相关论文: How the continuum hypothesis could have been a fun…
A tradition handed down among physicists maintains that classical physics is a perfectly deterministic theory capable of predicting the future with absolute certainty, independently of any interpretations. It also tells that it was quantum…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes "convincing evidence?" I will argue that, given the types of evidence that are currently…
The ongoing progress in quantum theory emphasizes the crucial role of the very basic principles of quantum theory. However, this is not properly followed in teaching quantum mechanics on the graduate and undergraduate levels of physics…
In view of the enormous difficulties we seem to face in quantizing general relativity, we should perhaps consider the possibility that gravity is a fundamentally classical interaction. Theoretical arguments against such mixed…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
We introduce neutrosophic choice functions, the neutrosophic counterpart of the Axiom of Choice, prove some results, and discuss how it effects the foundations of mathematics in a neutrosophic setting.
Abel's continuity theorem for power series is a great tool to compute sums and prove properties of special functions. However, apart from two basic examples, this no longer occupies a place in Analysis courses. This note is an invitation to…
The example of the calculus is used to explain how simple, practical math was made enormously complex by imposing on it the Western religiously-colored notion of mathematics as "perfect". We describe a pedagogical experiment to make math…
This thesis develops the theory of effectuses as a categorical axiomatic approach to quantum theory. It provides a comprehensive introduction to effectus theory and reveals its connections with various other topics and approaches.
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these…
This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.…
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all…
The cultural infrastructure that let Galileo invent the modern physics is discussed. The key new element of modern physics was firm belief in its fundamental structure, which could be expressed in the double postulate: 1) There are…
Remarks on mathematical proof and the practice of mathematics.
We consider fundamental physical constants which are among a few of the most important pieces of information we have learned about Nature after its intensive centuries-long studies. We discuss their multifunctional role in modern physics…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between…