Sentence examples for Provable truth from inspiring English sources

Or should a story instead be extrapolated from an external, rational and scientifically provable truth?

And if you lack provable truth, you do not get justice.

Any formal system of the usual sort could be 'reduced' into one in which there is only one provability predicate and truth (= provability) in the reducing system of the elementary proposition ⊢ ⟨φ⟩ holds only when φ is provable in the reduced system (pp. 34 35).

He had earlier reserved the term "fact" for non-provable, non-general truths (Frege 1950 §3, cf. §77; Levine 1996).

There is thus a sense in which such truths are not provable using today's "ordinary" mathematical methods and axioms, nor can they be proved in a way that mathematicians would today regard as unproblematic and conclusive.

Indeed, Hilbert saw that something stronger is true: not only does a consistency proof establish truth of real formulas provable by ideal methods, but it yields finitary proofs of finitary general propositions if the corresponding free-variable formula is derivable by ideal methods (1928, 474).

Leon Henkin put forward the question whether the sentence expressing its own provability ("I am provable") is true or false, and provable or not (Henkin 1952).

Now there are, by Gödel's first theorem, arithmetical truths that are not provable even in ZFC.

Tait's technical analysis yields that the finitistic functions are exactly the primitive recursive ones, and the finitistic number-theoretic truths are exactly those provable in the theory of primitive recursive arithmetic PRA.

Snyder calls this policy "implausible deniability"; you hear it in the tone of the current "debate" around the Salisbury attack: Russian power is displayed in a relativist blizzard of alternative theories, delivered in a vaguely absurdist spirit, as if no truth on earth is really provable.

The truth is plain, and it is provable.