Related papers: Set Theory as the Unified Scheme for Physics
Generalization is at the core of machine learning models. However, the definition of generalization is not entirely clear. We employ set theory to introduce the concepts of algorithms, hypotheses, and dataset generalization. We analyze the…
Proposed is system of consistent mathematical models describing physical laws of a system of energy emitting bodies in dynamics, relativity and nuclear physics. It is shown the use of developed models for the description of systems,…
Both relativistic mechanics and Newtonian mechanics are based on principles that have ontological implications. We propose a series of formalisms that rigorously define the ontology underlying mechanical theories, in order to clarify and…
In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be different in that its fundamental theory…
Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic should in general be the logic of subsets of a given universe set. Partitions on…
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…
However, the observations encompassed by classical physics excludes the observer from the physical reality, yet the deep-down understandung of nature --{\it the quantum theory}-- can not avoid the intrusion of observer into the measurement…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…
This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question…
One of the innovative approaches in contemporary philosophical ontology consists in the assumption of a plurality of ontologies based on different metaphysical presuppositions. Such presuppositions involve, among others, the identification…
In this paper the author maintains that the Standard Cosmology is not a Physical Theory. The Standard Cosmology is a narration similar to the historical or mythical narratives constructed from the Physical Sciences data. Also the author…
The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among matter with different levels of hierarchy is appreciated. It is shown that the generic perturbation…
While the relation between visualization and scientific understanding has been a topic of long-standing discussion, recent developments in physics have pushed the boundaries of this debate to new and still unexplored realms. For it is…
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
Imagine a naive organism who does not know anything about the world. It can capture signals through its sensors and it can make actions. What kind of knowledge about the world is accessible to the organism? This situation is analog to that…
Modern cosmology has created a tight link between particle physics / field theory and a wealth of new observational data on the structure of the Universe. These lecture notes focus on some of the most important aspects concerning the…
Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental…
Evidence is growing for the theory of embodied cognition, which posits that action and perception co-determine each other, forming an action-perception loop. This suggests that we humans somehow participate in what we perceive. So, how can…