On Learning Sequent Calculi
I find it easier to think of natural deduction as abbreviated sequent calculi, rather than to think of sequent calculi as expanded natural deduction derivations. In other words, I find it easier to think of sequent calculi first, and then to go from there to natural deduction. I’m not sure why: von Plato’s Elements of Logical Reasoning writes that it’s normally easier to learn natural deduction first and then move on to sequents, but I seem to work in the reverse order.
It reminds me of eskrima: apparently they teach you defence with knives first before teaching you bare-handed defence. The idea being that if you can defend yourself with knives (which requires more delicacy), then you can defend yourself easily with your bare hands. Just as apparently some magician (I think it was Houdini) practiced card tricks with gloves on in the cold trenches during a world war--and when the war was over, he could do card tricks with his gloves off even better.