Re: Results of Poll by Email No. 27

--- In conlang@yahoogroups.com, Tristan <kesuari@Y...> wrote:

 > > Why not? It's impossible only when you discuss about it using our
limited human-
 > > invented two-value logic. Why should the universe follow what is
mainly a human
 > > convention?
 >
 > Do you know of any other logics? How to they work?

The terms "true", "false", "implies" etc are defined
within our aedifice of logic -- if you were to change
into another system of logic [1], you'd have to
redefine all these expression.

[1] My poor human mind can't really imagine one of
     those, except maybe for trivial ones like "every
     statement is true"...  the logical aequivalent of
     the trivial group representation g -> 1 for all
     g in the group.



 > > > Tristan (has come to the conclusion that mathematicians *must*
have too
 > > > much
 > > > time on their hands to come up with things like that... And then to
 > > > prove that
 > > > 1+1=2...)

Well, one of the very first theorems we proved in
calculus must have been 0 != 1, that is, the
additive unit element is different from the
multiplicative unit element.  I can't think of the
proof though.  It most certainly makes use of the
Real Number Axioms, so I guess it might not be
applicable to all, um, *things* that have addition
and multiplication.



 > > Well, it was not that obvious ;))) (and it's not even always true
;))) ).
 >
 > When does 1+1 != 2? And saying that 1+1=10 in binary is cheating and
 > doesn't count, because 10 base 2 = 2 base > 2 :)

In the cyclic group Z_2, which is basically the set of
integer numbers modulo 2 (which is basically {0, 1})
together with the addition operator, you get 0 + 0 = 0,
0 + 1 = 1 + 0 = 1, 1 + 1 = 0 (since 2 == 0 modulo 0).
Interestingly, this group also has -1 = 1.  :-P



-- Christian Thalmann