Lovecraft's Lemma

Posted on May 27, 2019 by Jack Kelly
Tags: logic, fun

A few weeks back, some of us were working on a colleague’s chess problem. We’d made it partway to the solution, but had become stuck and started asking for hints. He told us that we’d already worked out every piece of information necessary to find the solution, and I pointed out that it is quite possible for a human to know p, q and p ∧ q ⟹ r without concluding r. We’ve since simplified this result and called it “Lovecraft’s Lemma”:

Lemma (Lovecraft’s Lemma): A human mind can believe p and p ⟹ q without necessarily believing q.

The name was chosen for two reasons: alliterative appeal, and this quote from The Call of Cthulhu:

The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents.

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