Aristotelian realist philosophy of mathematics

Teach Astronomy - Revolutions in Science and the Arts

http://www.teachastronomy.com/ Too often science is treated in isolation from other human pursuits. However the broad history of ideas from the time of Copernicus to the time of Newton parallels a similar evolution in the arts in Europe at that time period. The popular cliché goes that s

From playlist 03. Concepts and History of Astronomy and Physics

Problems with the Calculus | Math History | NJ Wildberger

We discuss some of the controversy and debate generated by the 17th century work on Calculus. Newton and Leibniz's ideas were not universally accepted as making sense, despite the impressive, even spectacular achievements that the new theory was able to demonstrate. In this lecture we di

From playlist MathHistory: A course in the History of Mathematics

Quantum Mechanics -- a Primer for Mathematicians

Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w

From playlist Mathematics

Logic: The Structure of Reason

As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be

From playlist Logic & Philosophy of Mathematics

Algebraic number theory and rings I | Math History | NJ Wildberger

In the 19th century, algebraists started to look at extension fields of the rational numbers as new domains for doing arithmetic. In this way the notion of an abstract ring was born, through the more concrete examples of rings of algebraic integers in number fields. Key examples include

From playlist MathHistory: A course in the History of Mathematics

Richard Rorty on Pan-Relationalism (1996)

Richard Rorty doing what he does. #Philosophy #Rorty #Pragmatism

From playlist Richard Rorty

3.13 EXTRA: A Brief History of Ontology

From playlist Knowledge Engineering with Semantic Web Technologies by Dr. Harald Sack

Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger

The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon

From playlist Math Foundations

Infinity: does it exist?? A debate with James Franklin and N J Wildberger

Infinity has long been a contentious issue in mathematics, and in philosophy. Does it exist? How can we know? What about our computers, that only work with finite objects and procedures? Doesn't mathematics require infinite sets to establish analysis? What about different approaches to the

From playlist Pure seminars

4: Introduction to Philosophy of Engineering I

MIT ESD.932 Engineering Ethics, Spring 2006 Instructor: Prof. Joel Moses View the complete course: https://ocw.mit.edu/courses/esd-932-engineering-ethics-spring-2006/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61YF5HCMnGUwJ8D-PNNs3OR This course introduces the theo

From playlist MIT ESD.932 Engineering Ethics, Spring 2006

Infinity: does it exist?? A debate with James Franklin and N J Wildberger

Infinity has long been a contentious issue in mathematics, and in philosophy. Does it exist? How can we know? What about our computers, that only work with finite objects and procedures? Doesn't mathematics require infinite sets to establish analysis? What about different approaches to the

From playlist MathSeminars

Numbers, the universe and complexity beyond us | Data structures Math Foundations 177

In mathematics, we want to write things down. That way we can check what we are actually talking about. Other people can look at it, and assess whether it makes sense or not. We can more easily compare what we are thinking about with other, perhaps related concepts/objects/patterns. But w

From playlist Math Foundations

Number theory and algebra in Asia (a) | Math History | NJ Wildberger

After the later Alexandrian mathematicians Ptolemy and Diophantus, Greek mathematics went into decline and the focus shifted eastward. This lecture discusses some aspects of Chinese, Indian and Arab mathematics, in particular the interest in number theory: Pell's equation, the Chinese rema

From playlist MathHistory: A course in the History of Mathematics

Number theory Full Course [A to Z]

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio

From playlist Number Theory

On Faith and Reason: Fides et Ratio by Pope St. John Paul II

In this first episode of this podcast series, Classical Theist and I will discuss the papal encyclical "Fides et Ratio" written by Pope St. John Paul II in 1998. "Fides et Ratio": http://w2.vatican.va/content/john-paul-ii/en/encyclicals/documents/hf_jp-ii_enc_14091998_fides-et-ratio.html

From playlist Philosophy/theology podcast

Number theory and algebra in Asia (b) | Math History | NJ Wildberger

After the later Alexandrian mathematicians Ptolemy and Diophantus, Greek mathematics went into decline and the focus shifted eastward. This lecture discusses some aspects of Chinese, Indian and Arab mathematics, in particular the interest in number theory (Pell's equation, the Chinese rema

From playlist MathHistory: A course in the History of Mathematics

God, Science, and Epistemology - A Conversation with Quentin Lee (Theism vs. Atheism)

Quentin Lee and I talk about epistemology, philosophy of science, and theology. To get in touch: Email: mathoma1517@gmail.com Twitter: @Math_oma Stuff mentioned in discussion: 1. "Five Proofs of the Existence of God" by Edward Feser: https://www.amazon.com/Five-Proofs-Existence-Edward-F

From playlist Conversations

1 The "Representational" Theory of Knowledge - Reid's Critique of Hume (Dan Robinson)

Professor Dan Robinson gives the first in a series of 8 lectures on Thomas Reid's critique of David Hume at Oxford in 2014. Hume defends the thesis according to which “ALL THE PERCEPTIONS OF THE HUMAN MIND RESOLVE THEMSELVES INTO…IMPRESSIONS AND IDEAS”. Accordingly, “We may prosecute this

From playlist Philosophy of Mind

Modern "Set Theory" - is it a religious belief system? | Set Theory Math Foundations 250

Modern pure mathematics suffers from a uniform disinterest in examining the foundations of the subject carefully and objectively. The current belief system that "mathematics is based on set theory" is quite misguided, and in its current form represents an abdication of our responsibility t

From playlist Math Foundations