Russell Standish writes: > [Hal Finney writes;] > > So I disagree with Russell on this point; I'd say that Tegmark's > > mathematical structures are more than axiom systems and therefore > > Tegmark's TOE is different from Schmidhuber's. > > If you are so sure of this, then please provide a description of these > "bigger" objects that cannot be encoded in the ASCII character set and > sent via email. You are welcome to use any communication channel you > wish - doesn't have to be email. And if you can't describe what you're > talking about, why should I take them seriously?
Well, first, I am not so sure of any of these matters. But as an example, how about "the positive integers"? That's a pretty simple description. Just start with 0 and keep adding 1. >From what we understand of Godel's theorem, no axiom system can capture all the properties of this mathematical structure. Yet we have an intuitive understanding of the integers, which is where we came up with the axioms in the first place. Hence our understanding precedes and is more fundamental than the axioms. The axioms are the map; the integers are the territory. We shouldn't confuse them. We have a direct perception of this mathematical structure, which is why I am able to point to it for you without giving you an axiomatic description. Hal Finney
