A cognitive system has its own properties as a self-contained system of propositions. It rides on the analog world in the way that a drama, with its own sort of reality, rides on the primary reality of material stage, actors and props. In the theatre, the fiction is interpreted in terms of the real experience of actors and audience jointly. Prisoners within the play of life are obliged to project the world of their script into the unknown reality offstage. Reality, on the other hand, appears in principle unfathomable, inexhaustible by mind, uncontainable by any formalism.
Formal knowledge is a game played according to certain rules, with defined payoffs.
The game may serve as a metaphor of reality, but it is not reality itself. The models of science bear a similar relationship to reality as do perceptual models. Like perception, there is always something which thought ignores. The mind has a tendency to deal with the residue that does not fit into its representational matrix as King Procrustes accommodated guests who were too long for his standard bed. Justifications then grow elaborate and spurious in the measure that more effort is required to force reality into the preconceived mold.