A system, which aims to deduce the memory with all the other functions
of intelligence, must of course place its first position from beyond the
memory, and anterior to it, otherwise the principle of solution would
be itself a part of the problem to be solved. Such a position therefore
must, in the first instance be demanded, and the first question will be,
by what right is it demanded? On this account I think it expedient
to make some preliminary remarks on the introduction of Postulates
in philosophy. The word postulate is borrowed from the science
of mathematics [50]. In geometry the primary construction is not
demonstrated, but postulated. This first and most simple construction in
space is the point in motion, or the line. Whether the point is moved
in one and the same direction, or whether its direction is continually
changed, remains as yet undetermined. But if the direction of the point
have been determined, it is either by a point without it, and then there
arises the straight line which incloses no space; or the direction of
the point is not determined by a point without it, and then it must flow
back again on itself, that is, there arises a cyclical line, which does
enclose a space. If the straight line be assumed as the positive, the
cyclical is then the negation of the straight. It is a line, which at
no point strikes out into the straight, but changes its direction
continuously. But if the primary line be conceived as undetermined, and
the straight line as determined throughout, then the cyclical is the
third compounded of both. It is at once undetermined and determined;
undetermined through any point without, and determined through itself.
Geometry therefore supplies philosophy with the example of a primary
intuition, from which every science that lays claim to evidence
must take its commencement. The mathematician does not begin with a
demonstrable proposition, but with an intuition, a practical idea.
Public-domain text, read in full here on John Shaqi.
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