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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 2:09 AM
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On Nov 3, 5:05 am, (Daryl McCullough) wrote:

> You could say that if you're not sure that <whatever>
> unassailable, then it's not unassailable.

Good point!!

> But then there's a kind of sorites paradox about
> the unassailable statements.

So it might seem. But sorities paradoxes are not unassailable!

I suspect that most sorities paradoxes are easily assailable.
And resolvable.

Consider the classic "heap paradox" - how many stones does it
take to make a heap?

If this is interpreted with potentative modaility,
i.e. how many stones *could* make a heap, then the answer is sharp!

It is - FOUR! One stone cannot possibly be "heaped",
and 2 or 3 cannot if they do not have pits and spikes to
help them out, which seem to be agin the definition of a stone.

But 4 stones can trivially make a heap - 3 in a close triangle and
one on top! Easy-peasy baby squeezy!

So that disposes of THAT!

I have on an earlier occasion disposed of the chicken and the egg,
though that is not *quite* of sorities type. And the mighty John Baez
agreed with me on that occasion! (Let's hear it for "authority"...)

-- Beaming Bill

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