Post by peteolcott
Direct quote from page 275
It is not true that x ∈ Pr if and only if p
(1) x ∉ Pr ↔ p
Where the symbol 'p' represents the whole sentence x.
p ∉ Pr ↔ p
p ∉ Provable ↔ p
p ↔ ~Provable(p)
Copyright 2018 Pete Olcott
Does anyone here have more than a dogmatic belief in the following?
A. For every formalized language a formally correct and materially
adequate definition of true sentence can be constructed in the
metalanguage with the help only of general logical expressions, of
expressions of the language itself, and of terms from the morphology
of language – but under the condition that the metalanguage possesses
a higher order than the language which is the object of investigation.
B. If the order of the metalanguage is at most equal to that of the
language itself, such a definition cannot be constructed.
I propose that any reasoning that attempts to show the above referenced
Truth predicate cannot be implemented directly in the object language is
incorrect. If anyone knows this material well enough to try to show that
the metalanguage / object language distinction is required I will point
out their error.