The Eternal Doorman

See  Small Fragment of the History of The Corporation of The City of London : Subscribe to Luke O'Sullivan . That sent me off thinking about triangles again, so I spent the whole evening talking to Google AI about Euclid and Aristotle. It told me Aristotle didn't refer to anything in Euclid's Elements because Aristotle died 20 years before Euclid wrote the Elements.  (See Andrei Rodin's letter in Support of Svetlana Mesyats ).  I made a video of the transcript but YouTube seems to have eaten it. This is to do with the comment I made on  About Logic - Analytic and Synthetic Mathematics  about the connection between Euclid's Proposition 32 in Book 1 and the Parallel Postulate. Q. what is the final lemma in book 13 of euclid's elements? A .  Q.  Q. I wonder whether this proposition or maybe proposition 18 is what Aristotle was referring to (Metaphysics, Book 9, Part 9) when he wrote "It is an activity also that geometrical constructions are discovered; fo...

This was in May 2015! Four years later he shows up again, completely misrepresenting Aristotle.  Why? Because what Aristotle wrote was that the same predicate could not be both asserted and denied of the same thing in the same sense at the same time. In ordinary propositional logic this is something like ¬(P∧¬P). That is not equivalent to the law of the excluded middle P∨¬P unless you use double-negation ¬¬P→P and de Morgan's law ¬(P∧Q)→(¬P∨¬Q), neither of which are intuitionistically valid. See weak excluded middle in nLab . You may now say that Aristotle wasn't an intuitionist, but Aristotle didn't do symbolic logic, so that is moot.  Wadler deserves everything he gets , if you ask me!  Subscribe to Philip Wadler . It's all about judgement, this intuitionism. See  Ways to Do Telecommunications .  12:18 Teaching philosophy.  Subscribe to  Logic and Foundations of Mathematics .  See  More History of London . 

Released today. Get it at  https://ginwigmore.lnk.to/BMS . See her post  on YT and the playlist .  Rodeo Subscribe to Gin Wigmore . 

There are an amazing number of different ways to do telecommunications on Unix systems. I have just been looking at HTTP/HTTPS connections such as are used to transfer data between web browsers and web servers, but there are a lot of different ways that you can connect these things. Traditionally one uses C programs and the Unix libc system interface library, but as SSL/TLS is a complex protocol typically another library such as OpenSSL or LibreSSL is used for the secure layer. The C program approach is a little complicated because you need to write your programs in a certain way to be able to use the libc and SSL libraries effectively. But there are other ways to do much of what most people need using higher-level tools such as socat .  I got sidetracked, but it' still relevant: it's a talk by Professor Conor McHugh, given at the University of Southampton in 2015 as part of the Philosophy Café series. See also the Internet Encyclopedia of Philosophy entry on The Problem of th...

Yesterday while listening to Tim Maudlin:  Physics and Physical Phenomena  I was struck by his idea that ( 1:40:09 ) he found he could do a path-counting procedure on 2+1 dimensional spacetime and recover an invariant that appeared like a relativistic interval.  Google go to great lengths to prevent people from accessing the text of the transcripts: See On the Emergence of Both Relativistic Structure and a Global Foliation from Discrete Space-Time .  I wondered why this didn't automatically apply to 3+1 dimensional spacetime too. I guess because he imagines a pre-existing lattice of some kind and the combinatorics are unmanageable. My thought was that maybe something like this would work inside a procedure which was effectively a completion process on a measure space as well. This would not have occurred to Maudlin because he's a realist! See  David Albert Talking Complete Nonsense . I found the above ERC talk he did on 2022: Subscribe to  PROTEUS And here ...

I had in idea about this whilst listening to this interview with Bernhard Schröder and Bernhard Fisseni : See their Natural language Proof Checking project  https://naproche-net.github.io/ : The Naproche system is an implementation of the ideas developed by the Naproche project. It accepts a controlled but rich subset of ordinary mathematical language including TeX-style typeset formulas and transforms them into formal statements. Linguistic techniques are adapted to allow for common grammatical constructs and to extract mathematically relevant implicit information about hypotheses and conclusions. Finally, automated theorem provers are used to prove the correctness of the input text.   42:20  Listening to this discussion around creating shared facts by locutionary acts it occurred to me that in a sense the idea of frames is partly psycho-linguistic and partly social. So I started to wonder whether there were any ancient Greek words which were to do with the idea of sha...

You would think these were more or less the same thing, ... but that's not true. 1:21:25 On what is a good theory and on space and time. See  The Category Enriched over the Category of Finite Sets, The Finitely Triangulated Manifold and the Magnitude of a Finite Category . My  comment : 21:52 I have been watching Dr Jorge Diaz's videos about the early history of Quantum Mechanics and it is clear from these that what they started with were indeed bona fide physical phenomena, reported in terms of drawings of spectrographs and things. Then the Quantum Theories were put forward, but these theories included 'entities' such as the spin states of free electrons. These things were not physical phenomena, they were part of the theory proposed to underlie the physical phenomena such as Zeeman splitting. So the theory was able to progress in terms of abstract, imaginary properties of physical systems with no clear idea of how or even whether any physical ...

This is absolutely brilliant, and there are lot's of great puns about burgery! My comment:   12:42 No you can't keep your secret things there because that belongs to the CIA. Subscribe to Luke O'Sullivan .

Not many people know who Emil Post was, but his model of computational processes as generating systems is one of the simplest to understand. It sits somewhere between the combinator calculus of Curry and Schönfinkel and Church's Lambda Calculus . See Geoffrey K. Pullum's  Creation myths of generative grammar and the mathematics of [Chomsky's] Syntactic Structures . Post proved his Normal Form Theorem for Post canonical systems which shows that "Given any Post canonical system on an alphabet A , a Post canonical system in normal form can be constructed from it, possibly enlarging the alphabet, such that the set of words involving only letters of A that are generated by the normal-form system is exactly the set of words generated by the original system" . What this shows is that a Post canonical system which generates a language can be abbreviated by adding non-terminal symbols which allow sub-structures to be reused at multiple places, thus potentially ...