Eliminating Undecidability in Formal Systems

When the conventional way that formal systems are defined is considered a necessary truth rather than merely a set of basic assumptions anything that is said from the perspective of philosophy of logic alternatives to these basic assumptions would be be misconstrued as erroneous.

Very slight changes can be made to the way that formal systems are defined eliminating undecidability in all of these formal systems. The key change is that undecidable sentences are decided to have a truth value of ~True.

The remaining sentences are True based on their provability or False based on the provability of their negation. By provability it is meant that these expressions are theorems on the basis of their having a empty sets of premises.

Tarski “proved” that there cannot possibly be any correct formalization of the notion of truth entirely on the basis of an insufficiently expressive formal system that was incapable of recognizing and rejecting semantically incorrect expressions of language.