references/addrresses in imperative languages

Kaz Kylheku kkylheku at
Tue Jun 21 07:50:57 CEST 2005

SM Ryan wrote:
> "Kaz Kylheku" <kkylheku at> 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.

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