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1831. May 26.
Posology.
ult
II. Morphoscopic
§. Sources of Demonstration &c
1.
Analogous to science
and art are theorem
and problem — medium
of demonstration and
medium of effectuation.
2.
Problems are ends in view —
media of effectuation,
means as to those ends.
3.
Media of demonstration
and effectuation
are both —
media of invention
or say discovery
— when new.
4.
No proposition in
Geometry but has
its media of invention
and demonstration
or effectuation.
5.
Hence in regard to
each comes a proper
question — what
is the medium of
demonstration or
effectuation belonging
to it?
6.
Strange that no
such question should
have been as yet
answered or propounded.
7.
As to media of invention
(effectuation
and demonstration)
first come those
which the nature of things
furnishes. This for
elucidation by exemplification
those
employed by Euclid
8.
1. Means furnished
by the nature of
things
1. Definition
2. Position, all-comprehensive
— Euclid's
Axioms
3. Supposition all-
comprehensive — Euclid's
Postulates.
4. Propositions, demonstrated
by the
above three and
serving as means
of effectuation
and demonstration
to those that
respectively follow:
say relatively
antecedent propositions.
9
1. Definitions. A definition
is nothing but
an exemplification
of one of the few
modes of equivalence
above mentioned.
1. Grammaticè, a
2. Logicè, an equivalent to
the term defined: use,
guarding against
its by the
words employed for
that purpose.
9
Preferable accordingly
to the word defined would
be the definition but
for the enlargement
of the words of the
sentence which it
constitutes with the
words of the sentence
into which there is
occasion to insert it,
in the quality of an
elementary part.
10.
Definition — its uses are
1. Insertion of the idea
into the mind.
2. Fixation of it
therein.
2. All-comprehensive
Positions what, or
say Axioms.
As in all other
arts and science, so in
Posology, before any
thing can be made
known, something
must have been already
known: and it is
only by its relation
to something
already known can
any thing be made
known. This holds good
throughout. By an
axiom is brought and
held up to view something
which is already
known.
12.
3. All-comprehensive
suppositions. A
supposition is a
which requires
that something
should be considered
as capable of being
done and is done
accordingly: it being
a thing of the number
of those which any
person is capable
of doing.
Identifier: | JB/135/129/001 "JB/" can not be assigned to a declared number type with value 135.
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