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
observation are ignorant of some of its particular instances. These
connexions have a perceptible existence though they are manifestations
of forms. For the mathematical sciences concern forms: they do not
demonstrate properties of a substratum, since, even though the
geometrical subjects are predicable as properties of a perceptible
substratum, it is not as thus predicable that the mathematician
demonstrates properties of them. As optics is related to geometry,
so another science is related to optics, namely the theory of the
rainbow. Here knowledge of the fact is within the province of the
natural philosopher, knowledge of the reasoned fact within that of the
optician, either qua optician or qua mathematical optician. Many
sciences not standing in this mutual relation enter into it at points;
e.g. medicine and geometry: it is the physician's business to know
that circular wounds heal more slowly, the geometer's to know the
reason why.

                                14

  Of all the figures the most scientific is the first. Thus, it is the
vehicle of the demonstrations of all the mathematical sciences, such
as arithmetic, geometry, and optics, and practically all of all
sciences that investigate causes: for the syllogism of the reasoned
fact is either exclusively or generally speaking and in most cases
in this figure-a second proof that this figure is the most scientific;
for grasp of a reasoned conclusion is the primary condition of
knowledge. Thirdly, the first is the only figure which enables us to
pursue knowledge of the essence of a thing. In the second figure no
affirmative conclusion is possible, and knowledge of a thing's essence
must be affirmative; while in the third figure the conclusion can be
affirmative, but cannot be universal, and essence must have a
universal character: e.g. man is not two-footed animal in any
qualified sense, but universally. Finally, the first figure has no
need of the others, while it is by means of the first that the other
two figures are developed, and have their intervals closepacked
until immediate premisses are reached.

  Clearly, therefore, the first figure is the primary condition of
knowledge.

                                15

  Just as an attribute A may (as we saw) be atomically connected
with a subject B, so its disconnexion may be atomic. I call 'atomic'
connexions or disconnexions which involve no intermediate term;
since in that case the connexion or disconnexion will not be
mediated by something other than the terms themselves. It follows that
if either A or B, or both A and B, have a genus, their disconnexion
cannot be primary. Thus: let C be the genus of A. Then, if C is not
the genus of B-for A may well have a genus which is not the genus of
B-there will be a syllogism proving A's disconnexion from B thus:

        all A is C,

        no B is C,

        therefore no B is A.

Or if it is B which has a genus D, we have

        all B is D,