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Re: [ontolog-forum] Historical footnote

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 14 Feb 2007 13:36:26 -0500
Message-id: <45D356AA.30702@xxxxxxxxxxx>
Pat and Chris,    (01)

1901 is hardly "early".    (02)

CM>> Russell sent his fateful letter to Frege informing him
 >> of the paradox in the Grundgesetze der Arithmetik in 1902;
 >> Padoa published his first paper on the theory of definitions
 >> (which included a notion of non-creativity) in 1901.    (03)

PH> Ah, I stand corrected. Thanks. I am amazed that it was
 > possible to even think of these ideas that early.    (04)

The ancient Greeks, among others, thought about, analyzed,
and debated paradoxes very seriously.  Epimenides the Cretan
stated his closely related "liar paradox" around 600 BC, and
it was analyzed and debated for centuries, especially by the
medieval scholastics.  Philetus of Cos (285 BC) is supposed
to have "died from considering the liar paradox."  See    (05)

    Ancient Greece, Mathematics Timeline    (06)

Cantor himself noticed the so-called "Russell paradox" and made
some informal remarks to express his concerns.  Zermelo noted
Cantor's remarks and had already developed the first version of
his axioms to avoid the paradox before he had heard anything from
Russell.  Hilary Putnam remarked "Zermelo presented his axioms
for set theory in Peirce-Schröder notation, and not, as one
might have expected, in Russell-Whitehead notation."  See    (07)

    Peirce the Logician    (08)

Russell and Frege were probably unaware of Cantor's earlier remarks,
but Russell was the loudest, if not the first.  And note that even
Putnam uses the phrase "Russell-Whitehead" notation despite the fact
that every feature of their syntax (including the dots for showing
precedence) had been published by Peano in 1895 -- and Peano gave
full credit to Peirce and Schröder as his primary sources.  (When
Peano corresponded with Frege, he refused to read Frege's examples
unless Frege translated them to the algebraic notation.)    (09)

John    (010)

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