>any error in the knowledge of the initial conditions, no matter how small, will fairly quickly grow to affect the entire system.
That's why it's only possible to theoretically predict the outcome of any event, rather than practically possible. You can't say that the future isn't deterministic just because we can't ever gather enough information to predict it. Your lack of knowledge of the initial conditions doesn't alter the fact that those conditions do indeed exist. I don't know how many jelly-beans are in the jar, and there may be far too many to count, but that doesn't alter the fact that there is indeed a specific number in the jar.