tag:blogger.com,1999:blog-3891434218564545511.post895519985488256761..comments2021-05-11T22:37:51.522-05:00Comments on Alexander Pruss's Blog: Grounding graphsAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3891434218564545511.post-55448984304172323412012-08-10T15:46:03.104-05:002012-08-10T15:46:03.104-05:00Yeah, I shouldn't have said "non-initial...Yeah, I shouldn't have said "non-initial" in Universality. Thanks for catching that.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-55608970412710476312012-08-10T15:25:13.329-05:002012-08-10T15:25:13.329-05:00Unless I'm mistaken-- and I very well may be--...Unless I'm mistaken-- and I very well may be-- it appears to be impossible for a graph to satisfy these axioms. Suppose there is such a graph g. Then by well-foundedness, there will have to be some proposition-- call it p-- which is fundamental (initial) in g; p will be true (by Truth), and by Absoluteness of Fundamentality, there is no graph in which p is non-initial. But by Universality, given that p is true, there is a graph in which p is non-initial. Contradiction.Brian Cutterhttps://www.blogger.com/profile/17059155559949747916noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-52621619391797048732012-08-09T22:21:53.485-05:002012-08-09T22:21:53.485-05:00Perhaps the problems with (1) and (2) come from th...Perhaps the problems with (1) and (2) come from their nature as statements that other truth statements are true: they are meta-grounding statements.<br /><br />Most paradoxes of truth values come from using statements about truth to speak about truth value itself, rather than data.Williamhttps://www.blogger.com/profile/12533263841520213358noreply@blogger.com