Algorithmically calculable answers must be part of Godel-incomplete systems, with true but unprovable statements. But a strange loop system can form a tangled hierarchy, a network of reinforcement and doubt, like language in use, where tentative uses for symbols are used then refined and meaning created relationally and through interplay and interaction.
When our brains cease to get input from the optic nerve, they don't close part of the brain. It (eventually) hijacks and bootstraps the area to continue to try and create a model of the world as isomorphic as possible to it - as demonstrated iteratively, by patterns of interaction, cross-reference, etc - ie by use.
Your premise that symbols are semantically vacant is untenable, in terms of viewing language in practice - they are imbued with it by use. Mathematical systems reveal consequences to statements already made, that is they don't generate meaning but unpack it. Creative mathematical thinking however, works forwards to consequences & backwards to axioms, then around again, in interaction with the world, creatively.
How, then, is it possible for a computer to come to know and understand the world?
Through interaction, trial and error, exploration, heuristics. Just like us. Whatever means it had to interact, they would be senses - including mental models & simulations, which we use for instance in motion prediction for game playing.
The Chinese room is only intelligent like a deck of cards, or an abacus, say. True Artificial General Intelligence would have to be in a strange loop, not such a flat hierarchy with explicit defined rules.