Meetup : First Cali, Colombia meetup
Discussion article for the meetup : First Cali, Colombia meetup WHEN: 02 July 2012 07:00:00PM (-0400) WHERE: Chipichape, Cali, Valle del Cauca, Colombia Specific Location: Juan Valdez Cafe inside Chipichape Mall http://lesswrong.com/lw/bc2/setting_up_lw_meetups_in_unlikely_places_positive/ motivated me to post this meetup on the off chance there are any LessWrongers in Cali, Colombia. Discussion article for the meetup : First Cali, Colombia meetup
Thanks Sam. I thought about this some more and realized where I went wrong - I was applying the deduction theorem incorrectly (as other comments in this thread have pointed out).
By the way, when you say that PA proves its own inconsistency, do you mean that PA⊢□(¬Con(PA)) or that PA⊢¬Con(PA)? From your reasoning I agree that if we assume ¬□C→C then we can arrive at PA⊢□C and PA⊢□(¬C), from which we can conclude that PA⊢□(¬Con(PA)). If you meant that PA⊢¬Con(PA) though, could you explain how you arrived at that?