[FOM] Did Goedel's result come as a surprise to Bertrand?

Irving ianellis at iupui.edu
Tue Apr 6 10:34:52 EDT 2010

The best general account of which I am presently aware of the first
reactions to Goedel's incompleteness theorems is John Dawson's, "The
Reception of Go"del's Incompleteness Theorems", in Thomas Drucker
(ed.), Perspectives on the History of Mathematical Logic
(Boston/Basel/Berlin: Birkha"user, 1991), 84-100.

Dawson discusses Russell's (and Wittgenstein's) reactions to
incompleteness at pp. 95-96, mention Russell's letter to Henkin
(which I discussed in a previous post). On p. 114 of his book My
Philosophical Development (London: George Allen & Unwin, 1959),
where he discusses Wittgenstein's Tractatus Logico-philosophicus,
Russell refers to his introduction to the Tractatus, and, referring
to languages of higher order for a language, states that this
"disposes of Wittgenstein's mysticism, and I think, also the newer
puzzles presented by Go"del."

Whether or not Russell here, in this particular instance, made a
distinction between a paradox and a puzzle, it is in any case clear
that, in 1959, he claimed to have regarded Godeel incompleteness as a
difficulty, but one which was easily repaired. Russell wrote (dated)
his introduction to the Tractatus in May 1922.

What I understood Russell to have said in My Philosophical
Development when suggesting that his discussion of higher-order
languages in his introduction to Wittgenstein's Tractatus could
handle both Wittgenstein's mysticism and Goedel's incompleteness
theorems, was *not* that he was originally responding in the
introduction to Goedel, but that, in 1959, *in retrospect*, his
account of 1922 on higher-order languages was also an answer to
Goedel incompleteness.

In 1922, Russell obviously could not have mentioned Goedel or
Goedel's theorems.

The best that we can do in this case is suppose that Russell,
while composing My Philosophical Development thought that his
discussion  of higher-order languages in his introduction to the
Tractatus thought that introduction of higher-order languages
could have provided in advance a ready-made remedy to

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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