The significance of Nathanson's 'boss' factor in legitimising Aristotle's particularisation: Why we need to revise current interpretations of Cantor's, Goedel's, Turing's and Tarski's formal reasoning

Abstract

I show--contrary to common beliefs tolerated by the 'bosses'--that any interpretation of ZF that admits Aristotle's particularisation is not sound; that the standard interpretation of PA is not sound; that PA is consistent but omega-inconsistent; that a sound finitary interpretation of PA is definable in terms of Turing-computability; and that PA cannot be consistently extended to ZF.