Hello Dan, On 15 Feb 2013, at 05:31, freqflyer07281972 wrote:

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Dear Bruno,I would like to know what 'doxastic models of consciousness' means,as well as what means "S4Grz" - I know Craig was the one whooriginally used the term 'doxastic models' but you seemed to knowright away what that meant, so I'd like to know from yourperspective what it means;

Epistemic = knowledge Doxastic = belief

`Epistemic logic are modal (most of the time) logics where the modal`

`box (here written with a B) represents a unary connector intended for`

`the knower (Bp = "the agent know p", or "I know p").`

`Doxastic logic are modal (most of the time) logics where the modal box`

`(here written with a B) represents a unary connector intended for the`

`believer (Bp = "the agent believes p", or "I believe p").`

`The main difference between knowledge and belief is that knowledges`

`are true, by definition, when beliefs can be false.`

`So among the axioms accepted for knowledge or epistemic logic, we have`

`that Bp -> p (I know p entails p is true).`

Contrariwise, modal doxastic logics will NOT have the axiom Bp -> p.

`For the ideally self-referentially correct machine I consider, the`

`belief B is modeled by provability. Before Gödel, most people`

`(mathematicians and philosophers) would have thought that in this case`

`we do have Bp -> p.`

`But as Gödel already remarked, the provability predicate, even in the`

`correct case, cannot be modeled by a (normal) modal logic having Bp ->`

`p. Indeed we would have Bf -> f, that is ~Bf, and that's consistency,`

`which cannot be proven by the machine, despite it being true. That's`

`why the logic of provability (belief) split into a true part and an`

`believable, or provable part.`

`But that is also why the Theaetetus definition works non trivially`

`when we define knowledge by Bp & p (that is I know p is I can justify`

`it, and it is the case that p). Bp & p implies trivially p, and in the`

`arithmetical setting we do get the classical modal logic of knowledge,`

`known as S4. Indeed we get S4 + a new "axiom":`

S4 is Know p -> p (main axiom for knowledge) Know p -> Know Know p (self-awareness, or introspective axiom)

`Know (p -> q) -> (Know p -> Know q) (rational "omniscience", more`

`used for "knowledgeable")`

`+ the logical inference rule (p/ know p). All this on the top of the`

`classical propositional logic.`

`In the arithmetical context, we inherit the following axioms, named`

`after a formula of Grzegorczyk, Grz):`

Know (Know (p-> Know p) -> p) -> p.

`It introduces a sort of antisymmetry on the Kripke accessibility`

`relations, and avoid circular structure (in the finite world case,`

`when used together with the other axioms). But there are other`

`semantics too.`

`Note that the Bp of G represent an arithmetical sentence (beweisbar`

`('p'), with beweisbar defining provability in arithmetic, and 'p'`

`being a representation in arithmetic of the sentence put for the`

`proposition p). We have no choice in the modal logic, and Solovay`

`provided the relevant completeness of G for the formal effective`

`theories, which correspond to the rich ideally correct machines.`

`For Bp & p, we have no similar direct definition in arithmetic, but we`

`can study them at the metalevel by modeling Bp & p for each individual`

`instantiated sentences, so "I know 2+2 = 4" is, in arithmetic:`

`beweisbar ('2+2=4') & 2 + 2 = 4.`

moreover, I want to know S4Grz or be pointed towards an advancedlevel logic book so I can understand what that means.

`S4Grz is quite well explained in Boolos 1979, and Boolos 1993.`

`Together with the logics of self-reference G and G*. Known also as GL`

`and GLS (Gödel, Löb, Solovay).`

`Boolos, G. (1979). The unprovability of consistency. Cambridge`

`University Press, London.`

`Boolos, G. (1993). The Logic of Provability. Cambridge University`

`Press, Cambridge.`

A good book on Modal logic is the book by Chellas:

`Chellas, B. F. (1980). Modal Logic, an introduction. Cambridge`

`University Press, Cambridge.`

`To get matter from arithmetic, we need to add a consistency condition`

`(so we get intelligible matter with Bp & Dt), and sensible matter with`

`Bp & p & Dt. This gives quantum-like logic. It is an open, but well`

`formulated problem to know if we get quantum computer from them, as we`

`should, if we are machine, and if the classical theory of knowledge is`

`correct, by the UD Argument.`

This is explained (concisely, with reference) in the sane04 paper: http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html

Finally, as a simple confirmation, I do assume that when you guystalk about Bp & p you mean the literal proposition "someone believesp & it is the case that it is p" --

OK.

if I don't get at least that, I should hang up my hat around here!

No worry :) Best, Bruno

On Wednesday, February 13, 2013 10:56:05 AM UTC-5, Bruno Marchalwrote:On 12 Feb 2013, at 20:05, Craig Weinberg wrote:When we talk about a Bp, relating to consciousness is that we aremaking an assumption about what a proposition is. In fact, if welook closely, a proposition can only be another level of B. p isreally nothing but a group of sub-personal Beliefs (logarithmicallynested as B^n)?which we are arbitrarily considered as a given condition...butthere is no given condition in actual experience.That's why we put Bp & p. To get the condition of 1p experience. Itworks as we get a non nameable, and non formalisable notion ofknowledge. S4 and S4Grz do succeed in meta-formalizing a thoroughlynon formalisable notion.All experiences are contingent upon what the experiencer is capableof receiving or interacting with.Any proposition that can be named relies on some pre-existingcontext (which is sensed or makes sense).The problem with applying Doxastic models to consciousness is notonly that it amputates the foundations of awareness,It does not for the reason above. Note that even Bp & p can lead tofalsity, in principle. Things get more complex when you add the nonmonotonic layers, that we need for natural languages and for themundane type of belief or knowledge. Here, of course, with the goalof deriving the correct physical laws; it is simpler to consider thecase of ideally correct machine, for which us, but not the machineitself can know the equivalence.Brunobut that the fact of the amputation will be hidden by the results.In Baudrillard's terms, this is a stage 3 simulacrum, (stage one =a true reflection, stage two = a perversion of the truth, stagethree = a perversion which pretends not to be a perversion).The third stage masks the absence of a profound reality, where thesimulacrum pretends to be a faithful copy, but it is a copy with nooriginal. Signs and images claim to represent something real, butno representation is taking place and arbitrary images are merelysuggested as things which they have no relationship to. Baudrillardcalls this the "order of sorcery", a regime of semantic algebrawhere all human meaning is conjured artificially to appear as areference to the (increasingly) hermetic truth.http://en.wikipedia.org/wiki/Simulacra_and_SimulationThis is made more important by the understanding that sense orawareness is the source of authenticity itself. This means thatthere can be no tolerance for any stage of simulation beyond 1. Inmy hypotheses, I am always trying to get at the 1 stage for thatreason, because consciousness or experience, by definition, has nosubstitute.Craig --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To unsubscribe from this group and stop receiving emails from it,send an email to everything-li...@googlegroups.com.To post to this group, send email to everyth...@googlegroups.com.Visit this group at http://groups.google.com/group/everything-list?hl=en.For more options, visit https://groups.google.com/groups/opt_out.http://iridia.ulb.ac.be/~marchal/ --You received this message because you are subscribed to the GoogleGroups "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?hl=en.For more options, visit https://groups.google.com/groups/opt_out.

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