On 04 Oct 2011, at 01:00, Russell Standish wrote:

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On Mon, Oct 03, 2011 at 05:31:21PM +0200, Bruno Marchal wrote:The states are countable, but not the (3-)states + the neighborhhood of (infinite) computations that you are mentioning yourselves. Not sure if I see where is the problem. It seems that you have answered it. The 1-OMs *are* set of histories, but with a particular 3-state, single out in the indexical way, and which will play the role of the "Bp". The "& p" will force the logic of the computational extensions to be different.The way I was talking about it, there is a 1:1 correspondence between the 3-states and the sets of histories making up the 1-OM. In that case the cardinality of 1-OM is the same as that of the 3-states - which you have already admitted is countable.

`OK, I see your point. You are right on this, and I should have`

`perhapssaid "set of sets of histories". This is related to the`

`possible semantics of the first person logics (S4Grz1).`

`The 1-OMs are mutiplied by the computations going through it, making`

`it as great as the continuum of those computations going through, and`

`that can be understood intuitively by UDA-like reasoning. This come`

`from the rule Y = I. To have the measure on the 1-OMs, we have to`

`count the computations going through, not the states themselves. So an`

`1-OMs can be defined just by one computations (perhaps infinite), but`

`this does not entirely work, and that is why we have to take into`

`account the structure imposed by the logic to which the first person`

`obeys.`

Perhaps I'm missing something? I don't quite get the "indexical" bit for instance.

`Examples of "indexical" are terms like "now, me, here, I, there".`

`Their meaning or referent depends on the locutor or of its current`

`(also an indexical) situation.`

`The 3-I of a machine, is an indexical, rather well handled by the`

`description of the machine as handled by the machine, like with`

`GĂ¶del's beweisbar "B". The precise (arithmetical contento of "B"`

`varies from one machine to another, but if the machine verifies some`

`conditions (rich, ideally correct, etc.) it obeys the same modal`

`logics (G, G*).`

`The "1-I" is similarly well captured by the conjunction of the 3-I and`

`truth (Bp & p). This is a drastic change, because that "I" is no`

`describable by the machine, it is *not* arithmetical, and it changes`

`the logic of self-reference (which becomes a logic of evolving states).`

`Sorry for having been unclear, but I continue to doubt about the`

`relevance of the term OMs terms. It did mislead me in my answer too`

`you, and I should stick on the person-views and their modalities.`

`Ask for any clarification. Nothing is really simple here. I will add`

`some info in my reply to Brent.`

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.