The map is not the territory, any model is an abstraction and will never be complete, the only complete model of the market is the market itself, and so on. I agree that this leads directly into Gödel, Turing, the halting problem, and other basic computability concepts.
Try this thought experiment: Imagine the market as a turing machine named M, reading and writing to a tape of infinite length. All past and future news events are on the tape. The market (our machine named M) reads a news event, and, based on its internal state and ruleset, writes a market data message to the tape. Because of the halting problem etc., we can't use a different machine to predict ahead of time what the next market data message will be. The only way to discover the next market data message is to execute M's next machine cycle.
Trying to write an exact model of the market is like trying to duplicate M's entire tape, including future news events, as well as M's internal ruleset. And before we can begin executing our own model, we also need to grab a copy of M's internal state, which, in the case of a real-world market, includes the internal state of all counterparties. Any turing machine that can do all of that is, in fact, identical to M. We would have to recreate the entire market, including future news, in order to model M.
If we try to write a macro-level model G that summarizes M's output, aggregating by timeframe, index, or somesuch, then we still run into the same problem: Macromarket G is just another machine, still with an infinite tape. We can assume that G's behavior is determined by a simpler ruleset, with smaller internal state than M. That's the whole point of a model. But again, in a real-world market, that internal state is stored amongst the counterparties, and the tape still includes future news events. And the next (aggregated) market data message is still not decideable without executing G's next machine cycle.
We can model this several other ways. For instance, instead of one big machine M or G, we can use a bunch of smaller machines, each representing a counterparty, all sharing the same tape. That just makes the complexity worse.
Of course, Turing only claimed that a turing machine could compute any problem that was decideable by machine. A real-world market includes players who are not machines. But even if we were to assume that humans are mechanistic in behavior, we'd still have the intractibility of getting a copy of their internal state in order to model M or G.
In reality we already know that no model is completely accurate, and no model's accuracy is constant over time. The above thought experiments, I think, might be able to illustrate some of the reasons why.