Trodding over the Propositional Calculus, I've nearly stumbled at the Switcheroo rule:
" and <~x implies y> are interchangeable".

The rigorist in me (which was probably born back during my freshman year in the MSU, when I've got the lower mark for my calculus exam for forgetting to state the condition which seemed obvious) only agrees to accept this rule together with the condition that x≠y. Otherwise it doesn't make sense. Yet Hofstadter seems to just assume it by default!

I am a Tortoise, sort of :)

PS. That is what the "Ganto's ax" tale might be about, by the way: in Tao, everything is assumed to be the same, therefore the rules of formal logic (or at least, this rule) wouldn't apply, and their implications wouldn't apply either.