Logic of Scientific Discovery: How Physical Induction Affects What Is Computable

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow

Publication Date

3-2014

Comments

Technical Report: UTEP-CS-14-16a

Published in Proceedings of the The International Interdisciplinary Conference Philosophy, Mathematics, Linguistics: Aspects of Interaction 2014 PhML'2014, St. Petersburg, Russia, April 21-25, 2014, pp. 116-127.

Abstract

Most of our knowledge about a physical world comes from physical induction: if a hypothesis is confirmed by a sufficient number of observations, we conclude that this hypothesis is universally true. We show that a natural formalization of this property affects what is computable when processing measurement and observation results, and we explain how this formalization is related to Kolmogorov complexity and randomness. We also consider computational consequences of an alternative idea also coming form physics: that no physical law is absolutely true, that every physical law will sooner or later need to be corrected. It turns out that this alternative approach enables us to use measurement results go beyond what is usually computable.