Posterior Analytics   

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,
no D is A,
therefore no B is A, by syllogism;

and the proof will be similar if both A and B have a genus. That the
genus of A need not be the genus of B and vice versa, is shown by
the existence of mutually exclusive coordinate series of