The assumption of Boolean algebra demands the paradox. However, every possible sequence of ones and zeros isn’t paradoxical. The synthesis of these two truisms will revolutionize logic. Moreover, language will be able to speak the impossible, unlimited from what we thought was every possible sentence.
Note that this phrasing doesn’t necessitate use of Gödel numbers.
Infinite language – Part 2 of 2
Earlier: Infinite Language
According to Boolean algebra, the paradox is both real and cannot be mapped to a Gödel number.
A sequence of ones and zeros constitutes a computer program. To assign indices to different sequences of ones and zeros would be possible. Those indices would then be equivalent to Gödel numbers. Those collective Gödel numbers would compose a traditional logical positivist framework. Paradoxes occur outside the limits of that mapping.
Infinite language – Part 1 of 2
Later: Infinite Language Continued