I am trying to setup a self study path to enhance my knowledge of mathematical logic. I haven't taken a logic course for a few years and my confidence on mathematical proofs is unnerving.

I am planning to attend college in a year to study physics and would perfer not to sit idle when I could be learning on my own. (I perfer self study anyway.)

I am currently going through the following books:

  • The Feynman Lectures on Physics Vol. 1
  • Basic Mathematics by Serge Lang (Checking on anything I'm not solid on before attempting calculus which I've only slightly dipped into)
  • Godel, Escher, Bach: An Eternal Golden Braid

I would like to supplement this all with a refresher on logic and then perhaps a second course level book on mathematical logic.

I picked up Alfred Tarski's Introduction to Logic and so far it has been great however I don't see many people talking about it online. It seems other books are more highly recommended especially in the "Teach Yourself Logic" pdf by Peter Smith.

I'm wondering if it would be a better use of my time to get a book that will be self sufficient as a preface to higher mathematical logic. I wouldn't want to read through Tarski's book if there was another introductory book that presents the same material alongside more valuable information.

Or am I needlessly worrying?

  • $\begingroup$ If this question is about logic, why is it tagged under calculus and mathematical physics? $\endgroup$ – Asaf Karagila Jul 4 '15 at 8:05
  • $\begingroup$ @AsafKaragila Sorry, this is my first question. I have removed the offending tags. $\endgroup$ – Silverbeard Jul 4 '15 at 16:34
  • $\begingroup$ If you want to be a physicist, studying a text book on mathematical logic would probably be a waste of time for you. For first year college science, I would recommend a good introductory book on calculus, another on Newtonian mechanics, maybe another on chemistry if that is a required course. Inquire at a physics forum. $\endgroup$ – Dan Christensen Jul 6 '15 at 3:09
  • $\begingroup$ It isn't a good idea to try reading the Feynman lectures if your math is at the level of Lang's Basic Mathematics. If you haven't yet learned calculus, and you want to learn some physics now, I'd suggest the PSSC textbook. Also, I wouldn't recommend studying mathematical logic at this point. People often wrongly believe that studying formal logic is going to help them argue mathematically. It is much more common for people to learn proofs by doing proofs - only later does it make sense to formalize things. $\endgroup$ – Keith Jul 8 '15 at 15:08

You won't be surprised to learn that in the last seventy-plus years since Tarski's book was first published in English, many other books have been appeared which will perhaps serve better as introductions to modern logic. And if you have downloaded my Teach Yourself Logic, you will have seen my "entry-level" suggestions on formal logic at the beginning of that Guide. And also my warm recommendation of Velleman's How to Prove It if you want to improve confidence in understanding modes of mathematical argument.

Still, Tarski's 1941 book is something of a classic -- a discursive and readable introduction at an elementary level to a range of topics in logic. If you are enjoying it, don't stop reading. It will teach you some important basic concepts in an accessible way. And at a pre-college level, it probably doesn't matter hugely what you read: finding things that you enjoy, that you are getting something out of, and that work well for self-study for you is more important. (After all, you are going to have years of the disciplined tread-mill of a fixed curriculum!)


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