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.
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