Related papers: Ren{\'e} Thom: From mathematics to philosophy
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…
Three thinkers of the 19th century revolutionized the science of logic, mathematics, and philosophy. Edmund Husserl (1859-1938), mathematician and a disciple of Karl Weierstrass, made an immense contribution to the theory of human thought.…
This paper proposes critical pragmatism as a philosophy of sustainable mathematics education to bridge the gap between critical theory and the existing patchwork implementations. Combining existential sustainability as a holistic concept…
A century ago, John Dewey observed that '[s]team and electricity have done more to alter the conditions under which men associate together than all the agencies which affected human relationships before our time'. In the last few decades,…
This paper deals with the ways that the issue of completing quantum mechanics was brought into laboratories and became a topic in mainstream quantum optics. It focuses on the period between 1965, when Bell published what now we call Bell's…
From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a…
Plato is well-known in mathematics for the eponymous foundational philosophy Platonism based on ideal objects. Plato's allegory of the cave provides a powerful visual illustration of the idea that we only have access to shadows or…
The novelty of the Jean Pierre Badiali last scientific works stems to a quantum approach based on both (i) a return to the notion of trajectories (Feynman paths) and (ii) an irreversibility of the quantum transitions. These iconoclastic…
This chapter takes a historical view of the development of mathematics education, from its initial status as a business mostly managed by mathematicians to the birth of mathematics education as a scientific field of research. Starting from…
We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian…
What are the effects of authoritarian regimes on scholarly research in economics? And how might economic theory survive ideological pressures? The article addresses these questions by focusing on the mathematization of economics over the…
Aristotelian logic and its related traditions in antiquity are often held to have been equivalent to monadic predicate logic and as such inadequate to formalize mathematics as well as scientific and philosophical discourse in general. In…
In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the…
I provide a critical commentary regarding the attitude of the logician and the philosopher towards the physicist and physics. The commentary is intended to showcase how a general change in attitude towards making scientific inquiries can be…
In the seminal essay, "On the unreasonable effectiveness of mathematics in the physical sciences," physicist Eugene Wigner poses a fundamental philosophical question concerning the relationship between a physical system and our capacity to…
The philosophy of science is a discipline concerning the metaphysical aspect of science. Recently, I proposed measurement theory, which is characterized as the metaphysical and linguistic interpretation of quantum mechanics. I assert that…
In this essay we examine some aspects of the classical theory of definition as codified in Aristotle's \emph{Topics} and Porphyry's \emph{Eisagog\^e} in the light of the way definition is carried out in modern mathematical practice. Our…
Philosophical thinking has a side effect: by aiming to find the essence of a diverse set of phenomena, it often makes it difficult to see the differences between them. This can be the case with Mathematics, Programming, Writing and…
In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the…
In this essay we give a general picture about the evolution of Grohendieck's ideas regarding the notion of space. Starting with his fundamental work in algebraic geometry, where he introduces schemes and toposes as generalizations of…