The paper referenced also defines Gentzen's sequent calculus, an even nicer formulation of logic:
http://www.digizeitschriften.de/download/PPN266833020_0039/P...
http://www.digizeitschriften.de/download/PPN266833020_0039/P...
http://www.digizeitschriften.de/download/PPN266833020_0039/P...
Thanks for the interesting blog piece though - maybe you could write one about Gentzen's consistency proof?