Another example, if you have an electron in a superposition of half spin-up and half spin-down, then the probability to measure up is objectively 50%.
Another example, GPT-2 is a probability distribution on sequences of integers. You can download this probability distribution. It doesn't represent anyone's beliefs. The distribution has a certain entropy. That entropy is an objective property of the distribution.
The others are both partial-information problems which are very sensitive to knowing certain hidden-state information. Your random number generator gives you a number that you didn't expect, and for which a formula describes your best guess based on available incomplete information, but the computer program that generated knew which one to choose and it would not have picked any other. Anyone who knew the hidden state of the RNG would also have assigned a different probability to that number being chosen.
So I would say the same of GPT-2. It's not a random variable unless you query it. But unless you know unreasonably many details, the best you can do to predict the query is the distribution that you would call "objective."
But I think if we take the view that it's not a random variable until we query it, that makes it awkward to talk about how GPT-2 (and similar models) is trained. No one ever draws samples from the model during training, but the whole justification for the cross-entropy-minimizing training procedure is based on thinking about the model as a random variable.
E.g. your random number generator generates 1, 5, 7, 8, 3 when you run it. It generates 4, 8, 8, 2, 5 when I run it. I.e. we have received different information about the random number generator to build our subjective probability distributions. The level of entropy of our probability distributions is high because we have so little information to be certain about the representativeness of our distribution sample.
If we continue running our random number generator for a while, we will gather more information, thus reducing entropy, and our probability distributions will both start converging towards an objective "truth." If we ran our random number generators for a theoretically infinite amount of time, we will have reduced entropy to 0 and have a perfect and objective probability distribution.
But this is impossible.
For example my cat weighs 13 pounds. That seems objective, in the sense that if two people disagree, only one can be right. But the claim is based on my observations. I think your logic leads us to deny that anything is objective.
Why, that would mean that...I really don't
know what the outside universe is like at
all, for certain.I don't think you need to have any information to have a probability distribution; your distribution already represents your degree of ignorance about an outcome. So without even sampling it once, you already should have a uniform probability distribution for a random number generator or a coin flip. If you do personally have additional information to help you predict the outcome -- you're skilled at coin-flipping, or you wrote the RNG and know an exploit -- then you can compress that distribution to a lower-entropy one.
But you don't need to sample the distribution to do this. You can have that information before the first coin toss. Sampling can be one way to get information but it won't necessarily even help. If samples are independent, then each sample really teaches you barely anything about the next. RNGs eventually do repeat so if you sample it enough you might be able to find the pattern and reduce the entropy to zero, but in that case you're not learning the statistical distribution, you're deducing the exact internal state of the RNG and predicting the exact next outcome, because the samples are not actually independent. If you do enough coin flips you might eventually find that there's a slight bias to the coin, but that really takes an extreme number of tosses and only reduces the entropy a tiny tiny bit; not at all if the coin-tossing procedure had no bias to begin with.
However the objective truth is just that the next toss will land heads. That's the only truth that experiment can objectively determine. Any other doubt that it might-have-counterfactually-landed-tails is subjective, due to a subjective lack of sufficient information to predict the outcome. We can formalize a correct procedure to convert prior information into a corresponding probability distribution, we can get a unanimous consensus by giving everybody the same information, but the probability distribution is still subjective because it is a function of that prior information.
Did you take stats at MIT? I'm going to through their online material, because I very much am very confused.
The best introduction that I can recommend is this type-written PDF from E.T. Jaynes, called "probability theory with applications in science and engineering": https://bayes.wustl.edu/etj/science.pdf.html
It requires a lot of attention to read and follow the math, but it's worthwhile. Jaynes is a pretty passionate writer, and in his writing he's clearly battling against some enemies (who might be ghosts), but on the other hand this also makes for more entertaining reading and I find that's usually a benefit when it comes to a textbook.
Thank you!