Sentence examples for all provable from inspiring English sources

Moreover, under the assumption that all provable sentences are true, it follows that there must be true sentences which are not provable.

Both groups were asked whether they agreed with statements such as: "We can only rationally believe in what is scientifically provable," "All the tasks human beings face are soluble by science," and "The scientific method is the only reliable path to knowledge".

In some countries labour claims not only have priority over all other provable claims but outrank even the rights of secured creditors.

Blok and Pigozzi have in mind the least consequence relation for which φ, φ → ψ ⊢ ψ and φ, ψ⊢ φ ∧ ψ and ⊢ φ for all φ provable in the Fmla logic R. (This third condition can be restricted to all axioms of any axiomatization of R with formula-to-formula rules corresponding to the first and second conditions).

For example in Boole's case the set-theoretic consequences that he relies on are all easily provable by formal proofs in first-order logic, not even using any set-theoretic axioms; and by the completeness theorem (see the entry on classical logic) the same is true for first-order logic.

Of course Media Matters and Rachel Maddow and so many others chronicle all their provable lies and ideological hysteria.

I worry that more and more today we lean toward that which is provable, when all the excitement is in the hard-to-prove.

As a consequence, this also settles Henkin's original problem: assuming that the arithmetized provability predicate is again "normal" (i.e., satisfies Löb's derivability conditions), all sentences "asserting their own provability" are provable.

Rule 17 states that an attack scenario, say α, is provable if: (a) all the actions it contains are provable; (b) all the remote executed actions, which were observed by the network observers and included in the aggregated network evidence, are in the generated scenario α; and (c) the order of appearance of remote actions in the aggregated network evidence is maintained in the scenario α. (17).

The axiom to be shown independent can then acquire some undesired value, whereas all the theorems that are provable without this axiom always get the desired values.

She also called on companies to be required to advertise all jobs as potential job shares, or as part-time roles, unless there was a provable requirement for the job to be full time.