[FOM] Russell and Skolem's paradox

Alasdair Urquhart urquhart at cs.toronto.edu
Thu Apr 8 17:35:07 EDT 2010

Aldo Antonelli asked:

> I remember being told that Russell thought that the greatest technical
> advance achieved between the first and second edition of PM was the
> introduction of Sheffer's stroke.
> Surely Alasdair can confirm this, if true, which would speak to the
> extent of Russell's involvement in technical advances in logic after the
> first edition.

In the Introduction to the Second Edition of PM, Russell wrote:

"The most definite improvement resulting from work in mathematical logic
during the past fourteen years is the substitution  ... of the one
indefinable "p and q are incompatible" for the two indefinables
"not-p" and "p or q."  This is due to Dr H.M. Sheffer."

This should be read in context.  Russell is NOT saying that Sheffer's
was the greatest advance in logic since the first edition.  He is saying
that Sheffer's work results in the most definite improvement to
the foundations of Principia Mathematica (the context makes this
reading clear).

It's hard to say how aware Russell was of work in logic
after he finished his main research.  The evidence is scanty.
In 1960, Robin Gandy proposed a visit by himself and two other logicians
to pay homage to Russell.  Russell accepted Gandy's proposal, but
warned him that "I am completely out of touch with recent logical
work and you will all have to treat me as an ignoramus."
(Source: "Dear Bertrand Russell" ed. Feinberg and Kasrils, 1969).

On the other hand, in 1951, Russell and Max Newman successfully proposed 
Alan Turing as a Fellow of the Royal Society, referring in their recommendation to
the work on computable numbers.  Russell is known to have read and
admired Turing's "Computing Machinery and Intelligence."
So, the late letter to Henkin may be somewhat misleading.

More information about the FOM mailing list