On 23 Oct 2013, at 17:39, Craig Weinberg wrote:

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http://en.wikipedia.org/wiki/DialetheismDialetheism is the view that some statements can be both true andfalse simultaneously. More precisely, it is the belief that therecan be a true statement whose negation is also true. Such statementsare called "true contradictions", or dialetheia.Dialetheism is not a system of formal logic; instead, it is a thesisabout truth, that influences the construction of a formal logic,often based on pre-existing systems. Introducing dialetheism hasvarious consequences, depending on the theory into which it isintroduced. For example, in traditional systems of logic (e.g.,classical logic and intuitionistic logic), every statement becomestrue if a contradiction is true; this means that such systems becometrivial when dialetheism is included as an axiom. Other logicalsystems do not explode in this manner when contradictions areintroduced; such contradiction-tolerant systems are known asparaconsistent logics.Graham Priest defines dialetheism as the view that there are truecontradictions. JC Beall is another advocate; his position differsfrom Priest's in advocating constructive (methodological)deflationism regarding the truth predicate.Dialetheism resolves certain paradoxesThe 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 theoriesbecause they cause the theories to explode—if a contradiction istrue, then every proposition is true. The classical way to solvethis problem is to ban contradictory statements, to revise theaxioms of the logic so that self-contradictory statements do notappear. Dialetheists, on the other hand, respond to this problem byaccepting the contradictions as true. Dialetheism allows for theunrestricted axiom of comprehension in set theory, claiming that anyresulting contradiction is a theorem.It occurs to me that MWI is a way of substantiating dialetheism as aphysical reality...in order to avoid having to internalize thepossibility 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.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.