Logic thread

>intro to proofs
I'll explain, brainlet. Intro to proofs are not logic courses, the object of study isn't logic, it isn't proof theory. They don't study a subject onto itself, their purpose is for you to get the necessary mathematical maturity to then do proofs in other courses. That is not logic.

I'll also let your brainlet fucktard mind in some other secrets. Most mathematics majors don't take logic courses, including in universities like cambridge, often a philosopher knows more about logic than a mathematician.

I'm a mathematician, and I tried studying it but failed. I think that you need the talent to remember long arrays of symbols (or the tenacy to practice this) in order to be succesful at more complicated logic stuff. Unfortunately, that is not my strength in math. I really admire pure logicians.

Logic is something that every human agrees on. We can't prove it, but we accept it as truth.

The consequence of logic is math describing the universe very accurately.

What exactly do you think intro to proofs classes are dude? Just purely theoretical abstraction of what proofs are like and how to do them?

No, the subject matter of the course is something simple like elementary logic or set theory, at a very low level and not with much depth because yes the point is to develop your proofwriting ability but you develop that ability through study of a simple mathematical subject.

My intro to proofs class covered elementary formal logic, that was the subject matter, it was at a laughably low level because the point was learning proofs but we literally studied formal logic.

Look, fucktard. You're really annoying me. There's no Intro to Proof class that covers what an elementary formal logic textbook would cover. Man, I fucking despise cunts like you. You think I didn't take that shitty class? You fucktard, get the fuck out of this thread you know nothing about logic. Go do your truth tables.

It's not called intro to proofs, because what kind of autistic university offers a class like that?

It's called Sets and Logic, and about 1/3 of the course material was literally equivalent to the Elementary Formal Logic course offered by the philosophy department. The latter went into more depth on the logic because the math class also covered notation, some set theory and proofwriting but much of the course material was literally identical.

>HAI GUISE I KNOW SET THEORY BECAUSE MY CLASS HAD "SET THEORY" IN THE NAME
Set theory is usually taught at graduate level. You do not know set theory, you use it informally. Just like you use logic informally. Stop fucking talking now.

I know how to use elementary set theoretic notation such as [math]A \subset B[/math], [math]a \in A[/math], etc in my Sets and Logic class, as well as extremely basic rules and theorems like DeMorgan's because I learned them in my sophomore level sets and logic class.

No, it wasn't graduate level set theory, you delusional buffoon, it was an elementary introduction to the very basics.

The logic part of the course, however, was an introduction to formal logic that was pretty much exactly the same as the first half semester of the philosophy department's Elementary Formal Logic course.

I may use logic informally in discussion as it is more conversational, but at least I don't ignore logic completely to throw an autistic shitfit trying to tell someone else what his classes were like.

I'll elaborate for your dumbfuck brain to understand.
You don't prove any metalogical results in those classes.
You don't go over all the main results of logic.
You don't get any nuanced understanding of logic.
Those courses are created strictly to prepare mathematicians for proofs.
What I'm saying that you saying that you took a logic course is the same as a highschooler saying he took real analysis because he knows how to differentiate.

Regarding set theory, pick ANY standard text on set theory. Most of those courses don't even go through the axiomatics of set theory.

Conclusion, this """logic"""" and """set theory""""" class you took is analogous to engineer math classes (but actually much more basic and pathetic). The focus isn't in logic itself, the focus is in using it as a TOOL for solving engineering problems, and in your case, using logic to present "rigorous" mathematical proofs. By the way, your DeMorgan and those notions of set theory are introduced in highschool here, congratulations for knowing what a highschooler knows about set theory. I guess you'd say they took set theory too?

Basically, you might want to say you took these courses, and in only some very weak notion of "logic course" and "set theory" course did you actually do it.

Look, you really don't seem to understand elementary formal logic so I'll try to spell it out for you and make the notation clear for you, ok?

There is a class called "Sets and Logic"
This class covers set theory
This class covers logic
A student takes this class
Therefore this student has taken a class that covers set theory and logic

Moreover:
The philosophy department's logic class covers elementary formal logic and notation
The mathematics department's logic class covers elementary formal logic and notation
Therefore both the math department's logic class and the philosophy department's logic class cover elementary formal logic and notation
Taking things a step further:
Therefore the math department's logic class and the philosophy department's logic class both cover at least some of the same material

I'm sorry this is so difficult for you, I hope this helps you understand

I really enjoyed Mendelson's book. That's as far as I got into logic, though.

>intro to proofs
Such a thing doesn't even exist in my country. You're supposed to learn how to prove things during your school years. Now that I think about it, the whole Geometry course was mainly about it.

Then "elementary formal logic" isn't a logic course. Now fuck off, brainlet fucktard who wasn't even taken a logic course.

>Hai guise look at my proof theory and formal logic textbook!! is rly good. Wat? My course is highschool level material? well but the title of the course has the words "Sets" and "logic" in it so i guess it took a logic course guise.

Yep, this guy's a joke. Just like these "intro to proofs" courses.

What are you so angry about?

So is comoutability a subfield of logic or a separate thing? Obviously they're (very) connected

>course has logic in the name
>'b-b-b-but it's not a real logic course because I took a logic course in grad school that was really hard and there's no way some dumb little undergrad could know logic! REEEEEEE!'

What's really hilarious is that you're being this illogical emotional stereotype throwing a temper tantrum and asserting logical fallacies, while discussing a course in logic ;)

You don't know logic. You know truth tables, you know how the meaning of some connectives and quantifiers. That's it. That's what you know. You do not know logic.

I took actual courses in logic not just "intro to proof" courses where one sees elementary logic.

I've taken basic, intermediate and advance courses in logic. I took a course in set theory where we covered topics such as weakly inaccessible cardinals, Ramsey theory and so on.

I took a course in recursion theory where we covered godels incompleteness theorems.

The lower level logic courses covered godels soundness theorems and the like.

I even did research in logic and intended to go to graduate school for a PhD in math logic.

Logic turns out not to be a popular field in mathematics, despite its connection to other areas (all of undergraduate mathematics) and interesting results in comparability.

Most math departments for some reason don't have many logicians (outside of places like Berkeley, Wisconsin, etc.)

I decided to go for a PhD in CS instead and focus on the more pure math side of CS.

Math logic is still one of my favorite areas of pure mathematics though.

Comparability was meant to be "computability"*

okay im not these guys and im not gonna be all patronising: but in mathematics, what we mean by "logic" as a field of study has a very specific meaning. take a look at some of these papers:
arxiv.org/list/math.LO/recent

its not just us being all "haha we know more logic". the logic people do is about as different to the logic youve done as number theory is from multiplying and adding numbers.
you might USE logic, but you havent STUDIED it.

Learning to read and write in English as a kid != studying English
(granted, there is a kind of weak equivalence if you squint really hard)

The same applies for logic, which is essentially the language of mathematics.

>Studying logic...
>Pshh, nothing personnel kid.
>*teleports behind your truth tables*