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18
Mathematical propositions have no other certainty than what belongs
to the conclusions of sense: for they are themselves derived from those
conclusions: the only advantage they have is, that they
the Ideas which form this terms of which they consist are may be
taken and therefore are taken from those objects of sense, the conclusions which can
concerning which are afford conclusions, and those taken under circumstances in which they are, least liable to error — A Mathematician
takes raises his abstract ideas of a line and a circle
from the most perfect right line & circle he ever saw, and these
placed at those distances from his eye at which he is least
liable to be mistaken in their figure: and if in these he
says any defects, any parts tending to curvature in the right
line or to streightness or a different curvature in the circle he may make
his ideal line & circle free even from these imperfections which he by
resolving not to suppose them to exist: & finally he may free
them from all possible imperfections by saying to himself,
if there are any behind, which I cannot see, be they will what
they will, I will disappear them out of the case as I do these.
Thus it is that he purifies his ideas of all the imperfections which
existed in the impressions of which they were the copies.
To say then with Montesquieu, that it was always true
that the three angles of a Triangle were equal to two right ones
before there were any Triangles figures with 3 angles or persons to think about their equality,
is to say that there were Ideas, that is thoughts, before there
were thinking persons.
If In this be the case — then also in the 2d place That it does not last so much the time it lasts is not so much as shorter than the time the other would last as to compensate the difference of intensity at the 1st commencement write from [Introd. a Law 8 cases of
in respect of refraining [BR] 4]
In the 4th place that it is not true that it is the nature of this pain in the 2d of the 2 cases to give gives way to any such invariably connected pleasure derived from the same cause as being subtracted from the pain (estimated in like manner by it's intensity multiplied into the of it's duration leaves a ballance of pain less than in the 1st case. In the 5th place, that neither is the like true concerning any such pleasures contingently
connected with the respective pains contingency as </p>
---page break---
contingent reversions and remainders on their estates
according to it's present value. viz. by 1st suppos.g
it present, & then dividing the amount of it by
not written. the number of chances to one of it's arrival
And this appears to be a Specimen of that
Mode of Investigation of which Locke had
an implicit Notion when he maintained
that proposition which has since been so
much dwelt upon by Subsequent Moralists
"That Moral Truths were susceptible of
Demonstration as truly as those of Mathematics;
as one may see by the Examples
he has adduced: tho' he had not settled
into the Track, rejecting all technical &
fictitious Standards, of resorting on all
Occasions to the one true & natural one
of Utility. The Seeds first sown by that
great & original Genius had not grown
up to that full Harvest of Intelligence
which has since been gathered: Hume,
D'Alembert, Voltaire, Helvitius, Brecaria
had not written.
The great Difficulty in Practice is to
determine to which of these Cases a given Law
belongs: a question, in Answer to which, in
many Instances, the most sanguine Schemer
will hardly flatter himself with being able to
produce any Thing but imperfect Probabilities
but which being once determined, the Answer to
the next viz: whether the Law be or be not
expedient becomes by this Means a Matter of
self-evidence. But this does not hinder but that
the Propositions concerning the Expediency or
Inexpediency of a Law according as it comes under
one or other of these Cases if not as incontestible
as any in Mathematics in their present Form
may become so in the Hands of a more accurate Observer.
Great Question in like Manner may there be
whether a Curve which I draw on a piece of Paper
be a Portion of a Circle or Parabola — but it is
not for this the less certain, that if it be a Portion of
a Circle all right Lines drawn from the Center of
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introd. jurisprudence whether susceptible of demonstration |
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