Posterior Analytics   

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 reasoned
fact; for the latter are in possession of the demonstrations giving
the causes, and are often ignorant of the fact: just as we have
often a clear insight into a universal, but through lack of