My paper has been published and should be available on the site of Elsevier (not freely, except if your institution has a free acces on Elsevier Journals).
The official reference are:

Marchal B. Theoretical computer science and the natural science, Physics of Life Reviews, Vol 2/4, pp. 251-289.

I will probably be busy until end of January. In the meantime I can give little exercises and then correct it. I know that a mailing list is not necessarily the best place for teaching. I do it because, at least concerning the approach I'm following, it is a path which can hardly be avoided. But I'm sure also this can be useful for a deepening of many everything-like issues, even if just to introduce the work of David Lewis (one of the main non quantum many-worlders).

Stathis has already shown that IF (W,R) is reflexive THEN (W,R) respects Bp -> p. And Tom Caylor agrees that IF (W,R) is symmetric THEN (W,R) respects p -> BDp.

Is it OK for everyone?
Tom, Stathis, could you show the inverse ? That is:
IF (W,R) respects Bp -> p, THEN the multiverse is reflexive.
IF (W,R) respects p -> BDp, THEN the multiverse is symmetric.

Could you show that all multiverse (W,R) respects B(p -> q) -> (Bp -> Bq) ?

I recall that a multiverse (W,R) respects a formula A if A is true in all illuminated (W, R, V). That is, whatever the illumination you choose (= whatever the value of the sentence letters you choose in each world) A is true in all the world of the multiverse.

Please feel free NOT trying to solve those problem. First the UDA, which is not technical, is enough, it seems to me, for a complete understanding that comp entails the reversal between physics and computer science/machine-psychology/theology (we can discuss naming issue later(*)). The math is needed ONLY for making *explicit* the derivation of physics from comp, showing that comp (or weaker) is a scientific hypothesis, i.e. comp is testable.

(*) Well, I'm certainly interested in that naming issue, and perhaps I could ask you right now what expression do you find the less shocking:
"Physics is derivable from machine psychology", or
"Physics is derivable from machine theology"  ?
'course, you can put "computer science" or "number theory" instead of machine psycho or theology, but then the reference to a soul or a person is eliminated, and giving the current tendency of many scientist to just eliminate the person from the possible object of rational inquiry, I prefer to avoid it. Note that in "conscience and mechanism" I have used the expression "theology", and in "computability, physics and cognition", I have been asked to use "psychology" instead. I find "theology" much more correct and honest, but then I realise (empirically) that it it could seem too much shocking for some people (especially the atheist). What do you think? I have already avoid "metaphysics" because it is confusing in the metamathematical (Godelian) context, and also I'm in a country where the word "metaphysics" already means "crackpot". Does the word "theology" means "crackpot" in some country ? I don't think so, but please tell me if you know about such practice.


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