The Complete Aristotle (eng.)

unless these theorems are related as
subordinate to superior (e.g. as optical theorems to geometry or
harmonic theorems to arithmetic). Geometry again cannot prove of
lines any property which they do not possess qua lines, i.e. in
virtue of the fundamental truths of their peculiar genus: it cannot
show, for example, that the straight line is the most beautiful of
lines or the contrary of the circle; for these qualities do not
belong to lines in virtue of their peculiar genus, but through some
property which it shares with other genera.
8
    It is also clear that if the premisses from which the syllogism
proceeds are commensurately universal, the conclusion of such i.e.
in the unqualified sense-must also be eternal. Therefore no
attribute can be demonstrated nor known by strictly scientific
knowledge to inhere in perishable things. The proof can only be
accidental, because the attribute’s connexion with its perishable
subject is not commensurately universal but temporary and special.
If such a demonstration is made, one premiss must be perishable and
not commensurately universal (perishable because only if it is
perishable will the conclusion be perishable; not commensurately
universal, because the predicate will be predicable of some
instances of the subject and not of others); so that the conclusion
can only be that a fact is true at the moment-not commensurately
and universally. The same is true of definitions, since a
definition is either a primary premiss or a conclusion of a
demonstration, or else only differs from a demonstration in the
order of its terms. Demonstration and science of merely frequent
occurrences-e.g. of eclipse as happening to the moon-are, as such,
clearly eternal: whereas so far as they are not eternal they are
not fully commensurate. Other subjects too have properties
attaching to them in the same way as eclipse attaches to the
moon.
9
    It is clear that if the conclusion is to show an attribute
inhering as such, nothing can be demonstrated except from its
‘appropriate’ basic truths. Consequently a proof even from true,
indemonstrable, and immediate premisses does not constitute
knowledge. Such proofs are like Bryson’s method of squaring the
circle; for they operate by taking as their middle a common
character-a character, therefore, which the subject may share with
another-and consequently they apply equally to subjects different
in kind. They therefore afford knowledge of an attribute only as
inhering accidentally, not as 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