A Purely Arithmetical, yet Empirically Falsifiable, Interpretation of Plotinus’ Theory of Matter

There is a vast literature where Gödel’s first and second incompleteness theorems are used to argue that human beings are different of, if not superior to, any machine. The most famous attempts have been given by J. Lucas in the early sixties and by R. Penrose in two famous books [53, 54]. Such type of argument are not well supported. See for example the recent book by T. Franzèn [21]. There is also a less well known tradition where Gödel’s theorems is used in favor of the mechanist thesis. Emil Post, in a remarkable anticipation written about ten years before Gödel published his incompleteness theorems, already discovered both the main “Gödelian motivation” against mechanism, and the main pitfall of such argumentations [17, 55]. Post is the first discoverer of Church Thesis, or Church Turing Thesis, and Post is the first one to prove the first incompleteness theorem from a statement equivalent to Church thesis, i.e. the existence of a universal—Post said “complete”—normal (production) system. In his anticipation, Post concluded at first that the mathematician’s mind or that the logical process is essentially creative. He adds :