On Wednesday, October 23, 2013 12:34:05 PM UTC-4, Bruno Marchal wrote:
> On 23 Oct 2013, at 17:39, Craig Weinberg wrote: 
> > http://en.wikipedia.org/wiki/Dialetheism 
> > 
> > Dialetheism is the view that some statements can be both true and   
> > false simultaneously. More precisely, it is the belief that there   
> > can be a true statement whose negation is also true. Such statements   
> > are called "true contradictions", or dialetheia. 
> > 
> > Dialetheism is not a system of formal logic; instead, it is a thesis   
> > about truth, that influences the construction of a formal logic,   
> > often based on pre-existing systems. Introducing dialetheism has   
> > various consequences, depending on the theory into which it is   
> > introduced. For example, in traditional systems of logic (e.g.,   
> > classical logic and intuitionistic logic), every statement becomes   
> > true if a contradiction is true; this means that such systems become   
> > trivial when dialetheism is included as an axiom. Other logical   
> > systems do not explode in this manner when contradictions are   
> > introduced; such contradiction-tolerant systems are known as   
> > paraconsistent logics. 
> > 
> > Graham Priest defines dialetheism as the view that there are true   
> > contradictions. JC Beall is another advocate; his position differs   
> > from Priest's in advocating constructive (methodological)   
> > deflationism regarding the truth predicate. 
> > Dialetheism resolves certain paradoxes 
> > 
> > The Liar's paradox and Russell's paradox deal with self- 
> > contradictory statements in classical logic and naïve set theory,   
> > respectively. Contradictions are problematic in these theories   
> > because they cause the theories to explode—if a contradiction is   
> > true, then every proposition is true. The classical way to solve   
> > this problem is to ban contradictory statements, to revise the   
> > axioms of the logic so that self-contradictory statements do not   
> > appear. Dialetheists, on the other hand, respond to this problem by   
> > accepting the contradictions as true. Dialetheism allows for the   
> > unrestricted axiom of comprehension in set theory, claiming that any   
> > resulting contradiction is a theorem. 
> > 
> > It occurs to me that MWI is a way of substantiating dialetheism as a   
> > physical reality...in order to avoid having to internalize the   
> > possibility of dialetheism metaphysically. 
> No problem with that. Like Everett restore 3p-determinacy, comp   
> restore also non-dialetheism, metaphysically, but does not (and   
> cannot) disallow it it in some machine's mind. 
> G*  says it; D(Bp & B~p), or <>([]p & []~p). read: it is consistent   
> that  p is believed  and that ~p is believed, by the Löbian machine.   
> The machine cannot know that, note. 
> Well, don't take this too much seriously. My problem is that you need   
> to do the math to evaluate how much seriously you can take this remark. 
> Note that in machines' theology, some theorem cannot be proved without   
> the reduction to contradiction, so that it misses them. (Unlike   
> intuitionism which can still get them by the use of the double   
> negation). 
> Classical logic is the simplest logic to (re) discover the many non   
> classical logics of the realities/dreams. 

"My problem is that you need   
to do the math to evaluate how much seriously you can take this remark."

Under comp, why couldn't I just imagine tasting the flavor of the math 


> Bruno 
> http://iridia.ulb.ac.be/~marchal/ 

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