Re: Is the universe a set? Probably not.
My particular approach is to base the universe on the idea that it is a physical isomorphism of but one of a set of incomplete, finite, consistent FAS [ifc-FAS]. Members of this set occasionally [no time connotations] freeze out spontaneously from a growing, seething, foamy fractal of bifurcations [say zeros and ones] I call a superverse. The superverse itself spontaneously arose from no absolute information because no absolute information is itself incomplete. It can not answer the question of its own stability. The simplest form of such a resulting initiating incomplete fc-FAS is one with a single axiom containing relative information only and a set of rules for operating on the axiom. The incompleteness of this FAS makes it indeterminant - it continues to grow by an ongoing Godelian type of freezing out process from the superverse. I identify these logic growth events as isomorphic [in our universe] to quantum perturbations. Aside from its incompleteness resolution process, the only dynamic supportable by such an ifc-FAS is a recursively enumerated cascade set of theorems that starts with the single axiom. The simplest SAS capable physical isomorphism seems to be a 3 space grid of isolated points that can not migrate, but can relocate relative to neighbor points within their region of the grid in a quantified way. Each configuration is isomorphic to a theorem of the ifc-FAS. While the points are identical they are distinguishable by their relative position thus they seem to form a set. A quantum mechanics and a relativity seem easy to derive on such a base. If I understand Russell correctly this may be a Hilbert space in the sense that the superverse may be a continuous set of bifurcations, but I am not a mathematician. However, each ifc-FAS describes a finite discrete subset of this space. So it seems to me that the universe is a set on multiple scales. If anyone is interested my model such as it currently stands is at: http://www.connix.com/~hjr/model01.html Hal
Re: Is the universe a set? Probably not.
Christoph Schiller wrote: What I meant with the word is in the title was: Is the most precise description of the uniwerse a set? I am not talking about ontology or epistemology, just about experiments and comparison with theory. Of course, both quantum theory and relativity *assume* sets to start with; the whole point is that despite this, when one takes them *together* (and in fact, it turns out, only then) one can deduce that these sets make no sense. I do not know how to think without sets, but I sure want to know whether and how far this is possible. That is the real fun here. It is said than one fallacy in the argument is that it is assumed that all sets used in the physical description of nature are derived from space-time and particle sets. I do not know of any others; I'd thought that all are built up from these. I am *very* curious if there are any other, independent sets. That is indeed extremely important for the argument, and would kill it. My understanding of QM is that it is based on a set (the Hilbert space of wavefunctions) that is neither a space-time set nor a particle set. It has infinite dimensionality while space-time sets are finite, and is continuous while particle sets are discrete. Let me know if I'm missing something here, but I would have thought that this does kill your argument. Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
