Why “new terms”? If the language can finitely express a concept, my scheme gives that concept plausibility. Maybe this could be extended to lengths of programs that generate axioms for a given theory (even enumerable sets of axioms), rather than lengths of individual finite statements, but I guess that can be stated within some logical language just as well.
By new “term” I meant to make the clear that this statement points to an operation that cannot be done with the original machine. Instead it calls this new module (say a halting oracle) that didn’t exist originally.
Why “new terms”? If the language can finitely express a concept, my scheme gives that concept plausibility. Maybe this could be extended to lengths of programs that generate axioms for a given theory (even enumerable sets of axioms), rather than lengths of individual finite statements, but I guess that can be stated within some logical language just as well.
By new “term” I meant to make the clear that this statement points to an operation that cannot be done with the original machine. Instead it calls this new module (say a halting oracle) that didn’t exist originally.
What machine???