Posterior Analytics   

and we give them the name of axioms par excellence. If a thesis
assumes one part or the other of an enunciation, i.e. asserts either
the existence or the non-existence of a subject, it is a hypothesis;
if it does not so assert, it is a definition. Definition is a 'thesis'
or a 'laying something down', since the arithmetician lays it down
that to be a unit is to be quantitatively indivisible; but it is not a
hypothesis, for to define what a unit is is not the same as to
affirm its existence.
Now since the required ground of our knowledge-i.e. of our
conviction-of a fact is the possession of such a syllogism as we
call demonstration, and the ground of the syllogism is the facts
constituting its premisses, we must not only know the primary
premisses-some if not all of them-beforehand, but know them better
than the conclusion: for the cause of an attribute's inherence in a
subject always itself inheres in the subject more firmly than that
attribute; e.g. the cause of our loving anything is dearer to us
than the object of our love. So since the primary premisses are the
cause of our knowledge-i.e. of our conviction-it follows that we
know them better-that is, are more convinced of them-than their
consequences, precisely because of our knowledge of the latter is
the effect of our knowledge of the premisses. Now a man cannot believe
in anything more than in the things he knows, unless he has either
actual knowledge of it or something better than actual knowledge.
But we are faced with this paradox if a student whose belief rests
on demonstration has not prior knowledge; a man must believe in
some, if not in all, of the basic truths more than in the
conclusion. Moreover, if a man sets out to acquire the scientific
knowledge that comes through demonstration, he must not only have a
better knowledge of the basic truths and a firmer conviction of them
than of the connexion which is being demonstrated: more than this,
nothing must be more certain or better known to him than these basic
truths in their character as contradicting the fundamental premisses
which lead to the opposed and erroneous conclusion. For indeed the
conviction of pure science must be unshakable.

3

Some hold that, owing to the necessity of knowing the primary
premisses, there is no scientific knowledge. Others think there is,
but that all truths are demonstrable. Neither doctrine is either
true or a necessary deduction from the premisses. The first school,
assuming that there is no way of knowing other than by
demonstration, maintain that an infinite regress is involved, on the
ground that if behind the prior stands no primary, we could not know
the posterior through the prior (wherein they are right, for one
cannot traverse an infinite series): if on the other hand-they say-the
series 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.