Hi Ronald,
On 19 Dec 2008, at 14:31, ronaldheld wrote: > > Bruno: > I may have missed something in the last two days. > I still do not understand. You say this starts with the real world, > which to me is the physical universe/Multiverse, but it actually > starts with arithmetic. Your remark is a bit "out of the reasoning", and as such is a bit unclear to me. The reasoning start from the mechanist hypothesis, which I take as the willingness to accept an artificial digital brain, with all the usual local sense of the world. It is a quasi-operational definition. Strictly speaking this does not presuppose your immateriality, still less the immateriality of the physical universe, this will appear in the conclusion of the reasoning. I suggest that you follow the KIM thread and that you interrupt when anything seems unclear to you. Meanwhile I sketch (only) basic explanation below. > How is there any mathematics with nothing to > conceive of it? I am afraid that, Like Einstein and some other physicists, you have a "conventionalist" view of mathematics. This explain probably why Einstein never commented on the work of Gödel (despite their friendship in Princeton). The work of "modern" logician is just NOT understandable by any "mathematical-conventionalist". I could argue that many results by logicians, including the incompleteness phenomenon, sign the end of the very possibility of conventionalism. So, to answer your question, now we have very good reason to believe that mathematics has something to conceive of it: a mathematical reality. The clearer way to see this is probably the discovery that the realm of the natural numbers, conceived together with their additive and multiplicative structure, escapes the power of any (axiomatizable) theory. There is just no complete theory of everything capable of just enumerating the truth about numbers. The reality of numbers escape our theoretical power, and provably so if we add the hypothesis that we are machines (or even super-machines or super...super-machines: the result is quite general). So mathematics has a proper field of study that we can aptly call the mathematical reality. Now we know that such a reality is an infinite reservoir of surprises. Even the apparently less rich arithmetic is such an infinite reservoir. > What are the computations running on, where did the > program come from and still what is it running on. It should still > take a net amount of enegry to run computations. If we abstract from the fact that in practice we have to write program and data, and read the results, it can be shown that computation per se does not need energy. There exist purely reversible universal computer. They compute without dissipating any energy. For example they never erase information, because it has been shown that this necessarily dissipate heath. But of course this is a physicalist answer, and has nothing to do with the fact that, if we assume comp, eventually energy itself is an emergent phenomenon, and that energy, as time and space will emerge from the mind, and the mind itself emerges from the computations. So, where does those computations come from? The computations are encoded, in many different ways, in the additive and multiplicative relations which exists among the natural numbers. So if you agree that a truth like "34 is an even number" or "17 is a prime number" is an atemporal truth not depending on anything contingent, the I could show to you that all the propositions having the shape of "the machine with number X stop on input Y after 3456655409812228 steps" are true or false and this independently of us in the same sense as above. Those truth are atemporal, even "aphysical", yet, machine will develop many growing set of "beliefs" about time, space and actuality (and discourses about things like that), albeit such development itself is atemporal and aspatial if I can say. Hope this helps, if not, just follow the slow explanation to Kim. Those explanations are slow because I am willing to work on any infinitesimal details, so please feel free to ask anything. Well, to be sure, the explanations are also slow because Kim and me appreciate to digress, also, but that's part of the fun. 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 -~----------~----~----~----~------~----~------~--~---
