A rigorous book on logic?

Hi Veeky Forums
Is there a book out there on logic, that doesn't use set theory or anything and builds every notion of logic from 0? I checked Mendelson's book, and it starts by talking about truth tables, which are functions, and the definition I know of a function uses set theory. Some other books I checked feel like they are designed for enginners/CSfags.
Also PDF is required since I'm poor.
Thanks.

Other urls found in this thread:

en.wikipedia.org/wiki/Gödel's_incompleteness_theorems
math.stackexchange.com/questions/264913/book-on-the-rigorous-foundations-of-mathematics-logic-and-set-theory
dpmms.cam.ac.uk/~ardm/bourbaki.pdf
twitter.com/SFWRedditGifs

I think truth tables aren't functions
if you're going to study logic you need to forget what you know about set theory, and just accept the primitives for what they are

Principia mathematica. It takes russell over eight hundred pages to get to 1+1=2

>that doesn't use set theory
why not ?

>builds every notion of logic from 0
You do realize that it's not possible right ?

I wouldn't read a book this old for anything other than historical interest.

Let's try something different. What is your purpose? Why do you want such a book? You seem to be asking the wrong question

I know the author has to define things (primitives as you say) in natural language before using them, but he should specify all these things in the beginning with all the details.
>>that doesn't use set theory
>why not ?
Because set theory uses logic in its construction?
>>builds every notion of logic from 0
>You do realize that it's not possible right ?
I don't understand, could you clarify?

I want to learn about the foundations of mathematics, how set theory is built, what exactly are mathematical theories...etc à la Bourbaki, but Bourbaki has not logic chapter I believe, and I can't find these books anyway.

not op but in a similar boat it sounds. i want to start from the bare bones of mathematics and work my way up to the more complicated structures so that i'm not missing any sort of intuition along the way

en.wikipedia.org/wiki/Gödel's_incompleteness_theorems

honestly, if what you want is a good foundation for math, read some nice book on naive set theory and move on

you aren't missing anything by starting with ZFC. that's enough, honestly. any decent set theory book (Halmos, first part of Jech) will be more than enough for your journey

if you want a foundation FOR math, then what I said above applies. if you want to know about the foundations OF math, then I've no fucking idea and most mathematicians won't either.

Well I'm not exactly sure what you mean but if you are looking for math books that take logic from scratch, then you are going to be disappointed. Mathematical logic is to math what mathematical physics is to physics, ie. an area of math that studies mathematical reasoning/mathematical structures/sets, but still a part of math.
You can't make a formalization of logic without having an underlying language and an underlying logic

I do want to learn about the foundations OF maths as I said earlier, as in how one can make theories using axioms and stuff, and set theory is just an example of a theory (something like that, forgive my ignorance).

The fact that I need set theory to build logic and logic to build set theory is itching me desu.

no clue then, math.stackexchange.com/questions/264913/book-on-the-rigorous-foundations-of-mathematics-logic-and-set-theory seems related

Yeah thanks a lot, that's exactly my question. I, for some reason, didn't find this question and I have searched a lot.

what's wrong with mendelson's book? i read it front to back. it's solid.

But the set theory that logicians study is not the set theory that mathematicians actually use.
It's "one level deeper" if you will. It actually requires to have some kind of naïve set theory.
Really, I don't think you can find an actual mathematical logic text that doesn't assume you already know math.

Any good ressource for predicate logic?

Thank you everybody for your answers.
I'm thinking about learning French and read the Bourbaki book on set theory (I can only find it in french and I want to learn french anyway).
Good luck Veeky Forums, I might come here and shitpost sometimes when I finish this set theory book.

>builds every notion of logic from 0
Why in fuck's name would you do that? Why are you allergic to set theory?

Not allergic to set theory, but logic should come before set theory therefore logic can be built without set theory.

Philosophy grad here. We have to study Logic as a compulsory part of philosophy degrees.

The standard go-to text is 'Logic' by Paul Tomassi

dpmms.cam.ac.uk/~ardm/bourbaki.pdf

"Ignorance of Bourbaki"

why would you read Bourbaki set theory? stop the memes and read Halmos or Jech

I am French and I read it and it's disgusting. Just don't think about it

listen faggot, your non-symbolic logic can suck a cock

Actually I just googled that book and holy jesus fuck that's so many words for such a babys first survey of logic.

This. It's pretty good. What you ask, OP, is to provide the definition of "definition". You can't start from zero, because you have nothing to start with.
And I wouldn't say that truth table require set theory in any sense of the world.