Many thanks! I'll give my current attitudes to your hints: Bruno:

You mentioned the ASSA. Yesterday, motivdated by your hint, I have read about the ASSA/RSSA debate that is said to have divided the list into two camps. Since I have trouble with the reasoning I read, I will probably send a new message hoping for leaving the misunderstanding behind. Searching for the Universal Dovetailer Argument, I found a quite formal demonstration that you wrote in the list, and an even more formal demonstration that you published in the original work. I do see the advantage to have such a formal demonstration when it comes to detailed discussions, but sometimes I'd prefer a simplified outline to get the basic idea and the main conclusions before going into detail. If you have written such an outline (in English or in French as well) I would be thankful to get the link. Otherwise I'll read one of the formal versions in the future. Hal (and partially Russell): I still like your approach to the Everything ensemble using a countable set P of 'properties'. In fact, if we describe any object or world by a sequence of properties, the objects form a set equivalent to {0,1}^P (e.g. we assign 0 if the object does not have the property and 1 if it has the property) which is the power set of P (equivalently we could have formed subsets of P). Since P is countable, we can work with the Everything ensemble {0,1}^IN of infinite bitstrings. As you have mentioned, this set is uncountable. So far, there isn't any mathematical problem. In contrast to Marc, I do also agree identifying objects with the corresponding subset of P. In this picture, "states and behaviours" as Marc calls it, must also lie in the properties. Thus, the term 'property' is used in a more comprehensive sense than in programming. But now, we come to much more serious criticism. Russell noticed that regarding the ensemble of infinite bitstrings to be based on properties jumbles the ensemble (a simple mathematical entity) with interpretations by the observer. His separation between "syntactic" and "semantic" space is essential. I agree with Russell, but I do also see the necessity to interpret (not in an exact sense) mathematical entities in our theories within our "everyday theory"; because this is what makes a mathematical theory a (meta)physical theory as I have pointed out. Russell also uses such an interpretation, but on a more implicit level: An observer reads bits of the world's description. In order to make this a (meta)physical theory, we must be able to find ourselves within the theory, namely as observers. So, we must know what the process of reading bits of the word's description is meaning for us. And I'd say that it means measuring 'properties' of the world. To give a concise explanation: Properties should not be a fundamental ingredient to the mathematical theory. The mathematical theory uses "syntactic" space. Though, in order to understand the mathematical theory by means of the everyday theory (and thus to link the mathematical theory to "concrete reality"), we need (at some point of our theories) a translation. This translation can possibly be done by interpreting the ensemble via 'properties'. Conversely, we can motivate the ensemble of infinite bitstrings (ant thus "syntactic" space) starting from a countable set of 'properties'. Maybe it would be the best for your theories, Hal, to interrupt after having motivated the ensemble of infinite bitstrings. Then, the infinite bitstrings are considered to be fundamental (and no longer the properties themselves). Russell (and surely others, too) has provided a good framework to work with this ensemble and the role of observers. Perhaps, you can try to translate some of your ideas to Russell's more strict and formal language. Then, it will be easier for us to follow your thinking. Marc: Thank you very much for the definitions. I did not know how this was commonly called. Brent: I do still defend extensional definitions even for infinite sets. Mathematics shows how useful this is. I come back to the example of a real function f that maps every real number to another real number. In mathematics, this function is defined by the infinite set {(x,f(x)); x being a real number}. And the space of all these functions has very nice mathematical properties, we can work with it and prove theorems. Of course, in practice I will not have the set but merely a formula defining f. For example f(x)=x+1. But this does not disprove the possibilty of working with the sets on an abstract level. Mathematics indeed proves that it is possible. Your second point, Russell's ("Bertie's") paradox, is much more striking. In fact, if we allow every property the English (or the German, following Cantor) language can express, we will end up with contradictions. This is why the set of properties is somehow restricted. We need, as I wrote, "a set of distinct and independent properties". I don't really know if such a postulate makes sense. Youness Ayaita --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---