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Topic: Mathematics as a language
Replies: 25   Last Post: Nov 10, 2010 9:15 AM

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Bill Taylor

Posts: 465
Registered: 12/8/04
Re: Mathematics as a language
Posted: Nov 4, 2010 2:01 AM
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On Nov 3, 4:15 am, Aatu Koskensilta <> wrote:

> Indeed. I like to talk about "ways of thinking". (Others speak of
> metaphors, conceptual pictures, what have you.) A way of thinking is
> neither true nor false. Rather, ways of thinking are useful, confusing,
> handy, what have you.

Yes, as I noted in my earlier reply.

> When first encountering Penrose's G delian
> arguments I was baffled by the notion that there is any determinate
> totality of "unassailably true" mathematical statements.

Yes; actually Penrose has got well out of his depth in that debate!

> I unassailably believe 1 + 1 = 2, perhaps.

It's an interesting point. Many of us would go along with that,
and extend it as far as 2 + 5 =7, perhaps, and even a little bit
And also maybe 2 x 3 = 6. But maybe not too much further?

Maybe not to 147 + 684 = 831 ? How sure are you of your
ability to avoid mistakes in this kind of thing?

Probably it's a bit of a silly discussion; but I recall an earlier
thread where Daryl McC remarked that he was totally happy with
those baby ones, but just not *quite* so cavalier with the later ones.

It's an interesting subject for a coffee-room discussion.

> But do I unassailably believe the cut
> elimination theorem for second-order logic? The existence of an
> ineffable cardinal? I have no idea.

Those things are surely subject to a tincture of doubt, due to
(if nothing else) the ability of the math world to accept mistakes
for a great many years.

All this is fascinating epistemology, but scarcely mathematical!

-- Wondering Willy

** For every philosopher there is an equal & opposite philosopher.

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