Casti's use of 'mirror-image' is a bit vague. Better terminology is available from linguistics - namely the reflective, intentional, and constructive models of language . Replace the notion of 'truth' with that of 'provability', thereby translating the Epimenides Paradox into the assertion 'This statement is unprovable'. Formal, axiomatic systems have axioms and theorems. Axioms are theorems which are assumed to be true for the particular formal systems.
Theorems are then true or false depending on the formal system used.
Symbolic systems cannot be assumed to give absolute meaning, meaning is contextual to the particular formal structure. An excellent confirmation of this thesis was given in the famous incompleteness theorem of K. Goedel. Construct an arithmetical statement asserting that 'arithmetic is consistent'. Prove that this arithmetical statement is not provable, thus showing that arithmetic as a formal system is too weak to prove its own consistency.