Posterior Analytics   

belonging to its subject as such: otherwise they would not have been
applicable to another genus.
Our knowledge of any attribute's connexion with a subject is
accidental unless we know that connexion through the middle term in
virtue of which it inheres, and as an inference from basic premisses
essential and 'appropriate' to the subject-unless we know, e.g. the
property of possessing angles equal to two right angles as belonging
to that subject in which it inheres essentially, and as inferred
from basic premisses essential and 'appropriate' to that subject: so
that if that middle term also belongs essentially to the minor, the
middle must belong to the same kind as the major and minor terms.
The only exceptions to this rule are such cases as theorems in
harmonics which are demonstrable by arithmetic. Such theorems are
proved by the same middle terms as arithmetical properties, but with a
qualification-the fact falls under a separate science (for the subject
genus is separate), but the reasoned fact concerns the superior
science, to which the attributes essentially belong. Thus, even
these apparent exceptions show that no attribute is strictly
demonstrable except from its 'appropriate' basic truths, which,
however, in the case of these sciences have the requisite identity
of character.
It is no less evident that the peculiar basic truths of each
inhering attribute are indemonstrable; for basic truths from which
they might be deduced would be basic truths of all that is, and the
science to which they belonged would possess universal sovereignty.
This is so because he knows better whose knowledge is deduced from
higher causes, for his knowledge is from prior premisses when it
derives from causes themselves uncaused: hence, if he knows better
than others or best of all, his knowledge would be science in a higher
or the highest degree. But, as things are, demonstration is not
transferable to another genus, with such exceptions as we have
mentioned of the application of geometrical demonstrations to theorems
in mechanics or optics, or of arithmetical demonstrations to those
of harmonics.
It is hard to be sure whether one knows or not; for it is hard to be
sure whether one's knowledge is based on the basic truths
appropriate to each attribute-the differentia of true knowledge. We
think we have scientific knowledge if we have reasoned from true and
primary premisses. But that is not so: the conclusion must be
homogeneous with the basic facts of the science.

10

I call the basic truths of every genus those clements in it the
existence of which cannot be proved. As regards both these primary
truths and the attributes dependent on them the meaning of the name is
assumed. The fact of their existence as regards the primary truths
must be assumed; but it has to be proved of the remainder, the
attributes. Thus we assume the meaning alike of unity, straight, and
triangular; but while as regards unity and magnitude we assume also
the fact of their existence, in the case of the remainder proof is
required.
Of the basic truths used in the demonstrative sciences some are
peculiar to each science, and some are common, but common only in
the sense of analogous, being of use only in so far as they fall
within the genus constituting the province of the science in question.
Peculiar truths are, e.g. the definitions of line and straight;
common truths are such as 'take equals from equals and equals remain'.
Only so much of these common truths is required as falls within the
genus in question: for a truth of this kind will have the same force
even if not used generally but applied by the geometer only to
magnitudes, or by the arithmetician only to numbers. Also peculiar
to a science are the subjects the existence as well as the meaning
of which it assumes, and the essential attributes of which it