A. Wolf wrote: >> I'm well aware of relativity. But I don't see how you can invoke it when >> discussing all possible, i.e. non-contradictory, universes. Neither do I see >> that list of states universes would be a teeny subset of all mathematically >> consistent universes. On the contrary, it would be very large. It would >> certainly be much larger than that teeny subset obeying general relativity or >> Newtonian physics or the standard model of QFT in Minkowski spacetime. > > You said: "So universes that consisted just of lists of > (state_i)(state_i+1)... would exist, where a state might or might not > have an implicate time value." > > I was trying to express that the universe in which we reside isn't > separable into a set of lists of states. It's more mathematically > complex than that. > > Some mathematical models are self-contradictory, and some are not. > This is true regardless as to how you formulate a foundation of > mathematics, and it forms the basis for understanding and proving > mathematical truths. I believe that a mathematical structure complex > enough to capture the entire set of events that define a universe must > be non-self-contradictory to be a truthful model for that universe. > There are mathematical structures which are self-contradictory because > they are predicated upon axioms which ultimately contradict > themselves; these structures are not well-defined and cannot be a > basis for existence. Such a basis would make existence itself > ambiguous, because all things would have to exist and not-exist at the > same time, and not in the quantum way--with no discernable structure > or foundation at all. > > I'm not certain what you're trying to argue, but it seems like you > think that anything you can imagine must have a well-founded > mathematical basis...?
So long as it is not self-contradictory I can make it an axiom of a mathematical basis. It may not be very interesting mathematics to postulate: Axiom 1: There is a purple cow momentarily appearing to Anna and then vanishing. but by the standard that everything not self-contradictory is mathematics it's just as good as Peano's. >You can imagine all you like, but it won't > bring into being a universe where Godel's incompleteness theorems > don't hold, for example. The fundamental things that we know about > mathematics itself transcend any particular realization of the > universe. > > Anna I'm arguing that "all mathematically consistent structures" is itself an ill defined concept. A mathematical structure consists of a set of axioms and rules of inference. So I supported my point my giving an example in which the set of axioms is an infinite set of propositions of the form "state i obtains at time i" where "state i" can be any set of self-consistent declarative sentences whatsoever. I leave the set of rules of inference empty - so there can be no contradiction inferred between states. Then according to the theory that all mathematically consistent structures are instantiated (everything exists) this set exists and defines a "universe" just as well as general relativity or quantum field theory (perhaps better since we can't be sure those theories are consistent). Brent --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
