Ming? Was that you???
On Wed, Oct 23, 2013 at 11:07 AM, Craig Weinberg <whatsons...@gmail.com>wrote:
> 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<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
>> 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
>> http://iridia.ulb.ac.be/~**marchal/ <http://iridia.ulb.ac.be/~marchal/>
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