Recommendation on Quine's text

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I'm planning to study logic seriously and I think Quine's style is fine to me so i'm going to read his book.

There are two famous books by him. Namely, "Methods of logic" and "Mathematical logic".

I don't know which fits to me. This is my first time learning logic seriously. Which of those are suitable to a first-learner?

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I would rather strongly recommend you to take a look at Peter Smith's Teach Yourself Logic Guide first. As the same suggests, this is a guide for students that want to learn serious logic by themselves, mostly Philosophy or Mathematics students that had just take some very elementary logic courses during their classes.

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There are many modern ML textbook (see PS' Guide in the answer above).

If you are really interested into Quine's approach to logic, I think that Methods of Logic (4th ed 1982) is more like a textbook (possibly to be supplemented with Warren Goldfarb, Deductive Logic (2003)), while Mathematical logic (2nd ed 1981) is more devoted to a "modernization" of W&R, Principia Mathematica.

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I strongly advice against Quines book as introduction of logic. (also against his notation btw)

They are just no good. (to much on bi valued logic , not enough on formal reasoning)

I would suggest "language proof and logic" by Barwise cs or (maybe bit to expensive)

"techniques of formal reasoning, second Edition " by Kalish cs (get it second hand for almost nil)

"logic" by Tomassi (I learned logic from it )

but read Paul smiths advice first

alther option do the free cousera course on logic :)

Good luck