The intuitive root of classical logic, an associated decision problem and the middle way

Abhishek Majhi (1)

1 Indian Statistical Institute [Kolkata]

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 = 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.

Domaines: Mathématiques [math]

Abhishek Majhi. The intuitive root of classical logic, an associated decision problem and the middle way. 2022. ⟨hal-03587270⟩