Reddit reviews A Beginner's Guide to Mathematical Logic (Dover Books on Mathematics)

For basic logic (first-order, classical) these are excellent textbooks...

• Goldrei, Propositional and Predicate Calculus
  
• Enderton, A Mathematical Introduction to Logic
  
• Smullyan, A Beginner's Guide to Mathematical Logic
  
  I should also mention that there are some free, open source textbooks on standard logic (good books, written by scholars in the field) such as the following...
  
  
• "Forall X" (Cambridge Edition)
  
  And if you want to go beyond classical logic, these are excellent textbooks...
  
  
• Priest, An Introduction to Non-Classical Logic
  
• Van Benthem, Modal Logic for Open Minds

Hey there.

You mention that your brother is bright -- how bright exactly? First of all, Computability and Logic is quite an advanced book that is typically aimed towards 2nd year logic students, and is usually for students who have taken a rigorous discrete mathematics course in their first year.

It delves quite deeply into the theory of logic and the philosophy of mathematics and would not be suited as a light exercise book for someone unless they have taken a math-heavy first-year logic course and are planning on taking up electrical engineering or something of the sort.

As for Hurley's book, a Concise Intro to Logic, well, this is on the other side of the spectrum -- it is very watered down compared to other logic readings, and pales in comparison (to most other introductory logic books) with regard to depth and breadth on formal logic.

It's usually aimed at first-year philosophy students who are taking introductory courses in logic or critical thinking, and most of it is simply rote-learning certain forms of argument as well as a lot of "quick and dirty" techniques which mimic that of a dry maths textbook. If you're looking for an interesting exposition into logic, then this book is certainly not it -- it would serve better as a high-school introduction for logic, and if prescribed to anyone older, would be very lackluster.

Here are some suggestions for you:

• Raymond Smullyan's A Beginner's Guide to Mathematical Logic
  
  
• Nicholas JJ's Logic: The Laws of Truth
  
  
• Peter Smith's An Introduction to Formal Logic
  
  
• RL Simpson's Essentials of Symbolic Logic
  
  If you're looking for mathematically-oriented logic puzzles, then you should check out Smullyan's series of puzzle books. You can find them on Amazon.
  
  
  
  
  

Smullyan's Beginner's Guide to Mathematical Logic is incredible and quite accessible: Link

Consider Raymond Smullyan's A Beginner's Guide to Mathematical Logic. It has some history of logic mixed in with pretty good coverage of propositional and first order logic, as near as I can tell. Lots of exercizes, which helps me personally.