I am reformulating the generic notions of {**Truth**} and {**formal provability**} from scratch. I cannot use the conventional terms of the art with their conventional meanings because these terms of the art have fundamental misconceptions built in to their definitions.

These conventional terms of the art are defined in terms of other conventional terms of the art and these terms also have fundamental misconceptions built in to their definitions, on and on.

My system analyzes specific instances the generic notion of finite strings of characters to determine if these finite strings correspond to the generic notion of {**Truth**}.

The generic notion of {**formal provability**} simply examines whether or not a specific preexisting set of finite string transformation rules allow one finite string to be derived from another. In the case where the first finite string has the Boolean property of True, then the derived finite string is also known to have this same Boolean property.

The set of finite string transformation rules includes a set of finite strings that have been defined to have the Boolean property of True. This corresponds to notion of Prolog Facts. From the Fact that “a can is made of tin” we can derive the fact that “a can is made of metal”.

The above systematic reconstruction of the notions of {**Truth**} and {**formal provability**} are applied to the following of specific concrete examples. The essence of these examples are reformalized and analyzed for logical coherence within a new formal system.

The Liar Paradox from antiquity

David Hilbert’s 1928 Entscheidungsproblem

Kurt Gödel’s 1931 incompleteness Theorem

Alfred Tarski’s 1936 Undefinability Theorem

Alan Turing’s 1937 Halting Problem