Related papers: Atomism Axiomatised Using Mereological Composition…
The interpretation of quantum theory known as QBism argues that many elements of the formalism have a subjective interpretation. At the same time, QBism claims to be a broadly realist program. This implies that reality in QBism must be…
The dual nature of matter and radiation and the concept of the structure of an atom share a number of key conceptual elements from quantum mechanics. Despite the similarities, we find that the concept of the structure of an atom is well…
This paper introduces a new representation method that is mainly based on chemical bonds among atoms in materials. Each chemical bond and its surrounded atoms are considered as a unified unit or a local structure that is expected to reflect…
To constitute atoms of a $\sigma$ algebra is not a easy task due to the large number of its elements. However, determining them via generators seems a feasible and simple way since most $\sigma$ algebras are generated by their smaller…
We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum…
We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure $M$. We prove that if $T$ is a complete $L$-theory, then $T$ is mutually algebraic if and only if there is some model $M$ of $T$ for…
A re-construction of the fundamentals of programming as a small mathematical theory (PRISM) based on elementary set theory. Highlights: $\bullet$ Zero axioms. No properties are assumed, all are proved (from standard set theory). $\bullet$ A…
The usual formulation of quantum theory is rather abstract. In recent work I have shown that we can, nevertheless, obtain quantum theory from five reasonable axioms. Four of these axioms are obviously consistent with both classical…
In this work, we attempt to define a notion of compositeness compatible with Quantum Field Theory. Considering the analytic properties of the S-matrix, we conclude that there is no satisfactory definition of compositeness compatible with…
Elementary particles are found in two different situations: (i) bound to metastable states of matter, for which angular momentum is quantized, and (ii) free, for which, due to their high energy-momentum and leaving aside inner a.m. or spin,…
Mereology in its formal guise is usually couched in a language whose signature contains only one primitive binary predicate symbol representing the part of relation, either the proper or improper one. In this paper, we put forward an…
There are investigated the generalized methods of cognition of the Existing, i.e. everything that is able to influence to the cognizer, and everything differed from the Existing is postulated as indistinguishable from the non-existing and…
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
The emergence of an objective reality in line with the laws of the microscopic world has been the focus of longstanding debates. Recent approaches seem to have reached a consensus at least with respect to one aspect, namely, that the…
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently…
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
We introduce and investigate the category $\mathsf{AtoMon}$ of atomic monoids and atom-preserving monoid homomorphisms, which is a (non-full) subcategory of the usual category of monoids. In particular, we compute all limits and colimits,…