3A Processual Effectiveness

To show the difference between an ontological-definitorial perspective and an effective-processual approach, it is best to start from a simple example, itself derived from modal logic.

Time travel poses formidable problems in logic. It is 1967. Suppose a Londoner hates Hitler and has a time machine. They travel back to Austria in the 1920s and kills him before he has committed his terrible deeds. However, this person did not know that their parents had met during the London bombings in 1940. Since Hitler was killed before this, the person’s parents do not meet, the person is not born and Hitler is not killed before committing his misdeeds. So, the bombings take place, the parents meet and the person is born, and in 1967 they can take the time machine back to kill the young Hitler… This paradox can be expressed in formal terms, but also, more simply, in natural language: “If Hitler is murdered, then he is not; and if he is not murdered, he is”1. [GIR 00, p. 139]. It seems that there is, therefore, a logical contradiction, translated into a temporal circle.

Why is that which is a contradiction in the eyes of logicians not also one here according to the effective-processual approach? The logicians spontaneously reason in ontological-definitorial terms: there is a (necessary) logical sequence of events. They follow a grid that has its fixity, the same causes automatically leading to the same effects. We are therefore faced with two contradictory sequences ...

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