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Two Things have made moral Ideas thought uncapable of Demonstration. Their Complexedness, and want of sensible Representations.
      §19. That which in this respect has given the advantage to the
Ideas of Quantity, and made them thought more capable of Certainty
and Demonstration, is,
      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 mis-
taken: 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 thus 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 ’tis very seldom,
that they are not different in different Persons.
      Secondly, Another thing that makes the greater difficulty in
Ethicks, is, That moral Ideas are commonly more complex than those
of the Figures ordinarily considered in Mathematicks. From whence
these two Inconveniencies 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 follows, 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 over-sight make the
— 551 —
Figure with one 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, one Angle, i.e. one simple
Idea is left out or put in, 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 Incon-
venience, (viz.) that the Mind cannot easily retain those precise
Combinations, so exactly and perfectly, as is necessary in the Exam-
ination of the Habitudes and Correspondencies, Agreements or
Disagreements, of several of them one with another; especially
where it is to be judg’d of by long Deductions, and the Intervention
of several other complex Ideas, to shew the Agreement or Disagree-
ment of two remote ones.
      The great help against this, which Mathematicians find in
Diagrams and Figures, which remain unalterable in their Draughts,
is very apparent, and the memory would often have great difficulty
otherwise to retain them so exactly, whilst the Mind went over the
parts of them, step by step, to examine their several Correspon-
dencies: And though in casting up a long Sum, either in Addition,
Multiplication, or Division, every part be only a Progression of the
Mind, taking a view of its own Ideas, and considering their Agree-
ment or Disagreement; and the Resolution of the Question be
nothing but the Result of the whole, made up of such particulars,
whereof the Mind has a clear Perception: yet without setting down
the several Parts by marks, whose precise Significations are known,
and by marks, that last and remain in view, when the memory had
let them go, it would be almost impossible to carry so many different
Ideas in Mind, without confounding, or letting slip some parts of
the Reckoning, and thereby making all our Reasonings about it
useless. In which Case, the Cyphers or Marks help not the Mind at
all to perceive the Agreement of any two, or more Numbers, their
Equalities or Proportions: That the Mind has only by Intuition of its
own Ideas of the Numbers themselves. But the numerical Characters
are helps to the memory, to record and retain the several Ideas
about which the Demonstration is made, whereby a Man may know
how far his intuitive Knowledge, in surveying several of the par-
ticulars, has proceeded; that so he may without Confusion go on
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to what is yet unknown; and, at last, have in one view before him
the Result of all his Perceptions and Reasonings.
Locke Hum IV, 3, §19, pp. 550-551-552