[FOM] alleged quote from Hilbert

Roger Bishop Jones rbj01 at rbjones.com
Fri Apr 8 03:31:32 EDT 2005

On Thursday 07 April 2005  7:50 pm, Martin Davis wrote:
> In Rebecca Goldstein's recent "Incompleteness" she quotes
> Hilbert as follows:
> 	Mathematics is a game played according to certain simple
> rules with meaningless marks 	on paper.
> I would appreciate any information about this quotation about
> which I'm dubious.

I did a bit of digging around myself some time ago to see
whether this kind of allegation about the degree of Hilbert's 
formalism could be substantiated, and failed to find anything.

I did find this in a letter from Hilbert to Frege about his
formalisation of geometry:

"On defining primitives I do not want to presuppose anything as 
known. I see in my explanation in section 1 the definition of 
the concepts point, straight line and plane, if one adds to 
these all the axioms of groups i-v as characteristics. If one is 
looking for other definitions of point, perhaps by means of 
paraphrase in terms of extensionless, etc., then, of course, I 
would most decidedly have to oppose such an enterprise. One is 
then looking for something that can never be found, for there is 
nothing there, and everything gets lost, becomes confused and 
vague, and degenerates into a game of hide and seek."

Letter to Frege, 1899

Hilbert's view seems to have been not that primitives are
meaningless, but that their meaning should exclusively
be given formally.

This is a more tenable position in a context in which
it is not know that there can be no complete formalisation
of arithmetic.  Was Hilbert still alive in 1930?

Roger Jones

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