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"I dispute the availability, and thus the value, of that reason which
is cultivated in any especial form other than the abstractly logical.
I dispute, in particular, the reason educed by mathematical study. The
mathematics are the science of form and quantity; mathematical reasoning
is merely logic applied to observation upon form and quantity. The great
error lies in supposing that even the truths of what is called pure
algebra, are abstract or general truths. And this error is so egregious
that I am confounded at the universality with which it has been
received. Mathematical axioms are not axioms of general truth. What is
true of relation--of form and quantity--is often grossly false in regard
to morals, for example. In this latter science it is very usually untrue
that the aggregated parts are equal to the whole. In chemistry also the
axiom fails. In the consideration of motive it fails; for two motives,
each of a given value, have not, necessarily, a value when united, equal
to the sum of their values apart. There are numerous other mathematical
truths which are only truths within the limits of relation. But the
mathematician argues, from his finite truths, through habit, as if
they were of an absolutely general applicability--as the world indeed
imagines them to be. Bryant, in his very learned 'Mythology,' mentions
an analogous source of error, when he says that 'although the Pagan
fables are not believed, yet we forget ourselves continually, and make
inferences from them as existing realities.' With the algebraists,
however, who are Pagans themselves, the 'Pagan fables' are believed, and
the inferences are made, not so much through lapse of memory, as
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