RE: Dialetheism
July 31, 2012 at 5:12 pm
(This post was last modified: July 31, 2012 at 5:13 pm by CliveStaples.)
(July 31, 2012 at 3:32 pm)Categories+Sheaves Wrote: Reminds me of a scene in Youth Without Youth (Coppola + Eliade) where the protagonist talks to his girlfriend about how there are actually four truth-states a statement can have: it can be true, it can be false, it can be simultaneously true and false, or it can be neither true nor false.
...and then they pursue the issue no further. I wanted to see some nontrivial use of paraconsistent logic. but no dice.(July 31, 2012 at 1:54 am)CliveStaples Wrote: ...kinda-sorta-not-really...I did cringe, but it's also nice to know I'm not the only one here who likes ring theory.
But there are non-trivial systems which implement dialetheism. So I guess you could think of these as non-integral domains, if you want to keep abusing mathematical terminology.
Linky to the nontrivial systems?
Well, I doubt it's anything you haven't already read, but this page has what looks like a formal approach to constructing such a system:
http://plato.stanford.edu/entries/logic-paraconsistent/
Since the principle of explosion relies on certain tautologies that can be deduced from the law of non-contradiction (I'm not sure if the Excluded Middle is also required), it seems the thought is to somehow deny an axiomatic law of non-contradiction in order to prevent explosion.
“The truth of our faith becomes a matter of ridicule among the infidels if any Catholic, not gifted with the necessary scientific learning, presents as dogma what scientific scrutiny shows to be false.”
