Dear Flavio,
Thank you for a well-written and highly accessible essay. I particularly appreciate your historical perspective on classical indeterminism.
I totally agree with your distinction between empirical observations, which only address finite-resolution states, and the "orthodox" interpretation, which assumes that variables (e.g. coordinates of position and momentum) are infinitely precise. As I emphasize in my essay, PIP describes a conceptual model and interpretation of physical reality, based on assumptions that cannot be empirically verified.
You note that the orthodox interpretation of classical mechanics is causal and deterministic. Causality implies that cause precedes effect in time, i.e. time asymmetry. Time asymmetry, along with determinism, is typically (I suspect necessarily) attributed to an initial low-entropy low-probability state. The origin of an exceptional low-probability initial state, one that has deterministically led to the current universe including this essay and response, is problematic. In addition, a deterministic model cannot formulate a definition of entropy as a fundamental property of state. This makes the asymmetrical increase in entropy a property of perception, rather than an objective property of nature. A much simpler and objective explanation for time asymmetry is irreducible indeterminism, as you propose. Determinism is not empirically necessary, and indeterminism is a far more reasonable, and objective, explanation of time asymmetry and causality.
Your alternative conceptual model, FIQ-based Interpretation, is very similar to my alternative conceptual model, DCM. Both replace infinite precision variables with finite precision variables. In DCM, I relate finite precision to a new physical property of state, ambient temperature. Ambient temperature is based on the recognition that absolute zero does not exist and no system is perfectly isolated from its ambient surroundings. The universe's background microwave radiation permeates all of space and it defines a positive ambient temperature for the universe as a whole.
The DCM defines irreducible objective randomness by the partition function of statistical mechanics, evaluated at the ambient temperature (see end-note 7 in my essay, and "reinventing time" reference). It is immediately evident that that the PIP and the orthodox interpretation represent a special case, in which the ambient temperature is assumed equal to absolute zero. Absolute zero, however, is an unattainable idealization and does not exist in physical reality.
You conclude that no experiment will ultimately discriminate between determinism and indeterminism. While I agree that there will always be some wiggle room for anyone who wants to maintain determinism, the cost is abandoning objective time asymmetry and causality or asserting that the universe's evolution is nothing but the playing out of fate for an exceptionally crafted, and unexplained, universe.
Harrison
