Posterior Analytics   

with the resulting inference that A inheres in C. This we have to
suppose a known and admitted impossibility; and we then infer that A
cannot inhere in B. Thus if the inherence of B in C is not questioned,
A's inherence in B is impossible.
The order of the terms is the same in both proofs: they differ
according to which of the negative propositions is the better known,
the one denying A of B or the one denying A of C. When the falsity
of the conclusion is the better known, we use reductio ad
impossible; when the major premiss of the syllogism is the more
obvious, we use direct demonstration. All the same the proposition
denying A of B is, in the order of being, prior to that denying A of
C; for premisses are prior to the conclusion which follows from
them, and 'no C is A' is the conclusion, 'no B is A' one of its
premisses. For the destructive result of reductio ad impossibile is
not a proper conclusion, nor are its antecedents proper premisses.
On the contrary: the constituents of syllogism are premisses related
to one another as whole to part or part to whole, whereas the
premisses A-C and A-B are not thus related to one another. Now the
superior demonstration is that which proceeds from better known and
prior premisses, and while both these forms depend for credence on the
not-being of something, yet the source of the one is prior to that
of the other. Therefore negative demonstration will have an
unqualified superiority to reductio ad impossibile, and affirmative
demonstration, being superior to negative, will consequently be
superior also to reductio ad impossibile.

27

The science which is knowledge at once of the fact and of the
reasoned fact, not of the fact by itself without the reasoned fact, is
the more exact and the prior science.
A science such as arithmetic, which is not a science of properties
qua inhering in a substratum, is more exact than and prior to a
science like harmonics, which is a science of pr,operties inhering
in a substratum; and similarly a science like arithmetic, which is
constituted of fewer basic elements, is more exact than and prior to
geometry, which requires additional elements. What I mean by
'additional elements' is this: a unit is substance without position,
while a point is substance with position; the latter contains an
additional element.

28

A single science is one whose domain is a single genus, viz. all the
subjects constituted out of the primary entities of the genus-i.e. the
parts of this total subject-and their essential properties.
One science differs from another when their basic truths have
neither a common source nor are derived those of the one science
from those the other. This is verified when we reach the
indemonstrable premisses of a science, for they must be within one
genus with its conclusions: and this again is verified if the
conclusions proved by means of them fall within one genus-i.e. are
homogeneous.

29

One can have several demonstrations of the same connexion not only
by taking from the same series of predication middles which are
other than the immediately cohering term e.g. by taking C, D, and F
severally to prove A-B--but also by taking a middle from another
series. Thus let A be change, D alteration of a property, B feeling
pleasure, and G relaxation. We can then without falsehood predicate
D of B and A of D, for he who is pleased suffers alteration of a
property, and that which alters a property changes. Again, we can