random
Alex Martelli
aleaxit at yahoo.com
Sat Jun 2 18:56:06 EDT 2001
"Lulu of the Lotus-Eaters" <mertz at gnosis.cx> wrote in message
news:mailman.991514764.4040.python-list at python.org...
...
> But if you are not happy with mere physical/empirical impossibility, it
> works equally well for mathematical impossibles:
>
> <2+2=5> IMPLIES <2+3=6>
>
> works fine by application of Peano arithmetic. Using the successor
> operator ' and some permitted reasoning:
>
> Premise: 2+2 = 5
> (1): 2+2'= 5' # successor of equals maintains equality
> (2): 2+3 = 6 # rewriting terms in conventional manner
>
> The reasoning is valid, so the conditional holds. The antecedent is in
> extremely bad shape--mathematically impossible--on its own. But so
> what?
So you can prove "_anything_ else" just as well -- any WFF in
the system is now a theorem. You took a simple case, but
it should be clear how with a little more work you can prove
any other equation for example -- as given x=y you may
legitimately add N*x to one side and N*y to the other, &c.
Thus, if "I can predict the next bit" was a WFF in the system,
<2+2=5> implies <I can predict the next bit>
and thus the negation of this implication doesn't hold.
Alex
More information about the Python-list
mailing list