An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

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are not -fallible" ;
IMMEDIATE INFERENCE.
its contrapositivc,
"No not -fallible
beings are human beings." The classes represented by
the italicised terms must be just as real as the other
classes, "human beings"
and "fallible
beings"; other
wise these inferences would be invalid. In the case of
Inversion,
it is assumed that both not-S and not-P are
real classes i.e., that neither S nor P is coextensive
with "existence." Thus, the Inverse of "All human
beings are fallible" is "Some not-human beings
fallible
"
beings ; and if
" human or if
being,"
beings," were coextensive with all beings,
are not
"
fallible
the inverse
proposition could not be intelligibly made.
This assumption as to not-S and not-P is the direct
result of reading propositions as statements about
classes. If the proposition expresses a relation be
tween two classes, it implies that the two classes them
selves, and the classes formed by what is outside each
of them, i.e., S, P, not-S, not-P, are all equally real.
And so, in the diagram, there is necessarily an actual
portion of the space corresponding
four terms.
EXERCISE VII.
to each of these
(1) State explicitly which of the following meanings
must be assigned to the mark of quantity "some" in the
Aristotelian : system some only ; some, perhaps none; some,
it may be all or none ; some certainly, and it may be all.
Point out the difficulties which arise from an erroneous in
terpretation of this word. [L.]
(2) What is Opposition ? What are the various forms
of Opposition ? Which of them has the greatest value, and
why? [O.]
(3) Why do Negatives distribute their Predicates ? Do
Affirmatives ever distribute theirs ? [O.]
(4) Express by means of ordinary categorical proposi-