engleski

Proofs, necessity and causality

There is a long tradition in logic, from Aristotle to Gödel, of understanding a proof from the concepts of necessity and causality. Gödel's attempts to define provability in terms of necessity led him to the distinction of formal and absolute (abstract) provability. Turing's definition of mechanical procedure by means of a Turing machine (TM) and Gödel's definition of a formal system as a mechanical procedure for producing provable formulas prompt us to understand formal provability as a mechanical causality. We propose a formalism which makes explicit the mechanical causal nature of a TM's work. We claim that Gödel's axiomatized ontotheology and his ontological proof give a clue for the understanding of the concept of absolute provability and the pattern of the corresponding absolute completeness proof, respectively.

proof, necessity, causality, Turing machine, justification logic, Gödel

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