It's possible, if not provable.
But the future is unknowable, and his extrapolations are, if not provable, at least plausible.
The assassination of Dr. King, too, has been surrounded by theories which, if not provable, are not quite disprovable.
However, neither SKK ≥ SK KK) nor SK KK) ≥ SKK is provable in CL≥; a fortiori, the equality of the two terms in not provable in CL=.
Thus, it can be shown, even inside F, that GF is true if and only if it is not provable in F. It is not difficult to show that GF is neither provable nor disprovable in F, if F only is 1-consistent.
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.
If this principle is not provable, there are no incontrovertible propositions and the goal of gnoseology will not be reached.
In sum, if F is consistent, then GF is not provable in F. For this first half, the assumption of the simple consistency of F suffices.
Residents-only policies, redolent of gated communities, are disturbingly undemocratic and too often have the effect, if not the provable intent, of excluding minorities and the poor.
The proof of this theorem consists essentially of a formalization in arithmetic of the arithmetized version of the proof of the statement, "If a system is consistent, then p is not provable"; i.e., it consists of a derivation within number theory of p itself from the arithmetic sentence that says that the system is consistent.
Then he added: "It would not surprise me if they came up with some information that is not provable, and they've shifted.
