On Thu, 28 Feb 2008, John F. Sowa wrote:
> Chris and Ravi,
>
> JFS>> Practicing mathematicians -- people who actually solve problems
> >> that other people pay somebody to solve -- dismiss the study of
> >> foundations as *irrelevant*.
>
> CM> I don't think they dismiss it so much as ignore it...
>
> I think we agree about what working mathematicians do, and the only
> difference is in word choice. I have no preference for either
> 'dismiss' or 'ignore'. (01)
Sort of like Obama and "denounce" vs "reject". :-) Be that as it may,
in my mouth, "dismiss" is much stronger than "ignore". In my mouth, one
needs reasons (perhaps bad reasons) to dismiss something, but one can
ignore just by an act of will. If you, for example, reject your
doctor's strong recommendation to lose weight because you feel it is
merely as a reflection of a social prejudice ungrounded in genuine
medical science, I would say you had dismissed it. If you go on eating
and avoiding exercise despite her recommendation with no more reason
than that you don't wish to change your ways, it doesn't sound right to
say you have dismissed her recommendation; you have simply ignored her. (02)
> In any case, I like the following quotation:
>
> Friend of CM> "Most working mathematicians would rather not think
> > about foundational issues, just as most meat-eaters would rather
> > not think about how the animals are slaughtered."
>
> That supports my point that foundational issues are "irrelevant"
> to the way that mathematicians think and discover their theorems. (03)
Well, there's an interesting ambiguity to "irrelevant" corresponding to
the "ignore"/"dismiss" distinction. Something can be irrelevant to me
because I simply choose to ignore it (perhaps at my peril) or because I
can reasonably dismiss it. At this point in time, after 100 years of
serious testing and use of our best modern set theories, it seems to me
that "working" mathematicians can reasonably dismiss foundational issues
and hence reasonably regard them as irrelevant. In the early 20th
century, however, with the foundational paradoxes still fresh and their
origins unexplained, it seems to me that foundations could be regarded
as irrelevant by ignoring them, as they still posed a threat to the most
basic mathematical arguments. (04)
So it seems to me, anyway. (05)
-chris (06)
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