Subject: Re: [HM] American mathematicians
From: Bill Everdell (Everdell@aol.com)
Date: Fri May 05 2000 - 14:16:12 EDT
In a message dated 5/4/00 4:55:51 PM, John.Harper@MCS.VUW.AC.NZ writes:
<<So did Josiah Willard Gibbs (he did for chemical thermodynamics what Newton
did for mechanics).>>
As a United-Statesian myself, I would feel remiss if no mention was made of
Gibbs's equally extraordinary contemporary, and Benjamin Peirce's son,
Charles Sanders Peirce, who I think should be credited (inter alia) with the
invention of the "logic of relatives" in a paper of 1873 (Peirce,
"Description of a Notation for the Logic of Relatives from an Amplification
of the Conceptions of Boole's _Calculus of Logic_" communicated, later
published in _Memoirs of the American Academy of Arts & Sciences n.s.
9(1873)) That was Peirce's own name for the proposition-as-function logic
which Bertrand Russell later rebaptized the "logic of relations, and which he
used in 1900-1903 to start the "foundations" hare with _The Principles of
Mathematics_. Though both Russell and Peirce were impressed with their
readings of Augustus De Morgan's "On the Syllogism No. IV, and on the Logic
of Relations," (_Transactions of the Cambridge Philosophical Society_
10(1859)), De Morgan's logic retained Boole's constricted idea of relation.
It was Peirce who made the important leap first. In his paper "Recent Work
on the Principles of Mathematics" (_International Monthly_, 4(July, 1901),
83-101) which Russell wrote in January, 1901, while working on _The
Principles of Mathematics_ this passage occurs:
"a new branch of logic, called the Logic of Relatives, has been invented to
deal with topics that wholly surpassed the powers of the old logic, though
they form the chief contents of mathematics." (in _Russell Papers_, v3, p367)
and in a footnote Russell credited Peirce:
"This subject is due in the main to Mr. C.S. Peirce"
This footnote did not reappear when Russell's paper, revised as "Mathematics
and the Metaphysicians," was reprinted in Russell, _Mysticism and Logic_,
1917, (cf. p76-77) but it does recur in the version reprinted by J. R. Newman
in _The World of Mathematics_ (v3, p1578). A generation later, in the
"Foreword" which he wrote for James Feibelman's _An Introduction to Peirce's
Philosophy_, Russell wrote:
"I am—I confess to my shame—an illustration of the undue neglect from which
Peirce has suffered in Europe. I heard of him first from William James when I
stayed with that eminent man in Harvard in 1896. But I read nothing of him
until 1900, when I had become interested in extending symbolic logic to
relations, and learnt from Schroeder's _Algebra der Logik_ that Peirce had
treated of the subject. Apart from his work on this topic, I had until
recently read nothing of him except the volume entitled by its editors
_Chance, Love and Logic_." (p xv)
Bill Everdell, Brooklyn
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