The intuitive rationale of this rule is that, in a sound axiomatic system, it is expected that every instance of a theorem α will be not merely true but necessarily true and in that case every instance of Lα will be true.
Voltaire's campaign on behalf of smallpox inoculation, which began with his letter on the topic in the Lettres philosophiques, was similarly grounded in an appeal to the facts of the case as an antidote to the fears generated by logical deductions from seemingly sound axiomatic principles.
As dutiful fans line up for "Attack of the Clones," and "Spider-Man" continues to test its legs (so to speak) after a record $114 million opening weekend, Kael's words sound less prophetic than axiomatic.
Axiomatic soundness and completeness can be proved.
Relative to a given criterion of validity, an axiomatic system is sound if every theorem is valid, and it is complete (or, more specifically, weakly complete) if every valid wff is a theorem.
That is, these axiomatic extensions are sound and complete for the corresponding temporal frames or classes of temporal frames.
The axiomatic system \(\mathbf{K}_{t}\) is sound and complete for validity in TL, in the sense that it can derive all valid formulae of TL and only them.
It is axiomatic that successful applied biology relies on sound taxonomy.
The axiomatic system PM can be shown to be both sound and complete relative to the criterion of validity already given (see above Validity in PC).
One version of Gödel's first incompleteness theorem states that for any consistent axiomatic theory of arithmetic, which can be recognised to be sound, there will be an arithmetic truth viz., its Gödel sentence not provable in it, but which can be established as true by intuitively correct reasoning.
