Sentence examples for is not provable from from inspiring English sources

While it is true that there is an analogy between the liar paradox and Gödel's construction of a sentence that says of itself that it is not provable from given rules, his work stands on its own and in no way "exploits" that paradox.

Thus ⊥ follows semantically from Γ, but is not provable from it in GL, contradicting the condition of strong completeness.

Logic programs consist of facts and rules describing what is true; anything that is not provable from a program is deemed to be false.

But consistency will never be intrinsic to the system; it must always be imported "from the outside," so to speak, as follows from the Second Incompleteness Theorem, which states that consistency is not provable from within any system adequate to formalize mathematics.

More exactly, Gödel showed that, if the system is consistent, then p is not provable; if it is ω-consistent, then ∼p is not provable.

Let us consider the sentence (2) This sentence is not provable in the system.

But then what f(i) = 0 says is just that the ith sentence is not provable.

Cohen, in 1963, showed that it is not provable under these hypotheses and hence is independent of the other axioms.

In particular, the consistency of mathematics, which may be taken, for instance, to be the metamathematical assertion that the mathematical statement 0 = 1 is not provable, ought to be a metatheorem that is, provable within the syntax of mathematics.

Then he added: "It would not surprise me if they came up with some information that is not provable, and they've shifted.

Thus, AC is not provable in Q0.