Le 09-mai-07, à 18:50, Brent Meeker a écrit :

## Advertising

> > Bruno Marchal wrote: >> >> Le 09-mai-07, à 09:08, [EMAIL PROTECTED] a écrit : >> >>> Of course reality doesn't change. The question of map versus >>> territory is *not* an all or nothing >>> question. *sometimes* the map equals the territory. Most of the >>> time >>> it does not. >> >> >> This is an important point where I agree with Marc. With or without >> comp the necessity of distinguishing the map and the territory cannot >> be uniform, there are "meaning"-fixed-point, like when a map is >> embedded continuously in the territory (assuming some topology in the >> map and in the territory, this follows by a fixed point theorem by >> Brouwer, which today admits many interesting computational >> interpretations. >> >> Bruno > > I don't think you can define a topology on "meaning" that will allow > the fixed point theorem to apply. A whole and rather important subfield of computer science is entirely based on that. It is know as denotational semantics. Most important contributions by Dana Scott. You can look on the web for "Scott domains". Or search with the keyword "fixed point semantics topology". Sometimes the topology is made implicit through the use of partial order and a notion of continuous function in between. Indeed the topological space used in this setting are not Hausdorff space, and are rather different from those used in geometry or analysis. A nice book is the one by Steve Vickers. It has provide me with supplementary reason to single out the Sigma_1 sentences as particularly important in the comp frame. (Topology via Logic, Cambridge University Press, 1989: http://www.amazon.ca/Topology-via-Logic-Steven-Vickers/dp/0521576512). Here are some links: http://www.ercim.org/publication/Ercim_News/enw50/schellekens.html http://www.cs.uiowa.edu/~slonnegr/plf/Book/Chapter10.pdf http://dimacs.rutgers.edu/Workshops/Lattices/slides/zhang.pdf I could say more in case I come back on the combinators. Cf: http://www.mail-archive.com/everything-list@eskimo.com/msg05958.html because there are strong relation between fixed point semantics, the paradoxical combinators, and the use of the (foirst and second) recursion theorem in theoretical computer science. But ok all that could become very technical of course. ... I thought you knew about fixed point semantics, perhaps I miss your point ... 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 [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---