Sentence examples for be provable by from inspiring English sources

Carnap responded by stating that arithmetic demands an infinite sequence of ever richer languages and by declaring analytic statements to be provable by non-finite reasoning (1934/37, §60a-d).

The court will determine whether the check writer simply made a mistake (he thought he had the money in the bank and made an error in calculations) or was intending to defraud you, which should be provable by a history of bad check writing.

It is provable by the infrared spectroscopy of CdSe powders obtained by evaporation of the colloidal solution of xylene.

Hence, if the consistency of Principia were provable by the methods used in Ackermann's proofs, it should be possible to formalize this proof in Principia; but this is what the second incompleteness theorem states is impossible.

If an underlying paraconsistent logic is used to formalise the arithmetic, and the theory therefore allowed to be inconsistent, the Gödel sentence may well be provable in the theory (essentially by the above reasoning).

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).

In typed theories of truth, only the truth of sentences not containing the same truth predicate is provable, thus avoiding the paradoxes by observing Tarski distinction between object and metalanguage.

However, there is a problem with this claim that can be exposed by noting that ◊□A→A is provable from (B).

the claim that the formula with such and such a code in the mathematical representation of the syntax (the code represented in the meta-meta-theory here by '⟨sin2θ + cos2θ = 1⟩') is provable.

(By 'theorems' we mean results that are provable within the branch of mathematics in question).

Reverse mathematics seeks to give a precise answer to this question by investigating which theorems of classical mathematics are provable in weak subsystems of analysis which are reducible to finitary mathematics (in the sense discussed in the preceding paragraph).