Superclassical

Logic and Nonsense ~ Thomas Ferguson @UNILOG2015 #unilog2015 pic.twitter.com/YyW6keGSBf

"On Arithmetic Formulated Connexively" T. M. Ferguson @UNILOG2015 pic.twitter.com/qz2Tktnxnk

Mohamed Khaled "Decidable Fragments Of First Order Logic" #UNILOG2015 pic.twitter.com/IVmkydk9YT

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Two Paradoxes of Semantic Information, Synthese

Oh, and right now it is an "Editor's Choice" article, meaning it is freely accessible.

Hi!

If you're teaching undergraduates of virtually any stripe, natural deduction systems or tableaux methods are the way to go (in my opinion). I tend to lean towards the former for instilling a sense of how logic operates, in that one can generally concoct a strategy for proving such-and-such a theorem in advance. While tableaux are a bit more mechanistic, they, too, have a certain salience that Hilbert-style proofs and Gentzen sequent calculi lack.

I suspect that after a first course the distinct needs of mathematics students, linguistics students, computer science students, and philosophy students become apparent. I've taken "intermediate logic" courses hosted in all four departments and the distinction is quite clear.

In computer science, for example, logic becomes less about how one can prove a particular theorem, and how proof in general operates. Gentzen calculi are suitable in this context.

As a mathematician, one will probably study Goedel's work quite a bit, in which one is less concerned with the feasibility of proof than the very possibility. Although Hilbert-style proofs are a pain in the toches, they make arithmetization of logic very easy.

As for philosophers, well, I don't know what to say about *those* people...

From Proceedings of the Society of Drinking a lot of Cough Syrup:

I argue that standard mereological axioms are incomplete and must be supplemented with the Ikea axiom: for any entity E composed of parts P1 … Pn, there is always some part P* that is left over. I demonstrate that P* both is and is not a part of E. I prove, as a theorem of the system, that only Graham Priest can assemble Ikea furniture.