SM Ryan wrote: > "Kaz Kylheku" <[EMAIL PROTECTED]> wrote: > # SM Ryan wrote: > # > # easy way to see this, is to ask yourself: how come in mathematics > # > # there's no such thing as "addresses/pointers/references". > # > > # > The whole point of Goedelisation was to add to name/value references into > # > number theory. > # > # Is that so? That implies that there is some table where you can > # associate names (or whatever type of locators: call them pointers, > # whatever) with arbitrary values. But in fact that's not the case. > > Do you really believe the Goedel number of a statement is the statement > itself? Is everything named Kaz the same as you?
The Goedel number is a representation of the statement in a way that the name Kaz isn't a representation of me. You cannot identify parts of the name Kaz with parts of me; there is no isomorphism there at all. I am not the translated image of the name Kaz, nor vice versa. A Goedel number isn't anything like a name or pointer. It's an encoding of the actual typographic ``source code'' of the expression. There is nothing external to refer to other than the encoding scheme, which isn't particular to any given Goedel number. The encoding scheme is shallow, like a record player; it doesn't contribute a significant amount of context. If I decode a Goedel number, I won't have the impression that the formula was hidden in the numbering scheme, and the Goedel number simply triggered it out like a pointer. No, it will be clear that each piece of the resulting formula is the direct image of some feature of the Goedel number. -- http://mail.python.org/mailman/listinfo/python-list
