I'm defining the Classical Reality as everything having a given state therefore with enough knowledge about the state of everything at the smallest particle level we can theoretically predict any seemingly random event.
I'm defining Quantum Reality as things being in an unresolved state until observed and therefore the probability of any random event is unknowable even with complete knowledge of state for every particle in the universe due to there being a probability distribution built into the fabric of reality itself.
I've run into a contradiction (In my head so it may just seem like one with my intuition) while considering the idea of constructing minimal models between inputs (facts) and an output (categorization and extrapolated facts).
Simply put in a classical model 1 + 1 always equals 2 and can be abstractly represented in mathematics with the probability(1+1 = 2) = 100% or true.
It seems to me that in a quantum reality the appropriate abstraction should be probability(1+1 = 2) is equal to the limit as observations go to infinity of the number of times we observe that 1 + 1 = 2. This would likely be less then 100% or infinitely close. I think specific results would be dependent on the reality of time and what could be considered an observation.
If the world is quantum does that imply that numerically based math (which is an abstraction by nature) cannot always hold?
Therefore, in a quantum universe is P(1+1=2) < 100% even though all observations should show P(1+1=2) = 100% since observed results in quantum mechanics are still a discrete set.
Do the implications of math being an abstraction in some way avoid the question entirely.
It makes sense that since we are abstractly modeling a world based on observations which in both a quantum and classical reality should adhere to laws of state. We should always be able to use integers or categorical sets to represent state with large enough numbers.
Imagine adding the mass of two objects together broken down by component molecules. (With impossibly perfect measurements) We would expect a discrete set of outputs and that can be perfectly modeled with whole integers.
Yet in a world of quantum mechanics and state being decided upon observation is it not likely that adding those same masses would only add up to the expected number most of the time, so the best model we would be able to produce would be a (discrete representation of a continuous number) a number to some decimal point plus or minus the error.
Some things like space between objects are continuous already so are impossible to represent discretely.
Does that imply the answer to my question is that, some things are discrete others are continuous. Math cannot precisely define anything that isn't discrete anyways so our abstraction is broken before we even consider a Quantum vs Classical reality?