The Complete Aristotle (eng.)

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.
33
    Scientific knowledge and its object differ from opinion and the
object of opinion in that scientific knowledge is commensurately
universal and proceeds by necessary connexions, and that which is
necessary cannot be otherwise. So though there are things which are
true and real and yet can be otherwise, scientific knowledge
clearly does not concern them: if it did, things which can be
otherwise would be incapable of being otherwise. Nor are they any
concern of rational intuition-by rational intuition I mean an
originative source of scientific knowledge-nor of indemonstrable
knowledge, which is the grasping of the immediate premiss. Since
then rational intuition, science, and opinion, and what is revealed
by these terms, are the only things that can be ‘true’, it follows
that it is opinion that is concerned with that which may be true or
false, and can be otherwise: opinion in fact is the grasp of a
premiss which is immediate but not necessary. This view also fits
the observed facts, for opinion is unstable, and so is the kind of
being we have described as its object. Besides, when a man thinks a
truth incapable of being otherwise he always thinks that he knows
it, never that he opines it. He thinks that he opines when he
thinks that a connexion,