Mathematical logic | Paradoxes of naive set theory | Mathematical paradoxes
Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F", requiring only a few apparently innocuous logical deduction rules. Since F is arbitrary, any logic having these rules allows one to prove everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic. The paradox is named after the logician Haskell Curry. It has also been called Löb's paradox after Martin Hugo Löb, due to its relationship to Löb's theorem. (Wikipedia).
Most paradoxes either stem from the misunderstanding of a topic, or aren't really paradoxes. However, here is a paradox that seems to contradict logic itself. What's going on here? And what does the liar paradox have to do with computer science? #some2
From playlist Summer of Math Exposition 2 videos
What is Bertrand Russels Barber Paradox?
Logical paradoxes are some of the most infuriating and frustrating problems that we can try to solve. As humans, we always want to find an answer and we naturally assume that an answer must exist. In the case of Bertrand Russell's Barber Paradox, a solution does exist, but it becomes even
From playlist Concerning Questions
Russell's Paradox - A Ripple in the Foundations of Mathematics
Bertrand Russell's set theory paradox on the foundations of mathematics, axiomatic set theory and the laws of logic. A celebration of Gottlob Frege. Thank you to Professor Joel David Hamkins for your help with this video. Hi! I'm Jade. Subscribe to Up and Atom for physics, math and com
From playlist Math
Newcomb's paradox | Famous Math Problems 7 | NJ Wildberger
Newcomb's paradox was first studied by American physicist William Newcomb, and popularized by articles by Robert Nozick and famously Martin Gardner in one of his 1974 Mathematical Games columns in Scientific American. The paradox involves notions of free will, determinism, choice, probabil
From playlist Famous Math Problems
Here's a re-enactment of the famous paradox known as the "infinite monkey theorem."
From playlist Cosmic Journeys
Set Theory (Part 2a): Russell's Paradox
Please feel free to leave comments/questions on the video below! In this video, I briefly speak about the Russell paradox and why ZFC avoids this paradox when discussing pathological sets. One should hopefully see why it is that this paradox is disastrous for the naive set theory adopted
From playlist Set Theory by Mathoma
Even More Paradoxical: The Twin Paradox in Curved Spacetime
The Twin Paradox gets a stranger, even more mind-bending upgrade in General Relativity's world of curved spacetime. We explore the surprising and relatively unknown results to these new scenarios, while getting our toes wet in some of GR's conceptual frameworks. And finally, after several
From playlist Summer of Math Exposition Youtube Videos
Curry’s Paradox (Version 3) Explained
From playlist Geometry TikToks
What is free will, really? Steven Pinker explains.
New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- Free will exists, but by no means is it a miracle.We use "free will"
From playlist Steven Pinker | Big Think
Mathematical Theories of Interaction with Oracles: Active Testing and Models - Liu Yang
Liu Yang School of Computer Science, Carnegie Mellon University February 11, 2013 With the notion of interaction with oracles as a unifying theme of much of my dissertation work, I discuss novel models and results for property testing and computational learning, with the use of Fourier ana
From playlist Mathematics
Relativity: how people get time dilation wrong
Einstein’s special theory of relativity is notorious for being easy to misuse, with the result that sometimes result in claims of paradoxes. When one digs more carefully into the theory, you find that no such paradoxes actually exist. In this video, Fermilab’s Dr. Don Lincoln describes a
From playlist Relativity
60 = 58 = 59 (Visual Curry triangle dissection)
This is a short, animated visual proof showing that 60 = 58 = 59, and then investigating where the diagram goes wrong. #math #paradox #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #calculus #dissection #area #currytriangle #missingsquar
From playlist Geometry
Wolfram Physics Project: Working Session Tuesday, Mar. 16, 2021 [Bibliographying Combinators]
This is a Wolfram Physics Project working session on bibliographying combinators. Begins at 4:33 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am
From playlist Wolfram Physics Project Livestream Archive
Category Theory 1.1: Motivation and Philosophy
Motivation and philosophy
From playlist Category Theory
From Scratch to Univalence | #SoME2
#SoME2 A brief journey through the many different ways that Type theory can be understood from. From nothing to it's most important axiom (at the time of writting): The axiom of univalence. Hope you fellas enjoy it! Down here I'll leave some links and references to a couple of interesti
From playlist Summer of Math Exposition 2 videos
Wittgensteinian Problem of Meaning & Rules
A clip of James Conant discussing a philosophical problem about meaning and rule-following that was famously discussed by the later Wittgenstein and many others, including various interpreters of Wittgenstein (e.g. Kripke). Note, Wittgenstein himself does not endorse the radical skeptical
From playlist Wittgenstein
Why Algebraic Data Types Are Important
Strong static typing detects a lot of bugs at compile time, so why would anyone prefer to program in JavaScript or Python? The main reason is that type systems can be extremely complex, often with byzantine typing rules (C++ comes to mind). This makes generic programming a truly dark art.
From playlist Functional Programming
Steven Pinker On Reason | Big Think
Steven Pinker On Reason New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- Free will exists, but by no means is it a mirac
From playlist Steven Pinker | Big Think
The Andromeda Paradox Explained: Loss of simultaneity in special relativity
#SpecialRelativity Bob is sitting on a park bench feeding pigeons. He sees Alice heading in his direction, enjoying a morning run. “How are you?” he calls. Breathless, she responds. “Fine. But an armada from the Andromeda Galaxy has just departed for Earth.” Bob laughs. “No, it hasn’t!” Wh
From playlist Special Relativity - A Gentle Introduction