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I plan to choose one and read it.

  • basic "I've never learned what 'valid' or 'sound' means" logic, philosophical logic, or mathematical logic? – Not_Here Sep 26 '18 at 23:37
  • If I have to pick, I guess mathematical. – 62a Sep 26 '18 at 23:47
  • so you have had exposure to a propositional calculus and natural deduction before? – Not_Here Sep 26 '18 at 23:48
  • I'm not familiar with those terms. I'm looking for books that could be considered competitors of "Logic: Techniques of Formal Reasoning" by Kalish. – 62a Sep 26 '18 at 23:53
  • 1
    Well I guess at this juncture I'd want to point out "I'm not familiar with those terms." and "Well I know perfectly well what valid and sound arguments are." are contradictory. My point stands though, Kalish's book is very much so dated but it's subject matter is almost entirely beginning logic with a few chapters at the end that graze mathematical and philosophical logic. So if that terminology and notation is foreign to you then you're looking for beginning logic. Which is absolutely fine, there's nothing wrong with that. Like I said, I just wanted to know which area you were looking for. – Not_Here Sep 27 '18 at 1:20
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This is a partial answer since I don't know what the most popular introductory logic textbooks are. However, I have one that I like: forall x: Calgary Remix with Klement's natural deduction proof checker.

The text is clear covering both truth-functional logic (propositional logic) as well as first-order logic. The proof checker is intuitive to use and it has an attractive display. It allows you to practice proving the exercises in the book using Fitch-style natural deduction.

This book is an introduction. It stops with only outlining how one might show that what one can prove with derivations can be shown with truth tables and vice-versa.

If you search on this site you will see multiple answers using these sources. The most recent being: https://philosophy.stackexchange.com/a/55798/29944

It is licensed under a Creative Commons Attribution 4.0 International License.

I suggest you look for other sources as well. Also this particular site may be a good place to give you a chance to ask and answer questions related to logic.


Reference

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/ Wikipedia, "Fitch notation" https://en.wikipedia.org/wiki/Fitch_notation

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I don't know if I would say that one is most popular (although obviously forallx, because it is free/open source, gets a lot of play on the internet). If you have access to a library, I would strongly advise you go to the shelf where the logic textbooks are and take them down off the shelf and look at them. What matters isn't really which one is best-selling, most reputable etc in some abstract sense but which is best for you. You're going to be doing a lot of exercises out of it...

The one thing to check for is that you're not using a textbook from the 1950s that does propositional logic but not predicate logic or syllogism. It's also nice to have a textbook that has a chapter on inductive inference (since sometimes logic textbooks produce people who are mentally crippled by their inability to entertain empirical hypotheses).

If you want to top off the textbook that seems most inviting to you with a bit more reading material to understanding the scope and value of logic, try Logic, a very short introduction (which however has no exercises).

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I really struggled with logic until I came across E.J. Lemmon's Beginning Logic. But what works for me wont necessarily work for you, the best thing you can do is to pick up as many of these elementary logic books as you can, read through them and see what works best for you.

I also found that reading different explanations by different authors of logical principles made understanding it easier. If what you're reading isn't making much sense, try a different source and see if it describes it in a clearer way.

  • To clarify, I took the question as meaning a basic introduction to a variety of formal logical systems, Lemmon's book providing an introduction to; syllogistic, propositional and predicate logic. – Matt-T Nov 6 '18 at 20:35

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