The Complete Aristotle (eng.)
number, and E even number. Then A is predicable of
E.
13
Knowledge of the fact differs from knowledge of the reasoned
fact. To begin with, they differ within the same science and in two
ways: (1) when the premisses of the syllogism are not immediate
(for then the proximate cause is not contained in them-a necessary
condition of knowledge of the reasoned fact): (2) when the
premisses are immediate, but instead of the cause the better known
of the two reciprocals is taken as the middle; for of two
reciprocally predicable terms the one which is not the cause may
quite easily be the better known and so become the middle term of
the demonstration. Thus (2) (a) you might prove as follows that the
planets are near because they do not twinkle: let C be the planets,
B not twinkling, A proximity. Then B is predicable of C; for the
planets do not twinkle. But A is also predicable of B, since that
which does not twinkle is near—we must take this truth as having
been reached by induction or sense-perception. Therefore A is a
necessary predicate of C; so that we have demonstrated that the
planets are near. This syllogism, then, proves not the reasoned
fact but only the fact; since they are not near because they do not
twinkle, but, because they are near, do not twinkle. The major and
middle of the proof, however, may be reversed, and then the
demonstration will be of the reasoned fact. Thus: let C be the
planets, B proximity, A not twinkling. Then B is an attribute of C,
and A-not twinkling-of B. Consequently A is predicable of C, and
the syllogism proves the reasoned fact, since its middle term is
the proximate cause. Another example is the inference that the moon
is spherical from its manner of waxing. Thus: since that which so
waxes is spherical, and since the moon so waxes, clearly the moon
is spherical. Put in this form, the syllogism turns out to be proof
of the fact, but if the middle and major be reversed it is proof of
the reasoned fact; since the moon is not spherical because it waxes
in a certain manner, but waxes in such a manner because it is
spherical. (Let C be the moon, B spherical, and A waxing.) Again
(b), in cases where the cause and the effect are not reciprocal and
the effect is the better known, the fact is demonstrated but not
the reasoned fact. This also occurs (1) when the middle falls
outside the major and minor, for here too the strict cause is not
given, and so the demonstration is of the fact, not of the reasoned
fact. For example, the question ‘Why does not a wall breathe?’
might be answered, ‘Because it is not an animal’; but that answer
would not give the strict cause, because if not being an animal
causes the absence of respiration, then being an animal should be
the cause of respiration, according to the rule that if the
negation of causes the non-inherence of y, the affirmation of x
causes the inherence of y; e.g. if the disproportion of the hot and
cold elements is the cause of ill health, their proportion is the
cause of health; and conversely, if the assertion of x causes the
inherence of y, the negation of x must cause y’s non-inherence. But
in the case given this consequence does not result; for not every
animal breathes. A syllogism with this kind of cause takes place in
the second figure. Thus: let A be animal, B respiration, C wall.
Then A is predicable of all B (for all that breathes is animal),
but of no C; and consequently B is predicable of no C; that is, the
wall does not breathe. Such causes are like far-fetched
explanations, which precisely consist in making the cause too
remote, as in Anacharsis’ account of why the Scythians have no
flute-players; namely because they have no vines.
Thus, then, do the syllogism of the fact and the syllogism of
the reasoned fact differ within one science and according to the
position of the middle terms. But there is another way too in which
the fact and the reasoned fact differ, and that is when they are
investigated respectively by different sciences. This occurs in the
case of problems related to one another as subordinate and
superior, as when optical problems are subordinated to geometry,
mechanical problems to stereometry, harmonic problems to
arithmetic, the data of observation to astronomy. (Some of these
sciences bear almost the same name; e.g. mathematical and nautical
astronomy, mathematical and acoustical harmonics.) Here it is the
business of the empirical observers to know the fact, of the
mathematicians to know the
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