premisses must be true: for that which is non-existent cannot be
known-we cannot know, e.g. that the diagonal of a square is
commensurate with its side. The premisses must be primary and
indemonstrable; otherwise they will require demonstration in order
to be known, since to have knowledge, if it be not accidental
knowledge, of things which are demonstrable, means precisely to have a
demonstration of them. The premisses must be the causes of the
conclusion, better known than it, and prior to it; its causes, since
we possess scientific knowledge of a thing only when we know its
cause; prior, in order to be causes; antecedently known, this
antecedent knowledge being not our mere understanding of the
meaning, but knowledge of the fact as well. Now 'prior' and 'better
known' are ambiguous terms, for there is a difference between what
is prior and better known in the order of being and what is prior
and better known to man. I mean that objects nearer to sense are prior
and better known to man; objects without qualification prior and
better known are those further from sense. Now the most universal
causes are furthest from sense and particular causes are nearest to
sense, and they are thus exactly opposed to one another. In saying
that the premisses of demonstrated knowledge must be primary, I mean
that they must be the 'appropriate' basic truths, for I identify
primary premiss and basic truth. A 'basic truth' in a demonstration is
an immediate proposition. An immediate proposition is one which has no
other proposition prior to it. A proposition is either part of an
enunciation, i.e. it predicates a single attribute of a single
subject. If a proposition is dialectical, it assumes either part
indifferently; if it is demonstrative, it lays down one part to the
definite exclusion of the other because that part is true. The term
'enunciation' denotes either part of a contradiction indifferently.
A contradiction is an opposition which of its own nature excludes a
middle. The part of a contradiction which conjoins a predicate with
a subject is an affirmation; the part disjoining them is a negation. I
call an immediate basic truth of syllogism a 'thesis' when, though
it is not susceptible of proof by the teacher, yet ignorance of it
does not constitute a total bar to progress on the part of the
pupil: one which the pupil must know if he is to learn anything
whatever is an axiom. I call it an axiom because there are such truths
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