renkov said:
I want to get started with FOL and decided to get through some very basic book first.
Currently looking at:
A Modern Formal Logic Primer - Teller
An Introduction to Formal Logic - P.Smith
Logic: The Laws of Truth - J.J. Smith
I guess I can give an (incomplete) opinion on this. I haven't heard about the third book.
I have gone through the first-half of the first book in quote (that was more than 5 years ago). It is written in a terse and easy to understand style, so I think that might be good for a first one. I think I should have gone through the second-half of book too (which I didn't), since I stopped reading on first sign of difficulty. This wasn't a good idea I think because all the other introduction of predicate logic that I have tried to go through (since then) seem to be harder than one in this book (and hence I had to stop reading).
But I think due to brevity for a more comprehensive coverage one would definitely need to cover at least one more book with similar title (but somewhat more advanced coverage). For a first pass, the book above should be fine. Another good book similar to first one is
http://www.homepages.ucl.ac.uk/~uctytbu/forallxcam.pdf, which I found recently. The coverage is, again, slightly terse.
The second book (in quote) is also probably an easy read (easier compared to many other books with similar title). But I think it might have a lot of text. You would probably need to take significantly more time to read.
So both of the first two books should be fine I think (both seem to be introductory books on similar level). It partly depends on how much time you want to spend.
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I do think I should mention one thing. I feel that logic can be a bit difficult to internalize (perhaps unless you keep at it continuously for a long time?). Maybe this is true for lot of other topics too.
That's why it might be a good idea to make notes while learning (from any book). Otherwise there is a good chance that one would forget it very fast. At least that was the case for me (my retention isn't good). I think I forgot what I learned (five years ago) pretty fast (even when I did all the exercises etc.). With notes at least I would know that I could get back to remembering things much quicker.