On 22 Nov 2012, at 19:26, Stephen P. King wrote:

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Dear Friends,In my research for my earlier post (Re: Nothing happens in theUniverse of the Everett Interpretation) I found the following:From http://en.wikipedia.org/wiki/Hierarchy_of_beliefs Hierarchy of beliefs"Construction by Jean-François Mertens and Zamir implementing withJohn Harsanyi's proposal to model games with incomplete informationby supposing that each player is characterized by a privately knowntype that describes his feasible strategies and payoffs as well as aprobability distribution over other players' types.Such probability distribution at the first level can be interpretedas a low level belief of a player. One level up the probability onthe belief of other players is interpreted as beliefs on beliefs. Arecursive universal construct is built—in which player have beliefson their beliefs at different level—this construct is called thehierarchy of beliefs.The result is a universal space of types in which, subject tospecified consistency conditions, each type corresponds to theinfinite hierarchy of his probabilistic beliefs about others'probabilistic beliefs. They also showed that any subspace can beapproximated arbitrarily closely by a finite subspace.Another popular example of the usage of the construction is thePrisoners and hats puzzle. And so is Robert Aumann's construction ofCommon knowledge (logic)."I think that we can identify the concept of a "privately knowntype" with the concept of 1p as discussed in the UDA. My concept ofa "reality" as that which is incontrovertible for some finitecollection of 1p can also we seen as synonymous with Aumann's CommonKnowledge which was mentioned above:"Common knowledge is a special kind of knowledge for a group ofagents. There is common knowledge of p in a group of agents G whenall the agents in G know p, they all know that they know p, they allknow that they all know that they know p, and so on ad infinitum."Bruno seems to use a radically flattened version of this idea -as do most logicians - where the 'players' have complete knowledge(ala Bp&p) of each other.

?

`Bp & p is not complete knowledge. Dt is true, but BDt & Dt is false,`

`for example.`

I see this as the natural reaction to the implications of the ideaof incomplete knowledge. We see a nice discussion of this here: http://plato.stanford.edu/entries/nonwellfounded-set-theory/harsanyi-type-spaces.html"Type spaces are mathematical structures used in theoreticalparts of economics and game theory. The are used to model settingswhere agents are described by their types, and these types give us“beliefs about the world”, “beliefs about each other's beliefs aboutthe world”, “beliefs about each other's beliefs about each other'sbeliefs about the world”, etc. That is, the formal concept of a typespace is intended to capture in one structure an unfolding infinitehierarchy related to interactive belief.John C. Harsanyi (1967) makes a related point as follows:It seems to me that the basic reason why the theory of games withincomplete information has made so little progress so far lies inthe fact that these games give rise, or at least appear to giverise, to an infinite regress in reciprocal expectations onthe part of the players."My claim is that we can avoid the problems of infinite regressby both taking the possibility of regress seriously andunderstanding that beliefs are the result of processes that involvethe consumption of resources.

`You need a linear logic for this, but you cannot impose it, you have`

`to get it from the material hypostases, so as to be able to`

`distinguish the quanta and the qualia. if not you are just doing`

`physics, and lost the relation with the mind body problem, as`

`formulated by the UDA.`

No activity of a mind -thought- can be said to occur without theoccurrence of work. Thought is an activity and does not just'exist'. Existence per se is property neutral, therefore to speak ofthe content of thought we must not ignore the requirements ofdiscovering what it might be. The same solution to the homunculusproblem that Roger and I have discussed previously applies: if thereis a finite quantity of resources or, equivalently, physical workinvolved in the implementation of a homunculus then there can onlybe a finite number of them.There is no problem in the infinite case that Bruno isconsidering because it can be collapsed with Kleene's theorems, butin so doing we make the possibility of distinguishing one mind fromanother (within a plurality of minds) vanish.

?

The measure problem that Bruno complains about is the direct resultof assuming perfect knowledge aka omniscient mind. This is a solubleproblem but to find solutions we must give up the idea of accessibleprefect knowledge.

`I do not complain on the measure problem. It is what all everythingers`

`agree on. Then I show that comp makes the problem both:`

1) equivalent with deriving physics from arithmetic/computer science,

`2) completely formulable in arithmetical terms, by using the`

`traditional definition of knowledge.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.