Connectionist symbol processing: any progress?

[Neil W Rickert]

On Wed, 12 Aug 1998 Lev Goldfarb wrote:

>                                         Hacking apart, the INPUT SPACE of
>a learning machine must be defined axiomatically, as is the now universal
>practice in mathematics. These axioms define the BASIC OPERATIONAL BIAS of
>the learning machine, i.e. the bias related to the class of permitted
>object operations (compare with the central CS concept of abstract data
>type).

Why?  This seems completely wrong to me.

It seems to me that what you have stated can be paraphrased as:

   The knowledge that the learning machine is to acquire must be
   pre-encoded into the machine as (implicit or explicit) innate
   structure.

But, if my paraphrase is correct, then one wonders why such a machine
warrants the name "learning machine."

Presumably we have very different ideas as to what is learning.  I
take it that human learning is the process of discovering the nature
of our world.  More generally I take it that, at its most fundamental
level, learning is the process of discovering the structure of the
input space, a process which may require the eventual production of
an axiomatization (a set of natural laws) for that space.