Probability is relative to the information you have. That doesn't make it not be real.

Probability is something we invented to describe systems, based on what we know about them, when we have imperfect information. If we had perfect information about the coin, its surroundings and how it was flipped, we could tell which side it will land on, but we don't. (Ignoring that there are some quantum things that physicist say can never have perfect information)

Generally we use the term real to refer to objective claims and consider subjective claims not to be real. You can certainly use the term real in a broader sense if you'd like. I don't think the concept of reality is particularly useful or coherent, but to the extent others use the term, probability is not real in the sense it's being used in.

Nitpick on definition of "real" and "objective" follows. Proceed at your own risk :-)

Would you agree that given exact info of conditions one can objectively assign concrete probability? That would give objectivity to it.

Definition of "real" for daily life is hard (impossible?). I would say "probabilities" are as real as other useful constructs that impact our lifes. Examples would be "countries" and "laws".

Is country X real? (what if it is recognised only by 1 UN nation?) Is law real? Is law real in <insert-country-in-turmoil-with-very-very-selective-enforcement>.

I could say "I have a job!" and that statement would be true, but only with the information I currently have available (what if my boss has already decided to fire me but I've just not received the information yet?). So the statement being true is based on my information about the world, just like probability.

Are particles on the quantum level real or just mathematical constructs that describe what we can observe, just like probability is?

Sure, it's as real as those other examples, i.e. not particularly except insofar as it affects peoples' expectations.

I don't think "exact info of conditions" is objective or coherent. This pre-supposes there's an external universe with exact conditions that produces our experiences, but there's no way to distinguish this possiblity from other possibilities (like a multiverse, for instance.) This lack of ability to distinguish, in my ontology, makes the distinction meaningless. Yours may differ.

Your example suggests to me the opposite: Probability is a real and objective way to describe the information you have. "Garbage in, garbage out" still applies when you have no information.

The distinction between objective and subjective collapses under your usage.

No, the distinction is clear. If your assigned probability is something that someone else can reproduce using the same steps given the same information, then it is objective (yet contextual). Your examples each have a clear reasoning behind the assigned probabilities, they're not just opinion-based assertions.

Bob has a very simple algorithm to output probabilities. He just answers 50/50 for any yes or no question. This is reproducible. Is this objective?

This doesn't strike me as a good example of reproducibility in this context. Let me offer another one. Let's go back to your example of the 66% weighted coin. Given the physical properties of the coin, different people could independently come to the same conclusion that the probability of heads is 66%. I would describe this as an "objective" probability, as it's a nice representation of the available information, independently reproducible by different people, given the same information. It's different than "Bob arbitrarily decides that any yes/no question has 50/50 probability", which is inherently subjective.

No two people ever have the same set of information. And very few cases are even as clean as the coin case.

A more typical example is using polls to predict elections. 538's model ended with Biden around 90% to win. Andrew Gelman's model at the Economist ended with Biden around 95%. Do either of those represent objective probabilities?

Or take weather predictions. Per https://www.metaculus.com/questions/4617/will-2020-be-the-wa..., Berkeley Earth gives a 16% chance to something that NOAA gives 29.2% to. Is either of those an objective probability?

I would say no, and I think that just because two people happen to agree on a number in a particular case doesn't make it objective. If you want to use the word objective, I don't have any particular objection. I'm not here to fight over words, and none of these words are really well defined enough to be worth fighting over. I don't think it's useful to think of probabilities as "real" in any sense.

Yeah, that's objective. It's just not a great model.

It sounds like you're argument is actually stating that probability is in fact a real attribute of physical systems, but the accuracy with which you can accurately predict a probabilistic event is dependant on the amount of information you have about the system. Interestingly, someone only observing results of a probabilistic event will eventually learn to predict events with an accuracy approaching ideal (I.e. the true probability distribution of the system - or someone who knows every single detail about the causal system down to the limits of physical reality - subatomic particles and all of the underlying physics we don't understand yet).

There's that phrase again - "true probability" (implying the word "True" == "Real"). You could imagine a system that yields non-linear results, such that no matter how many observations were made, your ability to accuratelt predict outcomes in the system never increases. In this case, you might conclude that you're dealing with one of two special cases: 1.) a non-probablistic event (i.e. a purely random (0% predicatable) event or 2.) on the other end of hyperbole, a purely deterministic event (100% predictable)).

>Interestingly, someone only observing results of a probabilistic event will eventually learn to predict events with an accuracy approaching ideal

This relies on various unstated assumptions.

I would deny the assumption that an event can be probablistic in nature. There are only ever predictions. The distinction between a probablistic world and a deterministic world is incoherent.

If quantum reality is objective, then probabilistic reality is objective.

Deterministic probability like Chaos or second law of thermodynamics imply the existence of incomplete information. This type of probabilistic reality might be subjective.

I don't think that's a coherent concept. It's not clear how one can assert that a particular model of reality is "correct" outside of any predictions than it makes.

How do you resolve the problems raised by Bell's theorem?

Bell's theorem rules out local realism. I view realism as incoherent, so I'm certainly not committed to local realism.

You said the distinction between a probabilistic world and a deterministic one is incoherent. But if there is no local realism, wouldn't it be more accurate to describe your position as saying all events are probabilistic rather than none of them?

No. All events being probabilistic is still realism, just in a weaker sense than Bell.

Yeah, I'm grasping at straws because I don't really understand what your position is from the things you said in this thread.