On 24 Oct 2013, at 00:15, meekerdb wrote:

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On 10/23/2013 9:34 AM, Bruno Marchal wrote:On 23 Oct 2013, at 17:39, Craig Weinberg wrote: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. Suchstatements are called "true contradictions", or dialetheia.Dialetheism is not a system of formal logic; instead, it is athesis about truth, that influences the construction of a formallogic, often based on pre-existing systems. Introducingdialetheism has various consequences, depending on the theory intowhich it is introduced. For example, in traditional systems oflogic (e.g., classical logic and intuitionistic logic), everystatement becomes true if a contradiction is true; this means thatsuch systems become trivial when dialetheism is included as anaxiom. Other logical systems do not explode in this manner whencontradictions are introduced; such contradiction-tolerant systemsare known as paraconsistent 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 problemby accepting the contradictions as true. Dialetheism allows forthe unrestricted axiom of comprehension in set theory, claimingthat any resulting contradiction is a theorem.It occurs to me that MWI is a way of substantiating dialetheism asa physical reality...in order to avoid having to internalize thepossibility of dialetheism metaphysically.No problem with that. Like Everett restore 3p-determinacy, comprestore also non-dialetheism, metaphysically, but does not (andcannot) disallow it it in some machine's mind.G* says it; D(Bp & B~p), or <>([]p & []~p). read: it is consistentthat p is believed and that ~p is believed, by the Löbian machine.The machine cannot know that, note.Sure. That's because logic assumes that if p<=>q then q can besubstituted for p. Hence if you believe the morning star is agoddess and the evening star is a planet, you may believe acontradiction - but not if you know it.

`That is a bit unclear to me. Substitution of equivalent if always`

`dangerous in modal contexts. The reason is perhaps more prosaic, which`

`is that a machine who believe in its inconsistency believes in some`

`infinite ("non-standard) number(s), she agrees that 0 is not Gödel`

`number of a proof of f, nor are 1, 2, 3, ... , but yet she believes in`

`some number representing a proof of f.`

`Humans have a big non monotonical logic layers, making them able to`

`say "I was wrong", and able to revise previews opinions.`

`Evolution might exploit truth and relative lies too. That leads to`

`complex questions.`

`Correcteness is when you forget all the lies, and nothing more. If you`

`survive that, you get Löbian by necessity, and your physics will not`

`change, normally (with comp).`

`No doubt that human actual theologies are more complex than the`

`theology of the correct universal machine, platonist, and believing`

`not in much more than the universal base (number, or combinator,`

`or ...).`

`But PA, ZF, are only sort of "Escherichia Coli" of the person. They`

`get personhood by the intensional nuances of the "provability"`

`predicate. Detrivializing their physics and theology (the simplest`

`one as it might be, but it is already quite rich).`

`Look how much information we already get in the UDA, where a person is`

`defined by just the accessible memory (the diary "entangled" though`

`their accompaniment in the annihilations and reconstitutions).`

`In the arithmetical version, a person is defined by a universal number`

`with enough introspection and induction ability. PA and ZF are "well`

`known" typical example. And incompleteness allows to define a notion`

`of knowledge associate to them, and a notion of observation.`

`We all have a Löbian part, as believer in PA's axioms, for example. I`

`think that that part is already conscious when we assume consciousness`

`is invariant for the genuine universal digital substitution. The`

`universal machine defines a canonical universal person, and the Löbian`

`one, which knows, in some weaker sense that the Theaetetus' one, that`

`they are (Turing) universal.`

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.