axiomatic

A statement is true if and only if there is no counterexample to it in any model of the axiomatic system you are dealing with.

An axiomatic system, in the context of Goedel's theorems, is a bunch of axioms with some inference rules.

You might be interested in the YNot[1] project, which is a library implementing Hoare-style axiomatic semantics in Coq.

From this it only follows that you can prove X if you have a complete axiomatic system.

They take an axiomatic approach, coming up with some general principles that they feel are self-evidently correct.

Free will is validated by introspection and no one can convince you of its axiomatic nature except your self, i.e.

An axiomatic system is complete if it can either prove or refute every possible statement.

If your model contains the natural numbers then this complete axiomatic system isn't computable.

So a complete axiomatic system is as powerful as possible w/o being inconsistent (if you prove both X and not-X, you're inconsistent).

You could have axiomatic systems that are built on axioms some of which are known to be false, and yet they're consistent.

The latter position is surely close to axiomatic but the former requires more thought.

This is clearly false unless you restrict yourself to recursively enumerable axiomatic systems.

It'd be a silly axiomatic system, but it would be one, and you wouldn't need to know anything about what the cards "mean".

Do you take it as axiomatic that a system that produces different outcome for different racial groups is "unfair"?

This meaning of "complete" is true for some axiomatic systems T and false for others.

It tells us that axiomatic systems for first-order logic are complete in the sense of "strong enough to prove all tautologies".

Axiomatic semantics, on the other hand, are really indirect.