Systems of set theory | Urelements | Type theory
In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled "New Foundations for Mathematical Logic"; hence the name. Much of this entry discusses NFU, an important variant of NF due to Jensen (1969) and clarified by Holmes (1998). In 1940 and in a revision in 1951, Quine introduced sometimes called "Mathematical Logic" or "ML", that included proper classes as well as sets. New Foundations has a universal set, so it is a non-well-founded set theory. That is to say, it is an axiomatic set theory that allows infinite descending chains of membership, such as… xn ∈ xn-1 ∈ … ∈ x2 ∈ x1. It avoids Russell's paradox by permitting only stratifiable formulas to be defined using the axiom schema of comprehension. For instance, x ∈ y is a stratifiable formula, but x ∈ x is not. (Wikipedia).
A celebration of 200 videos of MathFoundations | Data Structures Math Foundations 201
We have just arrived at the 200 video mark in the MathFoundations series, which aims to promote critical thinking about the foundations of mathematics and suggest new and improved directions for the subject. In this video we have a quick look backward at the series so far, summarize again
From playlist Math Foundations
MF150: What exactly is a set? | Data Structures in Mathematics Math Foundations | NJ Wildberger
What exactly is a set?? This is a crucial question in the modern foundations of mathematics. Here we begin an examination of this thorny issue, first by discussing the usual English usage of the term, as well as alternate terms, such as collection, aggregate, bunch, class, menagerie etc th
From playlist Math Foundations
Numbers as multipliers + particle/antiparticle duality II | Data Structures Math Foundations 211
In this video we introduce the idea of the anti of a mathematical object. This is a crucial, but perhaps surprising, ingredient in a systematic development of multisets as a basis for modern algebra. We are motivated by the remarkable (at least partial) symmetry discovered by 20th centur
From playlist Math Foundations
An introduction to the Tropical calculus | Data Structures in Mathematics Math Foundations 158
We give a short informal introduction to the Tropical calculus, which for us is a novel way of working with the algebra of sets and multisets. This involves defining rather unusual notions of addition and multiplication-- coming from union and addition respectively. **********************
From playlist Math Foundations
A new look at Hindu Arabic numbers and their arithmetic | Data structures in Math Foundations 193
In this video, we extend our vexel approach from binary arithmetic to base ten arithmetic. It may seem surprising that we are obliged to lay a proper foundation for such a familiar arithmetic but if we want to go beyond primitive natural numbers, it is certainly necessary. ***************
From playlist Math Foundations
Arrays and matrices II | Data structures in Mathematics Math Foundations 165
This video introduce matrices, first in a rather familiar fashion coming from linear algebra, and then moving towards a novel approach which is motivated by our study of data structures. Along the way we review some essential facts about linear algebra, matrix algebra and linear transform
From playlist Math Foundations
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
The Hindu Arabic number system revisited | Data Structures in Mathematics Math Foundations 189
When we start getting serious about the foundations of arithmetic, we have to acknowledge the possibility that natural numbers can be defined in intrinsically different ways. The most mathematically fundamental way is the one outlined in the previous videos: natural numbers as msets of mar
From playlist Math Foundations
The law of logical honesty and the end of infinity | Data structures in Math Foundations 178
It is time to end the delusion which pervades modern 20th century style mathematics, and move towards a true mathematics for the new millennium. Infinity needs to go! We need to accept the actual reality of mathematics, rather than some fairy-tale wishful dreaming that allows us to prop
From playlist Math Foundations
Inaugural and Welcome Remarks - 2/23/2015
Welcome remarks provided by: Thomas F. Rosenbaum, Edward M.Stolper, Hirosi Ooguri, and Walter F. Burke III. Learn more about the Inaugural Celebration and Symposium of the Walter Burke Institute for Theoretical Physics: https://burkeinstitute.caltech.edu/workshops/Inaugural_Symposium Pro
From playlist Walter Burke Institute for Theoretical Physics - Dedication and Inaugural Symposium - Feb. 23-24, 2015
Enough Foundations Already! - Simon Phipps
From OSCON 2015 in Amsterdam: In the explosion of new open source software “foundations” there’s a crucial element we’re overlooking; the core principle that got everything started and which is the basis for every developers’ success in a modern business. Before we start another Foundation
From playlist OSCON - Amsterdam 2015
ETHICS in AI? Are there RISKS for us? In Education or Medical treatment?
We look at the US response to Explainable AI (XAI) and Ethics in 2022. Stanford's HAI response on: Explainable AI / Foundation models / Large Language Models - can there be risks for us? A new group assembled by Stanford’s institute for Human-Centered Artificial Intelligence (HAI), called
From playlist Explainable AI (XAI) and Decision Intelligence (DI). Performance on Vision.
From playlist Guest Speakers
Sue Desmond-Hellmann: How Ebola Tested the Bill & Melinda Gates Foundation | Big Think.
Sue Desmond-Hellmann: How Ebola Tested the Bill & Melinda Gates Foundation Watch the newest video from Big Think: https://bigth.ink/NewVideo Join Big Think Edge for exclusive videos: https://bigth.ink/Edge ----------------------------------------------------------------------------------
From playlist Best Videos | Big Think
The Great Bill Gates Scam Explained
A billionaire philanthropist took control of the global public health. This is what happened to vaccine distribution. Support me through Patreon: https://www.patreon.com/thehatedone - or donate anonymously: Monero: 84DYxU8rPzQ88SxQqBF6VBNfPU9c5sjDXfTC1wXkgzWJfVMQ9zjAULL6rd11ASRGpxD1w6jQrM
From playlist Decrypted Lies
Foundation: Are We Predictable?
In which Jeff Goldblum, lemmings, and a pixelated photo of Obama help me uncover the mathematical reality of Isaac Asimov’s psychohistory. In his Foundation book series, Asimov invented psychohistory, a scientific description of history that can predict the future. This video asks whether
From playlist Video Essays
Is the NRA Being Sued Out of Existence? | LegalEagle’s Real Law Review
⭐️ Get my videos early & ad free (plus my exclusives!) only on Nebula. Save $10 per year! https://legaleagle.link/getnebula ⭐️ Is New York really going to dissolve the National Rifle Association? Can they do that? Get DEEP SENTINEL, the only security system with real human guards watchin
From playlist Law Review News!
Introducing the Foundation - Jim Zemlin (Kubernetes Launch)
From the Kubernetes 1.0 Launch, presented by Google. Watch Angel Luis Dias, the next speaker from the event: https://goo.gl/WtGSCC Subscribe to O'Reilly on YouTube: http://goo.gl/n3QSYi About Jim Zemlin: "Zemlin’s career spans three of the largest technology trends to rise over the last d
From playlist OSCON 2015
Definitions, specification and interpretation | Arithmetic and Geometry Math Foundations 44
We discuss important meta-issues regarding definitions and specification in mathematics. We also introduce the idea that mathematical definitions, expressions, formulas or theorems may support a variety of possible interpretations. Examples use our previous definitions from elementary ge
From playlist Math Foundations
Why Buildings Need Foundations
What the heck is a foundation and why do all structures need one? The bundle deal with Curiosity Stream has ended, but you can still get a great discount on Nebula and support Practical Engineering here: https://go.nebula.tv/practical-engineering If all the earth was solid rock, life woul
From playlist Civil Engineering