Foundations of geometry

Aristotle's axiom

Aristotle's axiom is an axiom in the foundations of geometry, proposed by Aristotle in On the Heavens. It states: If is an acute angle and AB is any segment, then there exists a point P on the ray and a point Q on the ray , such that PQ is perpendicular to OX and PQ > AB. (Wikipedia).

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The Logic of Aristotle

Gabriele Giannantoni explains the logic of Aristotle in the context of the history of logic in interview from 1990. These clips are from the Multimedia Encyclopedia of the Philosophical Sciences. The translation is my own. #Philosophy #Aristotle

From playlist Aristotle

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A Dose of Aristotle

A few introductory clips on Aristotle's philosophy which come from a program on classical Greek philosophy in a series on great ideas in philosophy. #Philosophy #Aristotle

From playlist Aristotle

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The History of Logic: The Logic of Aristotle

A few clips of Gabriele Giannantoni explaining Aristotelian logic, the logic of Aristotle. These clips come from the Multimedia Encyclopedia of the Philosophical Sciences. More Short Videos: https://www.youtube.com/playlist?list=PLhP9EhPApKE8v8UVlc7JuuNHwvhkaOvzc Aristotle's Logic: https:

From playlist Logic & Philosophy of Mathematics

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The perfect number of axioms | Axiomatic Set Theory, Section 1.1

In this video we introduce 6 of the axioms of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) The Axiom of Existence: (2:39) The Axiom of Extensionality: (4:20) The Axiom Schema of Comprehension: (6:15) The Axiom of Pair (12:16) The Axiom of Union (15:15) T

From playlist Axiomatic Set Theory

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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

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Zermelo Fraenkel Introduction

This lecture is part of an online course on the Zermelo Fraenkel axioms of set theory. This lecture gives an overview of the axioms, describes the von Neumann hierarchy, and sketches several approaches to interpreting the axioms (Platonism, von Neumann hierarchy, multiverse, formalism, pra

From playlist Zermelo Fraenkel axioms

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PHILOSOPHY - Aristotle

Aristotle was the master of virtues. For gifts and more from The School of Life, visit our online shop: https://goo.gl/OD73do FURTHER READING “Aristotle was born around 384 BC in the ancient Greek kingdom of Macedonia, where his father was the royal doctor. He grew up to be arguably

From playlist WESTERN PHILOSOPHY

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Causality: From Aristotle to Zebrafish - Frederick Eberhardt - 10/16/2019

Earnest C. Watson Lecture by Professor Frederick Eberhardt, "Causality: From Aristotle to Zebrafish." What causes what? If correlation does not equal causation, then how can we untangle the “why” behind processes that regulate the brain, the climate, or the economy? And how does this appl

From playlist Caltech Watson Lecture Series

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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

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Area of a Circle, the BEST COMPLETE PROOF by Archimedes | Tricky Parts of Calculus, Part 3

I give a complete proof that the area of a circle is pi r^2, or 1/2 C r, where C is the circumference, based on the original proof by Archimedes. I also provide some historical notes and commentary on this proof and other proofs. This is the third episode in a series called Tricky Parts o

From playlist Math

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Richard Rorty on Pan-Relationalism (1996)

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

From playlist Richard Rorty

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The Scientific Methods: Crash Course History of Science #14

Historically speaking, there is no one scientific method. There’s more than one way to make knowledge. In this episode we're going to look at a few of those ways and how they became more of the "norm." *** Crash Course is on Patreon! You can support us directly by signing up at http://ww

From playlist Back to School - Expanded

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Late Greeks | History and Philosophy of Astronomy 2.03

Learn about the history and philosophy of astronomy from Professor Impey, a University Distinguished Professor of Astronomy at the University of Arizona, with our Knowing the Universe: History and Philosophy of Astronomy course here on YouTube. This video is part of module 2, Greek Science

From playlist History and Philosophy Course Module 2: Greek Science

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"Counting Past Infinity" in All Spatial Dimensions

In this video, I explain the history behind infinity and briefly cover infinitesimals to construct infinite spatial dimensions. Sometimes I think more about my videos after posting them, these are my Post-Thoughts: * I originally had designed this video as follows: null set = 0th Dimens

From playlist Summer of Math Exposition Youtube Videos

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What's so wrong with the Axiom of Choice ?

One of the Zermelo- Fraenkel axioms, called axiom of choice, is remarkably controversial. It links to linear algebra and several paradoxes- find out what is so strange about it ! (00:22) - Math objects as sets (00:54) - What axioms we use ? (01:30) - Understanding axiom of choice (03:2

From playlist Something you did not know...

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Aristotle's Arguments Against Materialism

A clip of Martha Nussbaum discussing Aristotle's arguments against (reductive) materialism and his view of forms with Bryan Magee in a 1987 program on the Great Philosophers. The full interview can be found here: https://youtu.be/DbTUAqlLlHg #Philosophy #Aristotle #BryanMagee

From playlist Aristotle

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DjangoCon 2019 - Nothingness and identity in Python and Django by Daniele Procida

DjangoCon 2019 - Nothingness and identity in Python and Django by Daniele Procida There’s something rich, beautiful and mysterious in the several kinds of nothingness and identity that we encounter as Django programmers. Understanding the connections they make with ontology, epistemology

From playlist DjangoCon US 2019

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Teach Astronomy - Logic

http://www.teachastronomy.com/ Logic is a fundamental tool of the scientific method. In logic we can combine statements that are made in words or in mathematical symbols to produce concrete and predictable results. Logic is one of the ways that science moves forward. The first ideas of

From playlist 01. Fundamentals of Science and Astronomy

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The Road to Gödel's Incompleteness Theorems - Juliette Kennedy

Friends Lunch with a Member Topic: The Road to Gödel's Incompleteness Theorems Speaker: Juliette Kennedy Date: November 22, 2019

From playlist Friends of the Institute

Related pages

Euclidean geometry | Absolute geometry | Foundations of geometry | Hyperbolic geometry | Lotschnittaxiom | Proclus