Related papers: Metaphysics in Mathematics
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…
Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational…
This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
The philosophical foundations of statistics involve issues in theoretical statistics, such as goals and methods to meet these goals, and interpretation of the meaning of inference using statistics. They are related to the philosophy of…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…
Mathematical physics has many facets, of which we shall briefly give a (very partial) description, centered around those of main interest for Elliott and us (Moshe Flato and I). In our case these aspects had as a corollary a variety of…
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already…
Our primary purpose is to isolate the abstract, mathematical properties of circuits -- both classical Boolean circuits and quantum circuits -- that are essential for their computational interpretation. A secondary purpose is to clarify the…
In this essay we describe a platonic metaphysics where time is a fundamental idea such that the passage of time is independent of observers and the laws of physics. Furthermore, time serves to distinguish between a real and an abstract…
The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…
I argue that Immanuel Kant's critical philosophy -- in particular the doctrine of transcendental idealism which grounds it -- is best understood as an `epistemic' or `metaphilosophical' doctrine. As such it aims to show how one may engage…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
Various 'optimistic' attempts have been made to reasonably explain the undeniable effectiveness of mathematics in its application to physics. They range over retrospective, historical accounts of mathematical applicability based on…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
The mathematical study of infinity seems to have the ability to transport the mind to lofty and unusual realms. Decades ago, I was transported in this way by Rudy Rucker's book Infinity and the Mind. Despite much subsequent learning and…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
This soliloquy outlines some naive philosophical arguments underlying the thesis that mathematics ought to be viewed simply as a universal set of languages, some of precise expression, and some of effective communication.