There exist sentences (such as the Fermat-like primality claim) that are decidable in the formal sense but for which no concrete proof or refutation exists or could be manipulated by any human
manipulated by any human(epistemology (theory of knowledge) and philosophy of mind)
Worked through or solved by a person using calculation, logic, or other mental/computational methods—even with unlimited time and effort.
proof(Frege's formal system; the definition still used by logicians today)
Any finite sequence of statements such that each statement is either an axiom of the formal system or follows from previous members of the sequence by a valid rule of inference.
refutation(SR 6 168a37)
A proof of the contradictory of the thesis maintained by the answerer
(That is—with ‘2^\(n\)’ representing ‘2 to the power \(n\)’—‘[2^(2^(2^(2^(2^2))))]\(+1\) is prime’; cf. Tennant, 1997 p. 152.) They cannot deny the sentence exists, for there is the token before our very eyes. But there are strong grounds for thinking that no concrete proof or disproof will exist, for the only methods available may use up more time, space and material than any human could have at her disposal, perhaps than actually exists. There are countless sentences with this property: concre