Programs as the Language of Science (1811.05116v2)

Abstract: Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be implemented in the sciences is outlined in some detail. We start by constructing a simple formal system where statements are represented as programs and inference is based on computability as opposed to the classical notion of truth value assignments. The focus is on theories where the intrinsic properties and dynamic state of real world objects can be defined in terms of information and subject to laws based on simple deterministic rules and finite state arithmetic. Such models, it is argued, not only offer alternative simulation tools, as opposed to those based on discrete approximations of conventional continuum theories, but in themselves can be regarded as a language that describes the physical laws at a fundamental level. This book does not examine any specific application in detail but rather attempts to lay down a foundation for the validation of such theories by employing the inference scheme based on computability logic.