Russell vs Hilbert

[Tennant, Neil]

JS's Twitter friend was quoting from page i of Russell's Preface to
The Principles of Mathematics.

At pages vi-vii, Russell went on to clarify what he meant by
'proposition' as follows:

"Where two qualities
are commonly supposed inseparably conjoined, but are here
regarded as separable, the name which has applied to their
combination will usually have to be restricted to one or other.
For example, propositions are commonly regarded as (1) true
or false, (2) mental. Holding, as I do, that what is true or false
is not in general mental, I require a name for the true or false
as such, and this name can scarcely be other than proposition."

I don't know whether this clinches the interpretative question raised,
but it inclines me to the view that Russell was convinced that all
mathematical truths would be logically derivable.

Neil Tennant


________________________________
From: FOM <fom-bounces at cs.nyu.edu> on behalf of Joe Shipman <joeshipman at aol.com>
Sent: Tuesday, December 15, 2020 4:47 PM
To: Foundations of Mathematics <fom at cs.nyu.edu>
Subject: Russell vs Hilbert

One of my Twitter friends claims that the view that all mathematical propositions are decidable from a few axioms was held by Russell prior to Hilbert, and that Russell was claiming, in his books, not only to have reduced all mathematical reasoning to a few logical principles, but also to have claimed that those principles were sufficient to settle all questions.

This is based on his reading of the following 1903 passage:

"THE present work has two main objects. One of these, the proof that all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that all its propositions are deducible from a very small number of fundamental logical principles"

In my opinion, by “propositions”, Russell meant “theorems”, not “true statements”, and therefore one may not jump to the conclusion that Russell failed to achieve his object and did not prove what he claimed to be trying to prove.

Can any Russell experts shed light on this question?

— JS



Sent from my iPhone
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20201216/05cbbcab/attachment.html>