Re: Why Tarski is wrong --- Montague, Davidson and Knowledge Ontology providing situational context.

On 3/21/25 4:20 PM, Richard Heathfield wrote:

On 21/03/2025 19:30, Keith Thompson wrote:

My understanding is that Gödel proved that there are statements
that are true but not provable.

 Yes. Incompleteness.
 

It's still not possible for both
X and not-X to be provable.  If proofs exist for both, at least
one of the proofs must be flawed.

 I'd be interested to see a proof of that conjecture.
 

It comes from the definition of consistency.
If something is provable, then it must be true, as the proof shows the path from the fundamental truths the the stateemnt, establishing its truth.
If both x and not-x are probable then both x and not-x are true, which is the definition of a contradiction.
Most of these proofs start with the requirement that the system we are starting with in non-contradictory, i.e, there are no contradictions probable in it.
There are some more outlying logic systems, that due to built in weakness of their logic, do not support the principle of explosion, and thus can be defined to allow limited contradictions to exist in them, but these are on the fringe and not commonly used.