Where can I learn Mathematical Logic?

Ive been getting into Wittgenstein and Russell lately and I wanted to know where I can study such maths and logic.

It depends on your motivations. You can study mathematical logic from a philosophical point of view, a computer science point of view, a purely mathematical point of view... I don't know your background.

I think the best thing to do would be to check the "Teach Yourself Logic Guide (2016)" of Peter Smith : coming from there http://www.logicmatters.net/tyl/

Some (not too technical I think) introductions textbooks I can think of (but you can find plenty of them in the link above) :

General Introduction

• Mathematical Logic, Chiswell and Hodges. Very concise, easy to understand but not that complete.

Gödel's Theorems

• An introduction to Gödels Theorems, Smith

Proof Theory

It focuses on the study of proofs.

A bit old but still interesting

Interesting books from famous authors but use outdated notations and are more technical.

• Introduction to logic and to the methodoly of deductive sciences, Tarski
• Mathematical Logic, Kleene
• Could you please specify why are Tarski and Kleene recommended only from a historic point of view ? More precisely, which technics there are not used anymore? – Aili J. Dec 27 '16 at 15:08
• @AiliJ. It's not really that the concepts/technics used are totally outdated but rather that logic is described in a quite old way : not always clear and with old notations/presentations. I just think (maybe subjectively) that it doesn't fit for an introduction to Logic but rather for a technical investigation of the root of some ideas of logic. Moreover, it's not an exhaustive list, they're just two books that I happen to have. – Boris Dec 27 '16 at 16:20
• Funnily enough I am reading Tarski just now and I found it very easy to understand without any previous studies of logic; and Kleene I bought 2 days ago online so it would be interesting to know into which chapters I shouldn't perhaps concentrate too much :) – Aili J. Dec 27 '16 at 16:26
• @AiliJ. Oh ok. Maybe it was too subjective... and maybe it also depends on your background. I personally have a Computer Science background. – Boris Dec 27 '16 at 17:14
• Kleene's book is still conceptually just fine, but it uses outdated notation and terminology. Quine also wrote some basic logic texts but they have the same problem. – user20153 Dec 28 '16 at 6:37

This is a FREE and very well designed MOOC (Massively Open Online Course) by Professor Keith Devlin of Stanford University:

https://www.coursera.org/learn/mathematical-thinking

It was designed as a transitional course from high school to university level math and is a great indtroduction to mathematical thinking. He's also got some great lectures available on YouTube.

It's not specifically "mathematical logic" as stated in the OP title. But for someone interested in "math and logic" as stated in the post, the course is a great intro to mathematical thinking including truth tables, existential quantifiers, infinity, set theory and such.

• why is this downvoted? – user6917 Dec 27 '16 at 13:17
• hm well idk how much of it is logic based. cool link tho – user6917 Dec 27 '16 at 13:30
• @MATHEMETICIAN It's not specifically "mathematical logic" as stated in the OP title but for someone interested in "math and logic" as stated in the post, the course is a great intro to mathematical thinking including truth tables, existential quantifiers, infinity, set theory and such – Mr. Kennedy Dec 27 '16 at 13:33
• This seems valid as an answer to me. Why is this downvoted? – virmaior Dec 27 '16 at 14:43
• very useful link :) – Aili J. Dec 27 '16 at 15:16