As a matter of fact, it is modeled this way. To define probability function you need a sample space, from which exactly one outcome is “sampled” in every iteration of probability experiment.
No, that’s for random variables, but in order to have random variables you first need a probability distribution over the outcome space.
And this is why, I have troubles with the idea of “true randomness” being philosophically coherent. If there is no mathematical way to describe it, in which way can we say that it’s coherent?
You could use a mathematical formalism that contains True Randomness, but 1. such formalisms are unwieldy, 2. that’s just passing the buck to the one who interprets the formalism.
Do you actually need any other reason to not believe in True Randomness?
I think I used to accept this argument, but then came to believe that simplicity of formalisms usually originates from renormalization more than from the simplicity being Literally True?
No, that’s for random variables, but in order to have random variables you first need a probability distribution over the outcome space.
You could use a mathematical formalism that contains True Randomness, but 1. such formalisms are unwieldy, 2. that’s just passing the buck to the one who interprets the formalism.
Do you actually need any other reason to not believe in True Randomness?
Any argument is just passing the buck to the one who interprets the language.
I think I used to accept this argument, but then came to believe that simplicity of formalisms usually originates from renormalization more than from the simplicity being Literally True?