Put more simply, every formal proof must contain at least one
assumption and at least one undefined term. In practice, three
undefined terms and three postulates is a fairly tight, well contained
logical construct.
"This statement is false" isn't really anything profound. It does
illustrate there can exist internally inconsistent logical entities, but
really it is merely an artifact of the situation that just because a
string of words is grammatically correct does not imply it has any meaning.
Is this really a good discussion for the Debian User list?
On 6/21/2020 1:19 AM, Thomas Schmitt wrote:
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