What are the basics of mathematical logic? | Intro to Math Structures VS1.1

[@tommyhuffman7499]

Thank you for making the distinction between the formal logic and natural spoken language! I studied linguistics heavily before being introduced to these concepts, and got in a disagreement with my math professor, when I correctly pointed out that natural language does not perfectly conform to the mathematical structures. It's also really an under utilized form of analyzing arguments. Let's bring this back🙌

[@CHALKND]

It's something my students have issues with all the time so I make sure to point it out. You may already be aware, as you studied linguistics, but there are several areas of structured/proof based mathematics related to linguistics too so although there are some obvious issues at this level with propositional Calculus, there are fields of math that do a much better job at modeling natural language.

[@soniadalaklis1405]

Thanks!

[@CHALKND]

Thanks!

[@CHALKND]

Like woah mom why?

[@andrewlitfin1977]

"A proposition is a statement which is true or false but is not both true and false." Paraconsistent logics: "am I a joke to you?" :P

[@CHALKND]

In this context yes

[@rentristandelacruz]

Off topic: Since this is the CHALK channel and you talk about maths, do you use that famous Hagoromo chalk that mathematicians seem to prefer?

[@CHALKND]

Nope not yet. There are certain goals that I have set for the channel where if I reach them then I will start letting myself use Hagoromo chalk - that stuff is expensive

[@kernel8803]

Great series, thanks!

[@CHALKND]

Well we’ll see how it goes 😅

[@saptakbanerjee6495]

big up nathan

[@CHALKND]

👍🏼

[@andrefilipe8419]

what area of math is this?

[@mei2620]

Thank you!

[@NikolajKuntner]

Reject truth tables. Embrace Curry-Howard.

[@CHALKND]

sounds a tad extreme to simultaneously reject and accept two seemingly different but actually equivalent ideas.

[@CHALKND]

Ok i’ll take your word for it. I’ve only heard of it in passing/ without any rigor/proof as an equivalence between certain ideas - it isn’t my field of interest at that level of detail anyhow ¯\_(ツ)_/¯

[@NikolajKuntner]

@@CHALKND Okay then to be more explicit, on the logic side my example was double negation elimination (¬¬P➝P). But while not the same statements are validated, the situation can be salvaged to a large degree, as classical logic embeds into intuitionistic logic: There's simple formula rewritings (e.g. Gödel-Gentzen translation) so that for every classically provable statement you get a classically equivalent constructively provable statement. And the classically provable statements are those which are true in all models (by Gödel completeness in the first-order logic case). Looks like this Gödel guy did all the work, huh.