Arrows n=m+1 example

[Tril]

On Mon, 26 Apr 1999 dufrp@oricom.ca wrote:

> So it seems more intuitive to define an arrow as having two slots that
> can reference either an arrow or an 'atom (or object)'. I guess this must be
> wrong for you, since it would means to lose the homo-iconic property.
> But I don't see by myself yet why it would be so bad.

In a reflective system, what are "atoms" varies depending on the context.
We can't have one set of atoms for the entire system, because we want to
talk about what those atoms are defined by, which would necessitate
something at the "sub-atomic" level.  Of course, once you have a system
bootstrapped, you can use the atoms themselves in their own definitions,
but you don't always want to do that.

At a fundamental level, we don't like the concept of atoms.  In an
intensional system, the meaning of any part of the system is entirely
dependent on what other parts it is connected to.  So if you try to find
definitions in the usual sense of the term (with atoms at the base level, 
and more complex entities made of combinations of these atoms), you will
end up with circularity sooner or later.  This same problem occurs when
trying to write a dictionary.  You must describe language using language.
People complain that to understand a word, they must look up other words
recursively (ad infinitum).  In essence we are affirming that our world
view no longer views such circularity as taboo.

A more mundane answer is that you can use arrows that point back to
themselves (or any other designated shape of arrow you wish) as atoms.

David Manifold <dem@tunes.org>
This message is placed in the public domain.