An introduction to non-classical logic
by Graham Priest · first published 2008
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…the https://en.wikipedia.org/wiki/Paradoxes_of_material_implicat... : ~(A & ~B) is a very poor approximation of 'if A then B' once you leave the world of statements about mathematics. Graham Priest's /Introduction to Non-Classical Logic/ http://www.cambridge.org/ie/academic/subjects/philosophy/phi... is great (as is his lecturing on the subject: Priest really ought to do a MOOC...)
on “The Outer Limits of Reason: A look at paradoxes in language” ↗If this caught your interest, run out and buy Graham Priest's Introduction to Non-Classical Logic. https://www.cambridge.org/ie/academic/subjects/philosophy/ph... It's so good. It's just a pity that there doesn't seem to be video of Graham Priest teaching this material in person anywhere.
on “Many-valued logic” ↗Graham Priest's Introduction to Non-Classical Logic https://www.cambridge.org/core/books/an-introduction-to-nonc... is so good and deserves to have a SICP-like fandom. But it's certainly going to talk to you in terms of proof, formality and so on.
on “Category Theory Illustrated – Logic” ↗I'm no expert myself, but: An Introduction to Non-Classical Logic by Graham Priest. https://www.cambridge.org/core/books/an-introduction-to-nonc...
on “Ask HN: What are the best unknown books you have read?” ↗…that the informal meta-language in which the non-classical logics are explained in is traditional first-order logic, see e.g. [1]. I don't know what "dialectical logic" logic is. [1] Graham Priest, An Introduction to Non-Classical Logic
on “A Bridge Too Far: E.W. Dijkstra and Logic” ↗…puzzling. Yes, and for a reason: material implication (the kind of implication discussed in the article) cannot always explain our intuitive sense of implication. My favourite example, from Priest's Introduction to Non-Classical Logic: (A ⇒ B) ∧ (C ⇒ D) ⊦ (A ⇒ D) ∨ (C ⇒ B) is valid when ⇒ is material, yet the statement: "If John is in Paris he is in France, and if John is in London he is in England. Hence, it is the case either that…
on “Logical Literacy” ↗…I don't really think the logics presented solve these problems in a satisfactory way, but they are definitely of philosophical interest (o/w Cambridge University Press wouldn't have published his "An Introduction to Non-Classical Logic").
on “The logic of Buddhist philosophy” ↗