August 23, 2023
actual infinity, discrete solution of Zeno's Contradiction, dense order, discrete space and time, finiteness of the speed of light, foundation of physics, power of the continuum, spacetime continuum, Zeno's Contradiction, Zeno's Dichotomy, Zeno's Paradoxe
A photon replaces Achilles and the Tortoise in a variant of the famous Zeno's paradox discussed in this paper. The discussion takes place in the infinitist scenario of the spacetime continuum. In this theoretical scenario, and thanks to the dense order of real numbers, the paradox becomes first a dichotomy and then a contradiction, of which there are only two coherent solutions: either the speed of light is not finite, or the Hypothesis of the Actual Infinity is not consistent. An inconsistency that would change almost everything in modern mathematics and then in the formal foundation of modern physics. The article ends by pointing to a new finite and discrete scenario for space and time in which this and many other contradictions and paradoxes dissolve immediately. But it also warns of the extraordinary difficulties that will be involved in exchanging the hegemonic infinitist paradigm of our days for an alternative based on the finitist discreteness of space and time.