Dear Sabine;
I have read with great interest your essay and concluded that I agree with most of the deductions and conclusions. Only we are using different "words". Some remarks while reading your essay.
"A theory may have given us the most extraordinarily accurate predictions until today, and still tomorrow we could discover that it doesn't explain the next measurement." You are so right, my explanation (that may be different from yours) is that the next experiment may take place in the future, it is only the past that is deterministic and not the future.
Your paragraph 2 reminds me of the rules: rule1.The boss is always right. rule 2 If the boss is wrong, rule 1 is still valid. (your added axiom). The rules are mathematics, ignoring reality, so both are different things.
"Nothing real is infinite", is the same expression as "reality is finite", which does not mean that there is an infinity of realities. In my perception, this infinity of probable realities is "outside" our emerged reality.
"Lorentz "butterfly effect" is I think not only valid for predictions in the future, but also works for the past. The further we are reaching out in the past the lesser the chance that you will exist, the amount of IF's that are influencing your existence (meeting of ancestors, the female egg receiving the specific needed sperm etc, etc) is the butterfly effect in the past that leads to your existence. If all the IF's are fulfilled they amount to 10^2,685,007 !!!
"And since the singularity is hidden behind the event horizon, we can't just go and measure what is happening. ". This "event horizon" is in my perception behind the Planck length and time. It is the border of our reality.
"Given a sufficiently large and powerful computer, even human decisions could be calculated in finite-time" Human decisions are made as you say in "finite" time. Finite-time is deterministic because essentially it is already the past. The REAL choices are made in the seemingly future of the timeless unmeasurable entity outside our reality (Total Simultaneity).
I understand that you are a busy bird, but anyhow maybe you can find some time to read my essay .
Thank you
Wilhelmus