I don’t understand your notation. You have a disjunction of a formula and its negation, which is tautologically true, hence the whole statement is tautologically false.
P is a program; what meaning is intended by the predicate P(M,i)? In fact, what work is the object P doing in that formula? A Turing machine M is given an input string i; there is no other “program” involved.
I don’t understand your notation. You have a disjunction of a formula and its negation, which is tautologically true, hence the whole statement is tautologically false.
P is a program; what meaning is intended by the predicate P(M,i)? In fact, what work is the object P doing in that formula? A Turing machine M is given an input string i; there is no other “program” involved.