This reminds me of: - an argument I had with the authors of the Mercury logic programming language about "types" (that they were unnecessary kludges atop first order logic) <https://groups.google.com/g/comp.lang.prolog/c/8yJxmY-jbG0/m/ksBSe0AxyBEJ> - the claim that Tarski's "model theory" obviates the attempt by Russell and Whitehead to develop "relation arithmetic" as a theory of empirical structure <https://mulpress.mcmaster.ca/russelljournal/article/download/1756/1782/2072> - Quine dispensing with "names" as mere syntactic sugars within first order logic <https://jimbowery.blogspot.com/2009/01/quines-simplification-of-structural.html> - Tom Etter's use of relative (Quine) Identities to obviate set theory within first order logic <https://groups.io/g/lawsofform/files/Boundary%20Institute/Tom%20Etter%20Papers/threeplaceidentity.pdf> - The claim that "category theory develops its own take on first-order logic — it would be a wasted effort (and somewhat counter-philosophical) to study the subject in the traditional set-oriented version of logic <https://math.stackexchange.com/a/2384057/11347>".
Look, I've been looking for the proper foundation for programming languages all of my professional life and throughout those decades there has been this claim that category theory is it -- but it really reminds me of the way Witten did violence to physics with string theory. On Wed, May 1, 2024 at 1:12 AM YKY (Yan King Yin, 甄景贤) < [email protected]> wrote: > On Tue, Apr 30, 2024 at 3:35 AM Mike Archbold <[email protected]> wrote: > >> It looks tantalizingly interesting but to help me, somewhat more of an >> intuitive narrative would help me unless you are just aiming at a narrow >> audience. >> > > Sorry that's not my style usually but I find that my level of math is also > lagging quite a bit behind the category-theory experts 😆 > I will write an easier tutorial on this stuff... most of the material is > already covered in the 1984 book "Topoi" by Robert Goldblatt, > it really unbelievable (from my perspective) that so much of categorical > logic is already well-developed at that time... and I'm > still struggling to understand that book 😆 ... which is not a very > friendly book for beginners. I doubt if there's a good beginners' > introduction to categorical logic... but most importantly, I'd like the > readers to see what this theory may offer to AGI development... > > Maths is very fascinating... but it may not be super useful and may be > even quite disappointing... but it's not useless either... > and it's hard for anyone to judge its potential... This reminds me of the > invention of back-prop.... it was re-discovered a > couple times by different researchers... the original formulation > required some tedious derivations... but some people worked > through them anyway... it was hard to see the value of a discovery until > much later. > *Artificial General Intelligence List <https://agi.topicbox.com/latest>* > / AGI / see discussions <https://agi.topicbox.com/groups/agi> + > participants <https://agi.topicbox.com/groups/agi/members> + > delivery options <https://agi.topicbox.com/groups/agi/subscription> > Permalink > <https://agi.topicbox.com/groups/agi/T45b9784382269087-Mc4b0da15ec5d9cd95f956762> > ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T45b9784382269087-M191ee1ba5f0ba9ed1f08c9d7 Delivery options: https://agi.topicbox.com/groups/agi/subscription
