Related papers: Reductionism and the Universal Calculus
Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of…
I argue that European schools of thought on memory and memorization were critical in enabling the growth of the scientific method. After giving a historical overview of the development of the memory arts from ancient Greece through 17th…
We demonstrate that the system of fine-tuning constraints for life is, in a sense, overdetermined: the a priori probability of its feasibility is extremely low, especially in the chemical sector. This entails that the structure of the…
This article analyses some paragraphs of the Dissertatio de Arte Combinatoria (1666) where G.W. Leibniz considers the syntax of a language with a given number of primitive terms. We propose a new formulation which generalizes the…
Many physicists, following Einstein, believe that the ultimate aim of theoretical physics is to find a unified theory of all interactions which would not depend on any free dimensionless constant, i.e., a dimensionless constant that is only…
We investigate the structure common to causal theories that attempt to explain a (part of) the world. Causality implies conservation of identity, itself a far from simple notion. It imposes strong demands on the universalizing power of the…
Czachor's recent proposal introduces a form of non-Newtonian calculus built by pulling back arithmetic operations through arbitrary bijections between continua. Although the idea is mathematically inventive, it runs into serious conceptual…
At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has…
Reductionism has dominated science and philosophy for centuries. Complexity has recently shown that interactions---which reductionism neglects---are relevant for understanding phenomena. When interactions are considered, reductionism…
The comments relate to the often overlooked, if not in fact intentionally disregarded depths of what the so called internal aspects of mathematical knowledge may involve, depths concerning among others issues such as its unreasonable…
Dealing with Eugene Wigner's ideas on the measurement procedure in quantum physics and unearthing the controversy that pitted him against supporters of the interpretation of complementarity, I will show how Wigner and his followers…
Leibniz's mathematical texts are a perfect example of a type of historical document that is extremely difficult to deal with in the context of an editorial enterprise: the draft. The tables in Leibniz's mathematical manuscripts are a…
In this paper, we discuss the role of Mathematics in articulating reality in theoretical Physics. We propose a parallel between empirical and theoretical work and investigate how scientists can also speak about reality without performing…
The universal object oriented languages made programming more simple and efficient. In the article is considered possibilities of using similar methods in computer algebra. A clear and powerful universal language is useful if particular…
The Wigner's Friend thought experiment stands as one of the most intellectually provocative and challenging conceptual puzzles in quantum mechanics. It compels us to confront profound questions concerning the fundamental nature of reality,…
In this paper a novel calculus system has been established based on the concept of 'werden'. The basis of logic self-contraction of the theories on current calculus was shown. Mistakes and defects in the structure and meaning of the…
This article discusses the relationship between emergence and reductionism from the perspective of a condensed matter physicist. Reductionism and emergence play an intertwined role in the everyday life of the physicist, yet we rarely stop…
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…
We explore Leibniz's understanding of the differential calculus, and argue that his methods were more coherent than is generally recognized. The foundations of the historical infinitesimal calculus of Newton and Leibniz have been a target…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…