Indeterminism in Physics and Intuitionistic Mathematics

Indeterministic finite-precision physics and intuitionistic mathematics

In recent publications in physics and mathematics, concerns have been raised about the use of real numbers to describe quantities in physics, and in particular about the usual assumption that physical quantities are infinitely precise. In this thesis, we discuss some motivations for dropping this assumption, which we believe partly arises from the usual point-based approach to the mathematical continuum. We focus on the case of classical mechanics specifically, but the ideas could be extended to other theories as well. We analyse the alternative theory of classical mechanics presented by Gisin…

Classical and intuitionistic mathematical languages shape our understanding of time in physics

Physics is formulated in terms of timeless classical mathematics. A formulation on the basis of intuitionist mathematics, built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality.

Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real?

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can't contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is ``random numbers'', as their series of bits are truly random. I propose an alternative classical mechanics, which is empirically equivalent to classical mechanics, but uses only finite-info…

How Free Will Could Will

Many have proposed that free will would use quantum indeterminism. Strict adherence to the Born rule, which follows from the no-signal condition, seems to block this possibility. I propose here that if state collapse really does occur then there is a further form of indeterminism occurring in multipartite systems in that the basis upon which the collapse is to occur could be ambiguous. The choice of this basis is not covered by quantum mechanics nor subject to probability constraints and this provides a ground for a physical and eventually a mathematical model of free will.

决定论与非决定论作为模型艺术品：迈向物理的模型不变本体论

Determinism and Indeterminism as Model Artefacts: Toward a Model-Invariant Ontology of Physics

本文提出一种基于模型不变性的现实主义本体论，通过区分模型不变结构与建模惯例，解释物理基础问题的根源。

物理、数学、逻辑和哲学中的创造性时间和几何时间

Creative and geometric times in physics, mathematics, logic, and philosophy

本文区分了物理中的几何时间和创造性时间，探讨了它们在数学、逻辑及哲学中的应用及意义。