Thanks for your reply. I have a lot to say, so let me try to rate my breath, as it were.
1. It is nice to hear a human say this is uncharted territory. Since I am not in a graduate school now and have no affiliation, my research resources are limited compared to having free access to basically any relevant publication. I really had no idea if this was charted territory; if it was, that shoots down it being potentially used as part of a PhD problem (which I'm considering going for, but others have convinced me I'd have to move to Europe which is exceptionally logistically hard for me due to strong unmovable attachments, if you will -- I'm +not+ a 20-something person without a family, and such). 2. I appreciate immensely the last line of your message. Over the years, I've asked many authors something like, "do you think Russell's paradox might be false in other logics" I got, let's say, an extremely condescending response, and so forth. I'm not expecting praise, by God, just to not be condescended to. I suppose that is why I was touchy when I perceived someone totally derailing this line of discussion and that being continued by the third poster. My bad. I think my main improvement, while not really coming close to really answering my question, was changing the goal from prove Russell's Theorem is not always true to asking the question "Is Russell's Theorem true in all logics?" A bonus seems that now there is a theoretical physics, by way of the MUH, motivation for answering this question. 3. On that note, Physics/Philosophy actually what inspired me to go in this direction. I was mainly, back then when this idea of trying to find a consistent universal set theory occurred to me, trying to answer a intended-to-be serious argument against the existence of the universe. I was stunned at the notion that someone was trying to prove the universe does not exist. I think they were asserting some form of solipsism. In a nutshell, here was their argument. My opinion is that it is not at all formal but very clever and probably persuasive but, ultimately, like the many clever "proofs" that 1=2 and such. It's just going to be convincing to those who aren't vigorously attacking the argument, which I soon did. <begin their argument for the non-existence for the universe> Definition: To contain means <insert something most people would accept here>. The notation and word for 'is contained in' is is<in. Thing and exists are undefined or ... acceptably defined only be common intuitive sense of what a thing is, but neither formally (in her argument) Definition: the universe (call it U) is a thing that has the property that it contains all things, notated by (x) (x is<in U), where x is a thing. Theorem: If the universe exists then the (three or so) axioms of binary logic are inconsistent. Proof: The method is to show that if U exists then there is a logical statement (ie, a WELL FORMED formula) that is true if and only it is false, being simultaneously, to abuse language, true and not true, which violates the +definition+ of the words not and and. Suppose U exists. Then apply Russell's approach. Given how broad and vague 'thing' is defined, let's discuss the thing, call it S, this thing called S is the thing that contains all things that don't contain themselves. In the notation, let S be the thing (given the vagueness of 'thing', S is a thing) such that (x) (x is<in S if and only if x!<x). In other words, S is the thing such that for all things x, x is contained in S if and only if x is not contained in x. Since we wrote (x), then apply to S by an application of some universal quantifier rule, which most people would accept (and maybe they should qualify the universal sometimes) to S. Then you get, just as Russell's approach: (S is<inS if and only if S!<S). This contradiction proves the theorem. That if the universe exists, then binary logic is inconsistent. Corollary: The universe does not exist. "Proof:" Binary logic is consistent, therefore, by contraposition of the theorem, the universe does not exist. <end their argument for the non-existence for the universe> I've been banging away at this keyboard for a while so I'll post this and take a break. The idea came to me when I tried basically to prove her argument that the universe does NOT exist, wrong. It occurred to me that three truth values are sufficient to make the usual proof by contradiction +not a tautology+. And, therefore, even in 3-valued logic, her argument fails. Obviously, that doesn't prove the universe does exist, it just proves her argument that is doesn't is wrong. <end their argument for the non-existence for the universe> On Mar 23, 2:14 am, James N Rose <[EMAIL PROTECTED]> wrote: > Brian, > > Your inquiries about FL is an uncharted but important one. > > I'd like to suggest though that your approach is too > conventional and 'consistency' is not the ultimate > criteria for evaulating it's connection with validity > or more importantly - feasability - in context with > 'logic' - and mathematical value judgements. > > I've taken a wholly different/radical approach which > has been productive. "Existential Probability" is a > strong and broader base to use and in general is > an umbrella-space for all logic systems. I call the > most generalized form "Stochastic Logic". It has the > interesting attribute of placing FL and QM on a par, > in the scheme of things, with direct connection with > Boole, and Aristotelian logic before-that. > > In historical framing, it can be seen that the earliest > logics were limited-specific-condition logics and that > each new step was toward 'improved generalization'. > > The leap that FL makes is removing the boundaries of > the probability space and pushing toward a 'logic' > system that copes with Cantorian infinities and > transfinites. It pushes towards plural-criteria > logic (what you've indicated as akin to Multi-modal). > > It is a critically important step that out-paces > all the conventional analysis. Think of it as the > tool to developing utile computation/description > methods for 'logic' evaluation of the (so far) > intractible "many bodied" problem. Complexity math > is one way of coping with -some- factors of many-bodied > systems, but even that math hasn't been fully scrutinized > or (logically) evaluated for kladistic characteristics > yet. I've looked some of the equation forms and found > some interesting things going on in 'recursion' equations > that relate to breaking away from 'zero to one' boundary > restriction. > > I discuss a bit of it in general vernacular at > > <http://www.ceptualinstitute.com/uiu_plus/uiu05charting.htm> > > Feel free to contact me directly at integrity @ prodigy.net > (remove the spaces) if you'd like to discuss in more detail. > > I made an effort several years ago to get Lotfi Zadeh speaking > with Herb Simon (just before he died) in the hopes that traditional > and leading edge probability theories could find commonality. > > They did talk some but nothing definitive or fruitful came > from it - mainly because each had too much vested interest > in separate academic venues. And because second and third > generation 'probabilists' were so dedicated to their particular > stances on 'how the math "should" be done', instead of opening > themselves to combining the methodologies into a grander > schemata - it's going to take someone or someones with -your- > sensibility and intuitions to make it happen. :-) > > Jamie Rose --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---