Three books come to mind just now that I can characterize as follows:
The three that I am thinking about are:
- It is accessible to most smart high-school graduates.
- It is difficult.
- It is less than 300 pages.
- It is in plain English but introduces highly technical terminology.
- It is unambiguous, (rigorous)
- It conveys information that still today is considered a substantial body of knowledge limited to expters.
There are a few exemplary text books that might be added here but I have not studied them from this perspective.
- Quine’s “Mathematical Logic”
- Fitch’s “Symbolic Logic”
- IBM’s “System 370 Principles of Operation”
Anecdotes on Each Book
I skimmed thru Symbolic logic which seemed to me like a fluffy book but interesting and easy to read.
Over the next few years I would frequently come across a difficult paper only to realize that I already knew the material from Fitch’s book where it had been presented very clearly and had not seemed obscure.
While in school in Berkeley Benson Mates assembled a seminar nitpicking Quine’s book in minute detail.
One purpose was to formalize a bit further Quine’s logic.
We found and easily fixed a couple of bugs in his proofs.
Quine’s book is the best book I know on being rigorous while brief without introducing much notation beyond the formal mathematical logic which was the subject mater.
He defined a few technical terms using normal English, but with rigor.