The truth is that if the positive term or sign or necessary condition
is prominent as the basis of the argument, there is considerable risk
of fallacy. Sore throat being one of the symptoms of scarlatina, the
physician is apt on finding this symptom present to jump to a positive
conclusion. This is equivalent technically to drawing a positive
conclusion from premisses of the Second Figure.
All scarlatina patients have sore throat.
This patient has sore throat.
A positive conclusion is technically known as a Non-Sequitur (Doesn't
follow). So with arguments from the presence of a necessary condition
which is only one of many. Given that it is impossible to pass without
working at the subject, or that it is impossible to be a good marksman
without having a steady hand, we are apt to argue that given also the
presence of this condition, a conclusion is implicated. But really the
premisses given are only two affirmatives of the Second Figure.
"It is impossible to pass without working at the subject."
This, put into the form No not-M is P, is to say that "None who
have not worked can pass". This is equivalent, as the converse by
contraposition, with--
All capable of passing have worked at the subject.
But though Q has worked at the subject, it does not follow that he is
capable of passing. Technically the middle is undistributed. On the
other hand, if he has not worked at the subject, it follows that he
is not capable of passing. We can draw a conclusion at once from the
absence of the necessary condition, though none can be drawn from its
presence alone.
THIRD FIGURE.
Arguments are sometimes advanced in the form of the Third Figure. For
instance: Killing is not always murder: for tyrannicide is not murder,
and yet it is undoubtedly killing. Or again: Unpleasant things
are sometimes salutary: for afflictions are sometimes so, and no
affliction can be called pleasant.
These arguments, when analysed into terms, are, respectively, Felapton
and Disamis.
No tyrannicide is murder;
All tyrannicide is killing;
Some killing is not murder.
Some afflictions are salutary things;
All afflictions are unpleasant things;
Some unpleasant things are salutary things.
The syllogistic form cannot in such cases pretend to be a
simplification of the argument. The argument would be equally
unmistakable if advanced in this form: Some S is not P, for example,
M. Some killing is not murder, _e.g.,_ tyrannicide. Some unpleasant
things are salutary, _e.g.,_ some afflictions.
There is really no "deduction" in the third figure, no leading down
from general to particular. The middle term is only an example of the
minor. It is the syllogism of Contradictory Examples.
Public-domain text, read in full here on John Shaqi.
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