  A system with artificial intelligence usually relies on symbol manipulation,
at least partly and implicitly. However, the interpretation of the symbols -
what they represent and what they are about - is ultimately left to humans, as
designers and users of the system. How symbols can acquire meaning for the
system itself, independent of external interpretation, is an unsolved problem.
Some grounding of symbols can be obtained by embodiment, that is, by causally
connecting symbols (or sub-symbolic variables) to the physical environment,
such as in a robot with sensors and effectors. However, a causal connection as
such does not produce representation and aboutness of the kind that symbols
have for humans. Here I present a theory that explains how humans and other
living organisms have acquired the capability to have symbols and sub-symbolic
variables that represent, refer to, and are about something else. The theory
shows how reference can be to physical objects, but also to abstract objects,
and even how it can be misguided (errors in reference) or be about non-existing
objects. I subsequently abstract the primary components of the theory from
their biological context, and discuss how and under what conditions the theory
could be implemented in artificial agents. A major component of the theory is
the strong nonlinearity associated with (potentially unlimited)
self-reproduction. The latter is likely not acceptable in artificial systems.
It remains unclear if goals other than those inherently serving
self-reproduction can have aboutness and if such goals could be stabilized.
