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Could you give me a list of the most authoritative and prestigious manuals or textbooks for introduction to classic logic currently used in higher education?

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Not an exhaustive list, by any means, but here goes:

  • David Barker-Plummer, Jon Barwise, John Etchemendy: Language, Proof and Logic
  • George Boolos, John Burgess, Richard Jeffrey: Computability and Logic
  • Irving Copi, Carl Cohen, Victor Rodych: Introduction to Logic
  • Herbert Enderton: A Mathematical Introduction to Logic
  • Christopher Leary and Lars Kristiansen: A Friendly Introduction to Mathematical Logic
  • Elliot Mendelson: Introduction to Mathematical Logic
  • Mark Sainsbury: Logical Forms
  • Peter Smith: An Introduction to Formal Logic
  • Lori Watson, Patrick Hurley: A Concise Introduction to Logic

Of these, some are aimed more at math students and others more at philosophy students, and perhaps some at both.

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I suggest you also peruse Irving M. Copi's Symbolic Logic, which he is supposed to have written as a companion to the Introduction to Logic mentioned by Bumble. (see https://www.journals.uchicago.edu/doi/abs/10.1086/287494.)

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