Carroll's note What Achilles Said to the Tortoise holds many lessons, many of which related to putative justification - or lack of justification - for basic logical inferences. Recently, Romina Padro, pulling from coursework and discussions with Kripke, has argued one more lesson should be added to the list, namely, that under certain conditions adopting basic logical inferences is impossible. I've a few thoughts on this new lesson, in particular how it might play with the old lessons. Check it out a recent draft here!