Posts

About Logic interview with Giovanni Sambin

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You can read notes on Martin-Löf's lecture given in Padua in 1980 here:  Giovanni Sambin's notes on Per Martin-Löf's Intuitionistic Type Theory . My comment : 40:32 Thorsten "You only need the notion of a type... Then I can explain a proposition,..." I remember when you did that a few weeks ago , and you explained it, but did anybody actually understand your explanation? I know I didn't! 30:38 On intensional and extensional theories and "running them in parallel". I wonder how far you could get by modelling functions with bijections between pairs, i.e. permutations on graphs. I did something like this once in the iterative construction I described in this post:  Brady Haran interview with Terence Tao . It produced some very interesting constructions full of amazing symmetries. See also  Category Theory May Actually be a Disease  and Emma Tye on Martin-Löf Type Theory . What I did was construct something like a closure operator on an abstract algeb...

Rachel Phillips Ranking Geological Periods

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See Rachel Phillips and Luisa the Scottish Geologist .  Subscribe to  GEO GIRL . You can learn about her Scottish geology expeditions: https://www.scottishgeologist.co.uk/   Subscribe to Luisa the Scottish Geologist .

Pupina Plomer on the Children of Llullaillaco

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They were Inca human sacrifices made in the late fifteenth century. See  Children of Llullaillaco . In 1999 the almost perfectly preserved remains of these three children were discovered near the summit of the volcano. Since 2007 they have been exhibited in a specially constructed museum in Salta, Argentina. Descendents of these people still maintain the beliefs in the mountain deities to whom these sacrifices were made, ... Subscribe to Pupina Plomer . 

SAIR - On Open Math Models

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You really need these in computer science, chemistry, biology, physics and every other subject, because the potential for abuse by corporate, military-industrial power structures is enormous. See  Brady Haran Interview with Hugo Duminil-Copin  and  Brady Haran interview with Terence Tao .  Subscribe to  SAIR . 

Emma Tye on Martin-Löf Type Theory

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See https://msp.cis.strath.ac.uk/msp101.html  I wish I had read this description of it before, because now it makes a heck of a lot more sense!  The simply-typed lambda calculus (STLC) gives us a nice Curry-Howard correspondence with propositional logic by treating the function arrow of STLC as implication. From this we can compute proofs as programs. But a natural question is then: what about predicate logics instead of propositional? Martin-Löf Type Theory (or Intuitionistic Type Theory) is a type theory based on predicate logic, with type constructions representing existentially quantified variables (Sigma) and universally quantified variables (Pi). We can also construct inductively defined families - W-types - as well-founded trees. Note that Martin-Löf's original paper was inconsistent due to having the type-in-type paradox, and that he later introduced a predicative version with universe hierarchies. In this introduction, we assume knowledge of the STLC and natural-deduc...

Human Civilization does Advance

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... Now some people will learn to tie their shoelaces before they reach sixty, ... Support American industry:  https://awesomeforsale.com/ever-ties-set-of-2/  Think of it as non tax-deductable charitable giving for now, ... See  America is for Losers.   Subscribe to First Class Amateur .

Janet Akselrud Published a Book

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It's really good. See her website: https://curiouswanderingsouls.com/ and her substack too: https://giftsfromyoungerme.substack.com/ . Get your copy of  This book is not for reading, and I mean it. I’m not trying to get you to read the book by telling you not to read it. This is a piece of art. An act ... using something in a way it was not intended  from Amazon, ... Subscribe to Curious Wandering Souls .

Karolina and Maggie on Sense and Sensibility

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Subscribe to Karolina Żebrowska . Subscribe to Deepfocuslens .

Category Theory May Actually be a Disease

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I was just listening to people talking about how much time people spend communicating in text and how little people read, then I started looking again at Categories within the Foundation of Mathematics by Benjamin Horowitz and I realised that although he admits to leaving the idea of a collection undefined, he also leaves the idea of a map undefined, but then he is happy to make assertions about this undefined notion of a map, for example he says "It is important to note that a diagram doesn’t necessarily have to commute unless forced to by the properties of a category (as with the associativity and identity diagrams)." What on earth does he expect that to mean to someone? Then I remembered Steve Awodey's lectures being an unusually comprehensible introduction, so I went back to look at them again and I noticed this comment "Math joke: What do you call a category theorist who reads a paper? A co-author." See  Another Excellent Talk on HoTT by Steve Awodey . I...

Searle on Consciousness

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He starts ( 4:03 ) talking about the difference between epistemically objective and subjective claims . I was thinking about human experience and the idea that we share certain common experience on account of our being human beings in common situations. This is ultimately what we mean when we make claims about the existence of qualia, which Searle calls ontologically subjective claims (the immediate subjective experience of seeing a colour, for example). We say the qualia "exist" because we have plenty of epistemic justification for believing there is some common shared experience to seeing colours, for example. We usually get this justification through sharing linguistic representations of the subjective experience. The so-called "hard problem of consciousness" is to try to explain the ontological foundation of these qualia ( 38:48 ). Some people think that an explanation of this needs to be given in terms of physics. I wrote in 2010 that this is not so, because ...