[FOM] Mathematics ***is***, according to Peirce

Irving ianellis at iupui.edu
Sat May 29 14:52:52 EDT 2010

There is the following definition by Benjamin Peirce (1809-1880):

"Mathematics is the science which draws necessary conclusions."
from his Memoir on Linear Associative Algebra" read before the National 
Academy of Sciences in Washington, 1870.

to which his son Charles Peirce (1839-1914) responded:

"The one [the logician] studies the science of drawing conclusions, the 
other [the mathematician] the science which draws necessary 

Charles also said: "To draw necessary conclusions is one thing, to draw 
conclusions is another, and the science of drawing conclusions is 
another; and that science is Logic."

Also interesting in this regard, is Charles Peirce's famous outburst at 
an American Mathematical Society meeting, as recalled by Thomas Scott 
Fiske (1865-1944), who, in telling of Peirce's activities in the early 
1890s society meetings, adjudged Peirce as having a "dramatic manner" 
and "reckless disregard of accuracy" in cases dealing with what Peirce 
considered to be "unimportant detail"; but Fiske added that both in his 
speaking and his writing, Peirce was most engagingly entertaining and 
-- whether drunk or sober -- brilliant, and he provided an example by 
describing “an eloquent outburst on the nature of mathematics" when 
Peirce, Fiske says, "proclaimed that the intellectual powers essential 
to the mathematician were 'concentration, imagination, and 
generalization.' Then, after a dramatic pause, he cried: 'Did I hear 
some one say demonstration? Why, my friends,' he continued, 
'demonstration is merely the pavement upon which the chariot of the 
mathematician rolls.'" (pp. 14–15 of Thomas Scott Fiske, "The 
Beginnings of the American Mathematical Society. Reminiscences of 
Thomas Scott Fiske”, Bulletin of the American Mathematical Society 45 
(1939), 12–15; reprinted in Peter L. Duren, Richard A. Askey, & Uta C. 
Merzbach (editors), A Century of Mathematics in America, Pt. I 
(Providence: American Mathematical Society 1988), 13-17; and Fiske, 
"Mathematical Progress in America", Bulletin of the American 
Mathematical Society 11 (1905), 238-–246, reprinted in Duren, Askey, & 
Merzbach, 3-11, quoting from pp. 15, 16 of Duren, Askey, & Merzbach.

Irving H. Anellis
Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
URL: http://www.irvinganellis.info

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