (Q), it follows that: if Jill can run (at a speed

of) one mile in under 15 minutes (S), then surely so can Jack; and if he can’t, then neither can she.

Needless to say, the conditions are presumed identical in both cases; we are talking of the same course,

in the same weather, and so on. If different conditions are intended, the argument may not function

correctly. The a fortiori argument is stated categorically only if there are no underlying conditions.

Obviously, if there are conditions they ought to be specified, or at least we must ensure they are the

same throughout the argument.

c. The positive predicatal {+p} mood:

More (or as much) R is required to be P than (as) to be Q,

and S is R enough to be P;

therefore, all the more (or equally), S is R enough to be Q.

Notice that the valid inference goes ‘from major to minor’; that is, from the major term (P) to the

minor one (Q); meaning: from the major term as predicate of ‘S is R enough to be’ in the minor

premise, to the minor term as predicate of same in the conclusion. Any attempt to go from minor to

major in the same way (i.e. positively) would be invalid inference.

d. The negative predicatal {–p} mood:

More (or as much) R is required to be P than (as) to be Q,

yet S is R not enough to be Q;

therefore, all the more (or equally), S is R not enough to be P.

Notice that the valid inference goes ‘from minor to major’; that is, from the minor term (Q) to the

major one (P); meaning: from the minor term as predicate of ‘S is R not enough to be’ in the minor

premise, to the major term as predicate of same in the conclusion. Any attempt to go from major to

minor in the same way (i.e. negatively) would be invalid inference.