The Complete Aristotle (eng.)

since future events are not
‘contiguous’. But here too an immediate basic premiss must be
assumed. And in the world of fact this is so: if a house has been
built, then blocks must have been quarried and shaped. The reason
is that a house having been built necessitates a foundation having
been laid, and if a foundation has been laid blocks must have been
shaped beforehand. Again, if a house will be built, blocks will
similarly be shaped beforehand; and proof is through the middle in
the same way, for the foundation will exist before the house.
    Now we observe in Nature a certain kind of circular process of
coming-to-be; and this is possible only if the middle and extreme
terms are reciprocal, since conversion is conditioned by
reciprocity in the terms of the proof. This-the convertibility of
conclusions and premisses-has been proved in our early chapters,
and the circular process is an instance of this. In actual fact it
is exemplified thus: when the earth had been moistened an
exhalation was bound to rise, and when an exhalation had risen
cloud was bound to form, and from the formation of cloud rain
necessarily resulted and by the fall of rain the earth was
necessarily moistened: but this was the starting-point, so that a
circle is completed; for posit any one of the terms and another
follows from it, and from that another, and from that again the
first.
    Some occurrences are universal (for they are, or come-to-be what
they are, always and in ever case); others again are not always
what they are but only as a general rule: for instance, not every
man can grow a beard, but it is the general rule. In the case of
such connexions the middle term too must be a general rule. For if
A is predicated universally of B and B of C, A too must be
predicated always and in every instance of C, since to hold in
every instance and always is of the nature of the universal. But we
have assumed a connexion which is a general rule; consequently the
middle term B must also be a general rule. So connexions which
embody a general rule-i.e. which exist or come to be as a general
rule-will also derive from immediate basic premisses.
13
    We have already explained how essential nature is set out in the
terms of a demonstration, and the sense in which it is or is not
demonstrable or definable; so let us now discuss the method to be
adopted in tracing the elements predicated as constituting the
definable form.
    Now of the attributes which inhere always in each several thing
there are some which are wider in extent than it but not wider than
its genus (by attributes of wider extent mean all such as are
universal attributes of each several subject, but in their
application are not confined to that subject). while an attribute
may inhere in every triad, yet also in a subject not a triad-as
being inheres in triad but also in subjects not numbers at all-odd
on the other hand is an attribute inhering in every triad and of
wider application (inhering as it does also in pentad), but which
does not extend beyond the genus of triad; for pentad is a number,
but nothing outside number is odd. It is such attributes which we
have to select, up to the exact point at which they are severally
of wider extent than the subject but collectively coextensive with
it; for this synthesis must be the substance of the thing. For
example every triad possesses the attributes number, odd, and prime
in both senses, i.e. not only as possessing no divisors, but also
as not being a sum of numbers. This, then, is precisely what triad
is, viz. a number, odd, and prime in the former and also the latter
sense of the term: for these attributes taken severally apply, the
first two to all odd numbers, the last to the dyad also as well as
to the triad, but, taken collectively, to no other subject. Now
since we have shown above’ that attributes predicated as belonging
to the essential nature are necessary and that universals are
necessary, and since the attributes which we select as inhering in
triad, or in any other subject whose attributes we select in this
way, are predicated as belonging to its essential nature, triad
will thus possess these attributes necessarily. Further, that the
synthesis of them constitutes the substance of triad is shown by
the following argument. If it is not identical with the being of
triad, it must be related to triad as a genus named or nameless. It
will then be of wider extent than triad-assuming that wider
potential extent is the character of a