At dinner last night, Kit Fine mentioned that the following modal principle can be found in Aristotle. (I think he said it is in _Metaphysics_ Theta, but I could be misremembering.)

A: L (MA -> MB) -> L (A -> B)

As always here, we use L for box and M for diamond. The boxes here take narrow scope with respect to the main arrow.

He also said that A plus KT leads to modal collapse. That is, with those three principles, you can prove p Lp. This is true, but it’s actually quite a bit harder than it may first appear. So the entire point of this post is to give those of you who like Saturday morning logic puzzles a logic puzzle to work on: prove p Lp in the logic KTA.

Kit also said that the logic KA, without T, has a number of interesting properties, but trying to reproduce what was said at dinner on the blog would be pointless I fear, so you’ll have to wait until he writes about that.