Posterior Analytics   

All syllogisms cannot have the same basic truths. This may be
shown first of all by the following dialectical considerations. (1)
Some syllogisms are true and some false: for though a true inference
is possible from false premisses, yet this occurs once only-I mean
if A for instance, is truly predicable of C, but B, the middle, is
false, both A-B and B-C being false; nevertheless, if middles are
taken to prove these premisses, they will be false because every
conclusion which is a falsehood has false premisses, while true
conclusions have true premisses, and false and true differ in kind.
Then again, (2) falsehoods are not all derived from a single identical
set of principles: there are falsehoods which are the contraries of
one another and cannot coexist, e.g. 'justice is injustice', and
'justice is cowardice'; 'man is horse', and 'man is ox'; 'the equal is
greater', and 'the equal is less.' From established principles we
may argue the case as follows, confining-ourselves therefore to true
conclusions. Not even all these are inferred from the same basic
truths; many of them in fact have basic truths which differ
generically and are not transferable; units, for instance, which are
without position, cannot take the place of points, which have
position. The transferred terms could only fit in as middle terms or
as major or minor terms, or else have some of the other terms
between them, others outside them.
Nor can any of the common axioms-such, I mean, as the law of
excluded middle-serve as premisses for the proof of all conclusions.
For the kinds of being are different, and some attributes attach to
quanta and some to qualia only; and proof is achieved by means of
the common axioms taken in conjunction with these several kinds and
their attributes.
Again, it is not true that the basic truths are much fewer than
the conclusions, for the basic truths are the premisses, and the
premisses are formed by the apposition of a fresh extreme term or
the interposition of a fresh middle. Moreover, the number of
conclusions is indefinite, though the number of middle terms is
finite; and lastly some of the basic truths are necessary, others
variable.
Looking at it in this way we see that, since the number of
conclusions is indefinite, the basic truths cannot be identical or
limited in number. If, on the other hand, identity is used in
another sense, and it is said, e.g. 'these and no other are the
fundamental truths of geometry, these the fundamentals of calculation,
these again of medicine'; would the statement mean anything except
that the sciences have basic truths? To call them identical because
they are self-identical is absurd, since everything can be
identified with everything in that sense of identity. Nor again can
the contention that all conclusions have the same basic truths mean
that from the mass of all possible premisses any conclusion may be
drawn. That would be exceedingly naive, for it is not the case in
the clearly evident mathematical sciences, nor is it possible in
analysis, since it is the immediate premisses which are the basic
truths, and a fresh conclusion is only formed by the addition of a new
immediate premiss: but if it be admitted that it is these primary
immediate premisses which are basic truths, each subject-genus will
provide one basic truth. If, however, it is not argued that from the
mass of all possible premisses any conclusion may be proved, nor yet
admitted that basic truths differ so as to be generically different
for each science, it remains to consider the possibility that, while
the basic truths of all knowledge are within one genus, special
premisses are required to prove special conclusions. But that this
cannot be the case has been shown by our proof that the basic truths
of things generically different themselves differ generically. For
fundamental truths are of two kinds, those which are premisses of
demonstration and the subject-genus; and though the former are common,
the latter-number, for instance, and magnitude-are peculiar.