Posts: 3226
Threads: 244
Joined: April 17, 2012
Reputation:
54
Dialetheism
July 26, 2012 at 11:31 pm
I started studying from a book that teaches deductive logic with all the weird symbols. It has a chapter that introduces a concept called dialetheism which from what I understand basically says in some cases sentences can be both true and false, or neither, at the same time. I don't really understand it but it's fascinating and I'm going to study it more in the future.
http://en.wikipedia.org/wiki/Dialetheism
My ignore list
"The lord doesn't work in mysterious ways, but in ways that are indistinguishable from his nonexistence."
-- George Yorgo Veenhuyzen quoted by John W. Loftus in The End of Christianity (p. 103).
Posts: 242
Threads: 7
Joined: May 6, 2012
Reputation:
17
RE: Dialetheism
July 26, 2012 at 11:37 pm
Fascinating. Thanks for the link. I'm not formally trained in pragmatics or semantics (it's really not my area), but this definitely has ties with those aspects of linguistics.
![[Image: hoviksig-1.png]](https://images.weserv.nl/?url=i82.photobucket.com%2Falbums%2Fj241%2FDieste%2Fhoviksig-1.png)
Ex Machina Libertas
Posts: 3989
Threads: 79
Joined: June 30, 2009
Reputation:
41
RE: Dialetheism
July 30, 2012 at 12:40 pm
You ever get the feeling that some things exist just because some english major wanted a Phd?
Posts: 271
Threads: 27
Joined: February 8, 2012
Reputation:
6
RE: Dialetheism
July 30, 2012 at 1:07 pm
(July 26, 2012 at 11:31 pm)teaearlgreyhot Wrote: in some cases sentences can be both true and false, or neither, at the same time.
schrodinger's logic ?
Posts: 81
Threads: 1
Joined: February 21, 2011
Reputation:
3
RE: Dialetheism
July 30, 2012 at 10:59 pm
Interesting. Does that make dialetheisms the philosophical and semantic equivalent of zero?
"Listen, strange women lying in ponds distributing swords is no basis for a system of government! Supreme executive power derives from a mandate by the masses, not some farcical aquatic ceremony!"
- Dennis the peasant.
Posts: 532
Threads: 5
Joined: January 30, 2012
Reputation:
5
RE: Dialetheism
July 31, 2012 at 1:54 am
(This post was last modified: July 31, 2012 at 1:55 am by CliveStaples.)
(July 30, 2012 at 10:59 pm)toro Wrote: Interesting. Does that make dialetheisms the philosophical and semantic equivalent of zero?
Introducing dialetheism into any system that has the axiom of non-contradiction makes the system trivial--every statement, as well as its negation, is true. So you could think of it as "multiplication by zero", kinda-sorta-not-really.
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.
(July 30, 2012 at 12:40 pm)Rhizomorph13 Wrote: You ever get the feeling that some things exist just because some english major wanted a Phd?
BECUZ EVERRTHIN IS SIMPUL LAWGIC, RIGHT BOYS?!?!
“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.”
Posts: 169
Threads: 7
Joined: January 25, 2012
Reputation:
4
RE: Dialetheism
July 31, 2012 at 3:32 pm
(This post was last modified: July 31, 2012 at 3:35 pm by Categories+Sheaves.)
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...
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. I did cringe, but it's also nice to know I'm not the only one here who likes ring theory.
Linky to the nontrivial systems?
So these philosophers were all like, "That Kant apply universally!" And then these mathematicians were all like, "Oh yes it Kan!"
Posts: 532
Threads: 5
Joined: January 30, 2012
Reputation:
5
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...
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. I did cringe, but it's also nice to know I'm not the only one here who likes ring theory.
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.”
|
