Thank you, happy new year to you, too! On Dec 27, 8:36 am, Bruno Marchal <marc...@ulb.ac.be> wrote: > On 26 Dec 2010, at 22:51, Brian Tenneson wrote: > > > "Limits To Science: God, Godel, Gravity" > > >http://www.science20.com/hammock_physicist/limits_science_god_godel_g... > > > Here is my comment: > > An important question is whether or not a TOE will be finite in > > length. > > Of course, this is a matter of definition. Indeed.
> > > I am taking 'TOE' to be, as a working definition, a complete > > description of reality or a complete description of everything that > > exists. > > That does not exist. Arithmetical truth is already not recursively > enumerable. If a complete description of arithmetical truth is not possible, what exactly are we talking about? > > Then one *might* consider this program which generates a TOE to > > arbitrary precision to be "the" TOE, a compression of an infinitely > > long document into a finitely long document, thus showing that reality > > at its core does not possess the trait of Kolmogorov randomness. Being > > that reality contains the uncomputable, it *seems* unlikely that > > everything can be finitely describable. > > This is simply wrong. That's good! > > The argument is made that a TOE can be in the form of a logical > > structure which is a tuple consisting of an underlying set, a set of > > distinguished constants (like zero), functions (like successor), and > > relations (like less than) on this underlying set. Making the > > additional assumption that if there is a structure such that *all* > > logical structures can be "embedded" within it, then this type of > > universality endows such a structure with the same structure as > > reality. Thus this sort of ultimate structure would be in an intuitive > > sense like ultimate reality. Thus a description of this ultimate > > structure would be a description of reality. > > You have to distinguish the outside and inside view of the ultimate > reality. What is the outside view of the ultimate reality? How is it possible to have an outside view of the ultimate reality? -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.