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Inf. Pleasures and Pains _ how measured
denominates makes it's value only less by 1/3 only than it
would have been had the pleasure been present: while
leaving it equal to 2/3 of that of a present pleasure of the same magnitude
the degree of remoteness of the other pleasure is such
as makes it less by 2/3 than it would have been had
the pleasure been present: leaving it equal as to 1/3 only
of that of a present pleasure of the same magnitude.
To multiply a whole number by a fraction is to multiply
it by the numerator of the fraction, and divide the
product of the multiplication by the denominator
of 2/3 26 27 then multiplied by 2/3 or in other words 2/3
of 27 is 18: and 3 multiplied by 1/3, or in other
words 1/3 of 3 is 1. The gr value then of the greater
pleasure
will be to that of the lesser, as 18 is to 1.
The value magnitude number of the number expressive of the
magnitude of the pleasure supposing it to be present
must be
magnified by the fraction
expressing what it loses in value on the score of
it's remoteness from the not simply added: for the deduction
to be made on this account is applies equally
to every portion particle of it. If the fraction expressive of the
alteration made in its value by this circumstance
value was instead of being multiplied into the number
expressive of it's magnitude were added to it, the
value of it would be encreased by this circumstance
instead of lessened: the value of the greater pleasure
would be 27 and 2/3 instead of 18: that of the lesser
3 and 1/3 instead of 1.
After the same manner it may be shewn, that
the number expressive of the magnitude of the pleasure
is to be multiplied by the fraction expressive of its
degree of certainty, not added to it.
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Pleasures and Pains - how measured Inf.
The numbers expressive of the intensity of a pleasure
and those expressive of it's duration, must are to be
multiplied together, not merely added. For supposing
the pleasure to continue all along at the same degree
of intensity, every degree of intensity it possesses
is carried through every degree of duration: and
vice versa every degree of duration is extended over
every degree of intensity. Accordingly If of two pleasures, the
one be three times as great intense as the other, and at
the same time likewise continues three times as long, it is not six
times only as great, but nine times. The first pleasure,
(suppose) has three degrees of intensity, and likewise
suppose three minutes (suppose) of duration: the second
but one degree of intensity and one minute of duration.
The first then during the first minute has
three degrees of intensity, that is three times as
many as the second: during the second minute it
has the same three degrees of intensity over again:
that which makes it already six degrees times as great as the
other pleasure: during the third minute it
has the same three degrees of intensity still; which
makes it nine times as great.
In like manner the numbers expressive of
its magnitude and those expressive of it's proximity
must be multiplied together and not barely added
The magnitude of the first pleasure is 27,
that of the other, 3. At the same time the degree
of proximity or remoteness of the first is such as demonstrates<add>makes</add>
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Identifier: | JB/027/040/001 "JB/" can not be assigned to a declared number type with value 27.
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027 |
comment on the commentaries |
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040 |
pleasures and pains - how measured |
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f5 / f6 / f7 / f8 |
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jeremy bentham |
[[watermarks::w [britannia with shield motif]]] |
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