Related papers: The fourth Dimension
Logicians study and apply a multiplicity of various logical systems. Consequently, there is necessity to build foundations and common grounds for all these systems. This is done in metalogic. Like metamathematics studies formalized…
A system's apparent simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and…
This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
In order to legitimate and defend democratic politics under conditions of computational capital, my aim is to contribute a notion of what I am calling explanatory publics. I will explore what is at stake when we question the social and…
Transparency is a fundamental requirement for decision making systems when these should be deployed in the real world. It is usually achieved by providing explanations of the system's behavior. A prominent and intuitive type of explanations…
The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the…
The hypothesis that philosophy is driven by difference/innovation is checked in a quantitative manner. This was performed by assigning grades to eight main philosophical features with respect to seven prominent philosophers, which allowed…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
The aim of this paper is to show that Plato's theory of knowledge of Forms (intelligible Beings, Ideas) in the Sophistes, obtained by Division and Collection, is a close philosophic analogue of the geometric theory of periodic…
This is a philosophy-intense physics article, or, if you wish, a physics-intense philosophy article. Also, being a mathematician, I tend to view the physics, in particular the essence of quantum physics, in emphasizing the mathematical…
What is the "right way" to define dimension? Mathematicians working in the early and middle $20$th-century formalized three intuitive definitions of dimension that all turned out to be equivalent on separable metric spaces. But were these…
In this paper, we show how regular convex 4-polytopes - the analogues of the Platonic solids in four dimensions - can be constructed from three-dimensional considerations concerning the Platonic solids alone. Via the Cartan-Dieudonne…
When various observers obtain information in an independent fashion about a classical system, there is a simple rule which allows them to pool their knowledge, and this requires only the states-of-knowledge of the respective observers. Here…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
The tremendous popular success of Chaos Theory shares some common points with the not less fortunate Relativity: they both rely on a misunderstanding. Indeed, ironically , the scientific meaning of these terms for mathematicians and…
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.
Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…