Subject: Re: [HM] Mathematics and Time
From: John Conway (conway@math.Princeton.edu)
Date: Fri Mar 10 2000 - 12:32:17 EST
On Fri, 10 Mar 2000, Brendan Larvor wrote:
>
> JJ Sylvester took part in a dispute about the proper interpretation of
> Kant on space and time in 1869. So Hamilton was not alone among
> English-speaking mathematicians of the period in reading Kant (though he
> seems to have got a lot more out of it than JJS). Also it is clear that
> Kant's doctrines were not well understood--learned contributers to this
> dispute made mistakes that would be regarded as undergraduate howlers now.
>
> Kant thought that humans cannot understand completed infinities, so it is
> no wonder that few mathematicians bothered with him in the C20, except
> Brouwer.
I think the reason why mathematicians have largely gone off Kant is
rather that the discovery of non-Euclidean geometry made it clear that a
theory that implied the necessity of Euclidean geometry was just plain wrong.
In the same churlish mood may I wonder why Hamilton's theory that
algebra is the science of pure time is worth more than a paragraph of
discussion nowadays? Does affirming or denying this have any consequences
at all?
John Conway
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