Related papers: A formal theory of experimentation

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

A theory of everything should not only tell us the laws for matter, gravity, and possibly boundary condition for the universe. In addition, it should specify the relation between theory and experience. Here I argue for a minimal…

Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications,…

We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.

The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…

Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…

We motivate and describe a theory of belief in this paper. This theory is developed with the following view of human belief in mind. Consider the belief that an event E will occur (or has occurred or is occurring). An agent either…

Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in…

Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for…

There are several theories or processes which may underlie quantum mechanics and make it deterministic. Some references are given in the main text. Any such theory, plus a number of reasonable assumptions, implies the existence of what I…

Theoretical analysis proves that human survivability is dominated by an unusual physical, rather than biological, mechanism, which yields an exact law. The law agrees with all experimental data, but, contrary to existing theories, it is the…

To make precise the sense in which nature fails to respect classical physics, one requires a formal notion of classicality. Ideally, such a notion should be defined operationally, so that it can be subjected to a direct experimental test,…

Inspired by the theory of desirable gambles that is used to model uncertainty in the field of imprecise probabilities, I present a theory of desirable things. Its aim is to model a subject's beliefs about which things are desirable. What…

This is an attempt to formalize the conditions of possibility for free, libre, open access to scientific knowledge within a game. The challenge is to enunciate the terms under which agents participating in the Grand conversation of science…

The long lasting discussion on the completeness of quantum theory (QT) has not yet come to an end. The discussion is impeded by the lack of a clear understanding of what makes up the contents of a theory of physics in general and of QT…

Physics is introduced as a semantics of a formal set theory.

This short note first develops a general formalism for globally removing a factor from an obstruction theory. This formalism is then applied to give a construction of a reduced obstruction theory on the moduli of maps from a curve to a…

We give an elementary introduction to the theory of causal fermion systems, with a focus on the underlying physical ideas and the conceptual and mathematical foundations.

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…

We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…