Memorabilia Mathematica; or, the Philomath's Quotation-Book
Science
Memorabilia Mathematica; or, the Philomath's Quotation-Book
Mathematics; Mathematics -- Quotations, maxims, etc.
First, That they can be set down and represented by sensible
marks, which have a greater and nearer correspondence with them
than any words or sounds whatsoever. Diagrams drawn on paper
are copies of the ideas in the mind, and not liable to the
uncertainty that words carry in their signification. An angle,
circle, or square, drawn in lines, lies open to the view, and
cannot be mistaken: it remains unchangeable, and may at leisure
be considered and examined, and the demonstration be revised, and
all the parts of it may be gone over more than once, without any
danger of the least change in the ideas. This cannot be done in
moral ideas: we have no sensible marks that resemble them,
whereby we can set them down; we have nothing but words to
express them by; which, though when written they remain the same,
yet the ideas they stand for may change in the same man; and it
is seldom that they are not different in different persons.
Secondly, Another thing that makes the greater difficulty in
ethics is, That moral ideas are commonly more complex than those
of the figures ordinarily considered in mathematics. From whence
these two inconveniences follow:--First, that their names are of
more uncertain signification, the precise collection of simple
ideas they stand for not being so easily agreed on; and so the
sign that is used for them in communication always, and in
thinking often, does not steadily carry with it the same idea.
Upon which the same disorder, confusion, and error follow, as
would if a man, going to demonstrate something of an heptagon,
should, in the diagram he took to do it, leave out one of the
angles, or by oversight make the figure with an angle more than
the name ordinarily imported, or he intended it should when at
first he thought of his demonstration. This often happens, and is
hardly avoidable in very complex moral ideas, where the same name
being retained, an angle, i.e. one simple idea is left out, or
put in the complex one (still called by the same name) more at
one time than another. Secondly, From the complexedness of these
moral ideas there follows another inconvenience, viz., that the
mind cannot easily retain those precise combinations so exactly
and perfectly as is necessary in the examination of the habitudes
and correspondences, agreements or disagreements, of several of
them one with another; especially where it is to be judged of by
long deductions and the intervention of several other complex
ideas to show the agreement or disagreement of two remote ones.
--LOCKE, JOHN.
_An Essay concerning Human
Understanding, Bk. 4, chap. 3, sect.
19._
Public-domain text, read in full here on John Shaqi.
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