Logic

Onj,
@Onj@mastodonmusic.social avatar

It's 11 update day, so while I wait excitedly for a whole new version number to drop, as we go from V10 to V11, what better way to pass the time than to copy text I sent to a Logic WhatsApp group and email list into , chuck some music under it and make a silly production out of it? In Logic obviously.

RaymondsCorner,

@Onj Hi Andre is this email/WhatsApp group for logic you mentioned in this post open for everyone to join or is it something that is private or not open for everyone to join.

Onj,
@Onj@mastodonmusic.social avatar

@RaymondsCorner Wouldn't mention it publicly if it wasn't open to join.

consequently,
@consequently@hcommons.social avatar

Coming up in less than 18 hours, our two-day Proofs, Rules and Meanings extravaganza. Sophie, Viviane and Francisca have been working hard to organise a productive two days of logic, and our participants get to enjoy the fruits of their hard work very soon.

https://www.st-andrews.ac.uk/arche/event/workshop-proofs-rules-and-meaning

consequently,
@consequently@hcommons.social avatar

I think I’m ready for my talk at our two-day proof theory workshop, starting tomorrow: https://consequently.org/presentation/2024/lambda-mu-arche/ — I have a lot to pack in to 25 minutes, so the monster-sized handout contains some of the details I’ll skim over in the talk.

6d03,
@6d03@mathstodon.xyz avatar

@consequently I would be very interested to watch a recording of it, if there were to be one.

caten,
@caten@mathstodon.xyz avatar

I have a new(ish) preprint on the arXiv! You can find "Invariants of structures" at https://arxiv.org/abs/2402.18063. This is a somewhat embellished version of one half of my PhD thesis. A talk which I gave about this subject in the fall of 2022 is available at https://www.youtube.com/watch?v=5TeGZZ_mepc.

In this new version, I have finally added an explicit description of something I've been telling people for years: My main result shows that any first-order property of finite structures can be computed by counting small substructures. Perhaps surprisingly, this comes as a result of synthesizing a categorical treatment of Bourbaki's notion of mathematical structure with Hilbert's classical result on symmetric polynomials.

caten,
@caten@mathstodon.xyz avatar

Also, thanks to @johncarlosbaez for pointing out the related work of Lovász on "Operations with structures"! You can find this at https://lovasz.web.elte.hu/scans/opstruct.pdf.

johncarlosbaez,
@johncarlosbaez@mathstodon.xyz avatar

@caten - Thanks!

siblingpastry, (edited )
@siblingpastry@mastodon.world avatar

I came up with a kind of thought experiment this morning, but I'm not sure if it's valid or nonsense.


Either something has always existed, or at some point, nothing existed. Those are the only two possibilities.

Nothing means literally nothing -- no matter, no space, no time, nothing.

But that's not possible -- non-existence can't exist, that's a logical contradiction.

Therefore, something has always existed.


Is that logically sound, or is it just word play?

ollicle,
@ollicle@mastodon.social avatar

@siblingpastry I’ve heard theoretical physicists talking about the possibility of many dimensions outside our reach. Maybe there could have been nothing here in our realm of perceivable space, while there was something elsewhere.

siblingpastry,
@siblingpastry@mastodon.world avatar

@ollicle That is quite a compelling way of looking at it yeah. Like the question of free will -- it's possible for free will to exist, without implying that we actually have it.

rzeta0,
@rzeta0@mastodon.social avatar

Most of us agree that

P ⇒Q

is the same as

"If P is true, then Q is true"

But I can't see how it is also the same as

"P only if Q"

Help! 😵‍💫

fellwalker57,
@fellwalker57@mastodon.social avatar

@rzeta0 Try a Venn diagram, not proof but explanatory.

villares,
@villares@ciberlandia.pt avatar

@fellwalker57 @rzeta0 my intuition is also completely broken on this... because in my life, if P implies Q, P being false allows Q to be be true for other reasons. It is not the same as Q if P and only if P.

ByrdNick,
@ByrdNick@nerdculture.de avatar

If mapping arguments improves critical thinking, then argument mapping skills should correlate with critical thinking skills, right?

Alas, they didn't correlate among 115 Advanced Placement students across 4 high schools who mapped arguments for universal basic income (from a Douglas Murray article).

proquest.com/docview/2915819770/abstract/336A7C32595F4464PQ/1

Pages 18 and 19 explaining the critical thinking test and assigned reading by Douglas Murray.
An example of a student's scored argument map (Figure 5a).
Pages 46 and 47 showing correlations between critical thinking test scores and each argument mapping score.

lydiaschoch,
@lydiaschoch@mastodon.social avatar

Who else likes logic grid puzzles like these ones? https://www.brainzilla.com/logic/logic-grid/

I had a teacher who loved them. Sometimes she’d give us one to work on. After a while, she’d put up that same puzzle on the projector and explain how to solve it for anyone who didn’t find all of the answers.

Her enthusiasm for them made me a lifelong fan of them, too.

TheQuinbox,

Does anyone have recommendations for a good beginners midi controller that's fairly cheap, ideally a 25-key one? I don't want to break the bank just yet, but I'm getting incredibly tired of Musical Typing and trying to play complex melodies on a MacBook's internal keyboard.

FreakyFwoof,

@KyleBorah @bryansmart @TheQuinbox @tspivey Right, and it's a sub-$100 keyboard. Everything is a bit much.

bryansmart,

@KyleBorah @FreakyFwoof @TheQuinbox @tspivey Right, but I didn't want it because it was cheap. I wanted it because it was compact. Can't carry my full controller in my laptop bag. I guess what I want them to make is more like an M37 Pro. All of the features, just compact. Don't care if it costs more.

SirRantsALot,
@SirRantsALot@mstdn.party avatar

The major term (P): Revenge is a dish best served cold
The minor term (S): Gazpacho is a dish best served cold.
The middle term (M): Gazpacho is the best dish when served for revenge.
🤨

rrrichardzach,

Lolz

nando161,
@nando161@kolektiva.social avatar

placing value on like "crime" or "terrorism" reinforces the of the that terms them.

analyticus,

More than argument, logic is the very structure of reality

The patterns of reality

Some have thought that logic will one day be completed and all its problems solved. Now we know it is an endless task

https://aeon.co/essays/more-than-argument-logic-is-the-very-structure-of-reality

@philosophy @philosophie @philosophyofmind

tetranomos,
@tetranomos@mas.to avatar
PatternChaser,
@PatternChaser@mastodon.green avatar

@analyticus @philosophy @philosophie @philosophyofmind

I think it is often mistaken to refer to Logic or Reason, but only because the two are so intimately associated. That, and it isn't always clear where one ends and the other begins.

It would be more useful to have a word like "Rea-gic", that carries both meanings at the same time...? 🤔

leonardopacheco,
@leonardopacheco@mathstodon.xyz avatar

Toshiyasu Arai just put a preprint with a pretty big result in arxiv: "In this paper we give an ordinal analysis of a set theory with (\Pi_N)-Collection."

If right, he found the proof-theoretical ordinal of second-order arithmetic.

Link: https://arxiv.org/pdf/2311.12459.pdf

shepgo,
@shepgo@mastodon.social avatar

More than argument, is the very structure of reality

“Philosophers have sometimes fallen into that trap, thinking that logic had nothing left to discover. But it is now known that logic can never complete its task. Whatever problems logicians solve, there will always be new problems for them to tackle, which cannot be reduced to the problems already solved.”

https://aeon.co/essays/more-than-argument-logic-is-the-very-structure-of-reality

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