It is usually supposed that, with his dichotomy paradox, Zeno gave birth to the modern so-called supertask debate – the debate of whether carrying out an infinite sequence of actions or operations...

The standard coordinate-based formulation of the space-time theory of special relativity (Minkowski geometry) is philosophically unsatisfactory for various reasons. We here present an explicit axiomatic formulation of that theory in terms of primitives with a definitive physical interpretation, prove its equivalence to the standard coordinate formulation, and draw various philosophical conclusions concerning the physical content and assumptions of the space-time theory. The prevalent causal interpretation of physical Minkowski geometry deriving from Reichenbach is criticised on the basis of the present formulation.

We suggest that, far from establishing an inconsistency in the standard theory of the geometrical linear continuum, Zeno’s Paradox of Extension merely establishes an inconsistency between the standard theory of geometrical magnitude and a misguided system of length measurement. We further suggest that our resolution of Zeno’s paradox is superior to Adolf Grünbaum’s now standard resolution based on Lebesgue measure theory.

This paper examines three cases of the clash between science and philosophy: Zeno’s paradoxes, the Frame Problem, and a recent attempt to experimentally refute skepticism. In all three cases, the relevant science claims to have resolved the purported problem. The sciences, construing the term broadly, are mathematics, artificial intelligence, and psychology. The goal of this paper is to show that none of the three scientific solutions work. The three philosophical problems remain as vibrant as ever in the face of robust (...) scientific attempts to dispel them. The paper concludes by examining some consequences of this persistence. (shrink)

In this paper, we address an infamous argument against divisibility that dates back to Zeno. There has been an incredible amount of discussion on how to understand the critical notions of divisibility, extension, and infinite divisibility that are crucial for the very formulation of the argument. The paper provides new and rigorous definitions of those notions using the formal theories of parthood and location. Also, it provides a new solution to the paradox of divisibility which does not face some threats (...) that can possibly undermine the standard Lebesgue measure solution to such a paradox. (shrink)