Ive been getting into Wittgenstein and Russell lately and I wanted to know where I can study such maths and logic.
-
4On any textbook... See e.g. Stephen Simpson, Mathematical Logic (2013).– Mauro ALLEGRANZADec 27, 2016 at 9:25
-
More spcifically, on Russell, see The Cambridge Companion to Bertrand Russell and The Palgrave Centenary Companion to Principia Mathematica.– Mauro ALLEGRANZADec 27, 2016 at 9:27
-
On Wittgenstein, The Cambridge Companion to Wittgenstein and Michael Potter, Wittgenstein's Notes on Logic.– Mauro ALLEGRANZADec 27, 2016 at 9:28
-
i have a copy of lemmon's beginning logic, unread, but recommended to me. not really sure what "mathematical logic" is?– user6917Dec 27, 2016 at 13:17
-
1@MATHEMETICIAN proof theory, recursion theory, set, model theory & such– MmmHmmDec 27, 2016 at 14:04
2 Answers
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.
- An Introduction to Proof Theory (Comes from The Handbook of Proof Theory), Buss
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Interesting books from famous authors but use outdated notations and are more technical.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, 2016 at 15:08
-
1@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 It's not really that the concepts/technics used are totally outdated but rather that logic is described in a quite old way : not always clear and with old notations/presentations.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.– BorisDec 27, 2016 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, 2016 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.– BorisDec 27, 2016 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.– user20153Dec 28, 2016 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.
-
3why is this downvoted?– user6917Dec 27, 2016 at 13:17
-
hm well idk how much of it is logic based. cool link tho– user6917Dec 27, 2016 at 13:30
-
1@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– MmmHmmDec 27, 2016 at 13:33
-
2
-
2