The Complete Aristotle (eng.)

terminates and there are primary premisses, yet
these are unknowable because incapable of demonstration, which
according to them is the only form of knowledge. And since thus one
cannot know the primary premisses, knowledge of the conclusions
which follow from them is not pure scientific knowledge nor
properly knowing at all, but rests on the mere supposition that the
premisses are true. The other party agree with them as regards
knowing, holding that it is only possible by demonstration, but
they see no difficulty in holding that all truths are demonstrated,
on the ground that demonstration may be circular and
reciprocal.
    Our own doctrine is that not all knowledge is demonstrative: on
the contrary, knowledge of the immediate premisses is independent
of demonstration. (The necessity of this is obvious; for since we
must know the prior premisses from which the demonstration is
drawn, and since the regress must end in immediate truths, those
truths must be indemonstrable.) Such, then, is our doctrine, and in
addition we maintain that besides scientific knowledge there is its
originative source which enables us to recognize the
definitions.
    Now demonstration must be based on premisses prior to and better
known than the conclusion; and the same things cannot
simultaneously be both prior and posterior to one another: so
circular demonstration is clearly not possible in the unqualified
sense of ‘demonstration’, but only possible if ‘demonstration’ be
extended to include that other method of argument which rests on a
distinction between truths prior to us and truths without
qualification prior, i.e. the method by which induction produces
knowledge. But if we accept this extension of its meaning, our
definition of unqualified knowledge will prove faulty; for there
seem to be two kinds of it. Perhaps, however, the second form of
demonstration, that which proceeds from truths better known to us,
is not demonstration in the unqualified sense of the term.
    The advocates of circular demonstration are not only faced with
the difficulty we have just stated: in addition their theory
reduces to the mere statement that if a thing exists, then it does
exist-an easy way of proving anything. That this is so can be
clearly shown by taking three terms, for to constitute the circle
it makes no difference whether many terms or few or even only two
are taken. Thus by direct proof, if A is, B must be; if B is, C
must be; therefore if A is, C must be. Since then-by the circular
proof-if A is, B must be, and if B is, A must be, A may be
substituted for C above. Then ‘if B is, A must be’=’if B is, C must
be’, which above gave the conclusion ‘if A is, C must be’: but C
and A have been identified. Consequently the upholders of circular
demonstration are in the position of saying that if A is, A must
be-a simple way of proving anything. Moreover, even such circular
demonstration is impossible except in the case of attributes that
imply one another, viz. ‘peculiar’ properties.
    Now, it has been shown that the positing of one thing-be it one
term or one premiss-never involves a necessary consequent: two
premisses constitute the first and smallest foundation for drawing
a conclusion at all and therefore a fortiori for the demonstrative
syllogism of science. If, then, A is implied in B and C, and B and
C are reciprocally implied in one another and in A, it is possible,
as has been shown in my writings on the syllogism, to prove all the
assumptions on which the original conclusion rested, by circular
demonstration in the first figure. But it has also been shown that
in the other figures either no conclusion is possible, or at least
none which proves both the original premisses. Propositions the
terms of which are not convertible cannot be circularly
demonstrated at all, and since convertible terms occur rarely in
actual demonstrations, it is clearly frivolous and impossible to
say that demonstration is reciprocal and that therefore everything
can be demonstrated.
4
    Since the object of pure scientific knowledge cannot be other
than it is, the truth obtained by demonstrative knowledge will be
necessary. And since demonstrative knowledge is only present when
we have a demonstration, it follows that demonstration is an
inference from necessary premisses. So we must consider what are
the premisses of demonstration-i.e. what is their character: and as
a preliminary, let us define what we mean by an attribute ‘true in
every instance