General Mathematics

    

The Intuitive Root of Classical Logic, an Associated Decision Problem and the Middle Way

Authors: Abhishek Majhi

We revisit Boole's reasoning regarding the equation ``$x.x=x$'' that sowed the seeds of classical logic. We discuss how he considered both ``$0.0=0$'' and ``$0.0\neq 0$'' in the ``same process of reasoning''. This can either be seen as a contradiction, or it can be seen as a situation where Boole could not decide whether ``$0.0=0$'' is universally valid -- an elementary ``decision problem'' in the words of Hilbert and Ackermann. We conclude that Boole's reasoning, that included a choice of ignorance, was founded upon the middle way of the Buddha, later mastered by Nagarjuna. From the modern standpoint, the situation can be likened to Turing's halting problem which resulted from the use of automatic machines and the exclusion of choice machines.

Comments: 4 Pages.

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[v1] 2022-06-18 12:27:12

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