Hi,
i wrote:
statements which are neither true nor false.
Kurt Goedel. Incompleteness theorem.
Celejar wrote:
No - Gödel proved that any such (formal) system will contain statements
such that neither they nor their negations are *provable within the
system*. These statements are actually "true", using a normal
definition of truth.
A system which contains this "normal definition of truth" must itself
contain statements which cannot be proven within that system - unless
it is too weird to be written down or too dull for the theory of numbers.
Consider the normal pitfall of philosophy to believe that human mind
and reasoning can cope with everything. I.e. axioms are for cowards.
So what does the free-wheeling philospher think about the truth of the
following statement:
"This statement itself is false."
Have a nice day :)
Thomas