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 ω-inconsistent; that a sound finitary interpretation of PA is definable in terms of Turing-computability; and that PA cannot be consistently extended to ZF. 1 Preamble: ...

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 ω-inconsistent; that a sound finitary interpretation of PA is definable in terms of Turing-computability; and that PA cannot be consistently extended to ZF. 1 Preamble: ...

In the last decade, with the publication of his Complete Works, there has been renewed interest in Walras’s methodology, mostly in the French economic literature. In particular, some scholars have argued that Walras characteristically confused positive and normative statements, a mistake all the more surprising given his impressive knowledge of philosophy (the so-called ‘Walras paradox’). This ...

Much of Mathematics, and therefore Physics as well, have been limited by four rather consequential restrictions. Two of them are ancient taboos, one is an ancient and no longer felt as such bondage, and the fourth is a surprising omission in Algebra. The paper brings to the attention of those interested these four restrictions, as well as the fact that each of them has by now ways, even if hard...

In this paper, we discuss a well-known self-referential paradox in foundational game theory, the Brandenburger Keisler paradox. We approach the paradox from two different perspectives: non-well-founded set theory and paraconsistent logic. We show that the paradox persists in both frameworks for category theoretical reasons, but, with different properties.

Proponents of “truth-value glut” responses to the paradoxes of selfreference, such as Priest [7, 8] argue that “truth-value gap” analyses of the paradoxes fall foul of the strengthened liar paradox: “this sentence is not true.” If we pay attention to the role of assertion and denial and the behaviour of negation in both “gap” and “glut” analyses, we see that the situation with these approaches ...