Subject: Re: [HM] Euclid and USA Politics (was: "President Garfield's Proof")
From: R. E. Taylor (leesoft@mindspring.com)
Date: Thu Jan 27 2000 - 17:33:44 EST
The excerpt below from the Federalist website:
http://www.Federalist.com/fedpapers/fedpapers.html
It is not clear to me that Hamilton had studied Euclid so much a
Euclidean geometry perhaps from one of the several "updatings" of
Euclid which were available. Is there anyone in the current political
mix who could touch Hamiliton or any of the others mentioned on
this thread? Alan Keyes perhaps?
Regards,
Bob Taylor
Federalist No. 31
The Same Subject Continued:
Concerning the General Power of Taxation
From the New York Packet.
Tuesday, January 1, 1788.
Author: Alexander Hamilton
To the People of the State of New York:
IN DISQUISITIONS of every kind, there are certain primary
truths, or first principles, upon which all subsequent reasonings
must depend. These contain an internal evidence which,
antecedent to all reflection or combination, commands the assent
of the mind. Where it produces not this effect, it must proceed
either from some defect or disorder in the organs of perception,
or from the influence of some strong interest, or passion, or
prejudice. Of this nature are the maxims in geometry, that "the
whole is greater than its part; things equal to the same are equal
to one another; two straight lines cannot enclose a space; and all
right angles are equal to each other." Of the same nature are
these other maxims in ethics and politics, that there cannot be an
effect without a cause; that the means ought to be proportioned to
the end; that every power ought to be commensurate with its
object; that there ought to be no limitation of a power destined to
effect a purpose which is itself incapable of limitation. And
there are other truths in the two latter sciences which, if they
cannot pretend to rank in the class of axioms, are yet such direct
inferences from them, and so obvious in themselves, and so
agreeable to the natural and unsophisticated dictates of
common-sense, that they challenge the assent of a sound and
unbiased mind, with a degree of force and conviction almost
equally irresistible.
The objects of geometrical inquiry are so entirely abstracted
from those pursuits which stir up and put in motion the unruly
passions of the human heart, that mankind, without difficulty,
adopt not only the more simple theorems of the science, but even
those abstruse paradoxes which, however they may appear
susceptible of demonstration, are at variance with the natural
conceptions which the mind, without the aid of philosophy, would
be led to entertain upon the subject. The INFINITE DIVISIBILITY
of matter, or, in other words, the INFINITE divisibility of a
FINITE thing, extending even to the minutest atom, is a point
agreed among geometricians, though not less incomprehensible to
common-sense than any of those mysteries in religion, against which
the batteries of infidelity have been so industriously leveled.
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