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

TL;DR

This paper challenges common beliefs by showing that interpretations of ZF and PA admitting Aristotle's particularisation are unsound, and that PA is omega-inconsistent, redefining foundational understanding of formal reasoning in mathematics.

Contribution

It revises the interpretation of ZF and PA, demonstrating their unsoundness and omega-inconsistency, and links finitary interpretations to Turing-computability.

Findings

Interpretations of ZF admitting Aristotle's particularisation are unsound.

Standard interpretation of PA is not sound.

PA is consistent but omega-inconsistent.

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.