Re: [lojban] Sapir-Whorf Hypothesis

[Robin Lee Powell <rlpowell@digitalkingdom.org>]

On Tue, Jun 12, 2001 at 12:50:20PM -0700, Edward Cherlin wrote:
> The best recent example is non-standard arithmetic, which comes in two
> forms, one from Robinson's model theory, and the other from Conway's
> advances in game theory. Both provide consistent but significantly
> different arithmetics with actual infinitesimals, and both can be
> extended to analysis. Without the appropriate definitions of terms and
> proofs of theorems, there is no way anybody outside the field can
> understand what either form is talking about, since mathematicians had
> previously "proved" that arithmetic with infinitesimals was
> impossible, and in particular Peano thought that he had proved the
> impossibility of any non-standard models of the natural numbers.

As someone who almost has a math degree <grin>, I'm intrigued.

What are infinitesimals, and where do I find out about game-theory based
arithmetic?

-Robin

-- 
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