@atlanta_amyish @KevinMKruse@dandrezner Obviously I don't know you or the exact level of your deference and respect for doctors and lawyers, but I have a feeling you would be well advised to trust them a little less than you do right now.
@JDHamkins I wish I had time to think more about these things. Maybe I should've been a logician. Anyway, thanks for the fun puzzles and please don't feel obliged to respond to these ramblings.
@JDHamkins But I guess my point is that in that puzzle, the proof (so far as I am recalling it correctly) exploits something recursive in the nature of the problem. Could there be a similar problem whose solution really does *require* reasoning directly about (knowledge-about-)^n?
@JDHamkins But it made me wonder if some people have a facility for knowledge-about-knowledge, or if it can be cultivated. Or rather if it is more like our inability to parse iteratively imbedded phrases like "dogs dogs dogs dogs bite bite bite bite,"