Re: If (P & ~P) -> Q is not derivable then Goedel's formula is not derivable


Confutus wrote:
Rejection of the excluded middle principle implies a multi-valued
logic.

I replied,
*2* values ALREADY constitute MULTIPLE values.
Going from 2 to 3 is not a big deal.

Multi-valued logic is usually understood to mean three or more values.
If you think going from 2 to 3 is no big deal, you should try it some
time...

I have tried it; we've all tried. Not only is it not a big
deal, it is NO deal at all, actually. Going from 2 values to
3 IS NOT going from 2 values to 3: it IS STAYING at 2.
The point is, either way, the resulting number of outcomes
is exponential in the number of variables. It just plain doesn't
matter what the exponent is. Put another way, you can count
just as high in base 2 as you can in base 3. Your numerals
will be longer in base 2 BUT ONLY BY A CONSTANT LINEAR FACTOR.
It will always be less than double as long, in fact (log2 of 3 as long,
in fact).

Similarly, if you are going to allege that 33 variables can take any of
3 possible values, I can just LAUGH IN YOUR FACE and insist that
what YOU are actually saying is that 66 variables can take any of *2*
possible values, but we just won't get around to using one of the
combinations. My point being that I can replace any of your alleged
3-valued variables WITH TWO 2-valued variables, and except for slightly
longer variable-names (WHICH DON'T MATTER), there is NO important
difference happening. Phrased another way, using strings of bits vs.
using strings of bytes to represent data on a computer IS NOT a
DIFFERENCE
because bytes ARE strings of bits (and strings-of-strings are
strings).
In other words, not only does it not matter whether you use a 2 or a 3
valued logic, it ALSO doesn't matter whether you use a 2 or a
256-valued
logic.

.

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