The chief risk of error is in determining the quantity of the subject
about which the Contingent or Possible predicate is made. When it is
said that "Victories may be gained by accident," is the predicate made
concerning All victories or Some only? Here we are apt to confuse the
meaning of the contingent assertion with the matter of fact on which
in common belief it rests. It is true only that some victories have
been gained by accident, and it is on this ground that we assert in
the absence of certain knowledge concerning any victory that it
may have been so gained. The latter is the effect of the contingent
assertion: it is made about any victory in the absence of certain
knowledge, that is to say, formally about all.
The history of Modals in Logic is a good illustration of intricate
confusion arising from disregard of a clear traditional definition.
The treatment of them by Aristotle was simple, and had direct
reference to tricks of disputation practised in his time. He specified
four "modes," the four that descended to mediaeval logic, and he
concerned himself chiefly with the import of contradicting these
modals. What is the true contradictory of such propositions as, "It
is possible to be" ([Greek: dynaton einai]), "It admits of being"
([Greek: endechetai einai]), "It must be" ([Greek: anankaion einai]),
"It is impossible to be" ([Greek: adynaton einai])? What is implied in
saying "No" to such propositions put interrogatively? "Is it possible
for Socrates to fly?" "No." Does this mean that it is not possible for
Socrates to fly, or that it is possible for Socrates not to fly?
A disputant who had trapped a respondent into admitting that it is
possible for Socrates not to fly, might have pushed the concession
farther in some such way as this: "Is it possible for Socrates not to
walk?" "Certainly." "Is it possible for him to walk?" "Yes." "When you
say that it is possible for a man to do anything do you not believe
that it is possible for him to do it?" "Yes." "But you have admitted
that it is possible for Socrates not to fly?"
It was in view of such perplexities as these that Aristotle set forth
the true contradictories of his four Modals. We may laugh at such
quibbles now and wonder that a grave logician should have thought them
worth guarding against. But historically this is the origin of the
Modals of Formal Logic, and to divert the names of them to signify
other distinctions than those between modes of qualifying the
certainty of a statement is to introduce confusion.
Public-domain text, read in full here on John Shaqi.
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