By demonstration I mean a syllogism productive of
scientific knowledge, a syllogism, that is, the grasp of which is eo
ipso such knowledge. Assuming then that my thesis as to the nature
of scientific knowing is correct, the premisses of demonstrated
knowledge must be true, primary, immediate, better known than and
prior to the conclusion, which is further related to them as effect to
cause. Unless these conditions are satisfied, the basic truths will
not be 'appropriate' to the conclusion. Syllogism there may indeed
be without these conditions, but such syllogism, not being
productive of scientific knowledge, will not be demonstration. The
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.
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