Here is a dialogue from Edgar Allen Poe's *The Purloined Letter*:
(The French symbols, I'm sorry to say, can't be fixed in my editor in what
follows)
"But is this really the poet?" I asked.
"There are two brothers, I know; and both have attained
reputation in letters. The minister I believe has written
learnedly on the Differential Calculus. He is a mathema-
tician, and no poet."
"You are mistaken; I know him well; he is
both. As poet and mathematician, he would reason well;
as mere mathematician, he could not have reasoned at all,
and thus would have been at the mercy of the Prefect."
"You surprise me," I said, "by these opin-
ions, which have been contradicted by the voice of the
world. You do not mean to set at naught the well-digest-
ed idea of centuries. The mathematical reason has long
been regarded as the reason par excellence."
"'Il y a a\… parier,'" replied Dupin, quoting
from Chamfort, "'que toute idee publique,, toute conven-
tion rec‡ue, est une sottise, car il a convenue au plus
grand nombre.' The mathematicians, I grant you, have
done their best to promulgate the popular error to which
you allude, and which is none the less an error for its
promulgation as truth. With an art worthy a better
cause, for example, they have insinuated the term 'analy-
sis' into application to algebra. The French are the
originators of this particular deception; but if a term
is of any importance -- if words derive any value from
applicability -- then 'analysis' conveys 'algebra' about
as much as, in Latin, 'ambitus' implies 'ambition,'
'religio' 'religion,' or 'homines honesti' a set of honor-
able men." "You have a quarrel on hand, I see," said I,
"with some of the algebraists of Paris; but proceed."
"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; mathe-
matical 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 egre-
gious 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 con-
sideration 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 numer-
ous 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..."
Ralph A. Raimi (Mathematics) Tel. 716 275 4429, or (home) 716 244 9368
University of Rochester Fax (at math.dept.): 716 244 6631
Rochester, NY 14627 Homepage: http://www.math.rochester.edu/u/rarm