This is actually the best way to understand it. But without some background (Proof Theory 101, The Deductive Theorem, Metalogic 101), I'm sure this sounds like

This is actually the best way to understand it. But without some background (Proof Theory 101, The Deductive Theorem, Metalogic 101), I'm sure this sounds like gibberish :) NB: Although you muddy the waters a bit. "A => B" is literally "A proves B". And to see why an inconsistent set implies anything at all, we just need to look at the Principle of Explosion[1] -- which is probably less contentious than material implication. [1] https://en.wikipedia.org/wiki/Principle_of_explosion https://en.wikipedia.org/wiki/Principle_of_explosion