At some point the meaning has to be grounded in something other than just more strings of symbols. My candidate for that grounding is sensorimotor representations. Mental Rotation of Three-Dimensional Objects. The categorical representation is what is left when one filters out what is NOT invariant among the members of a sensorimotor category. To do that we need an internal mechanism that can learn to detect and abstract these invariants.
Neural nets are one possible candidate for doing that.
The result would be a categorical representation. It has no meaning if you don't know the actual causal mechanism, and it has no usefulness if you do. It's somewhat premature to look for neurobiology here. What we are doing first is cognitive modeling. Then those are our candidate causal mechanisms, and if they are sufficiently powerful and general in their cognitive capacities, then it might be a good time to look for their implementation in the brain.