Bayesian probability theory is the mathematical formulation representing ideal reasoning under uncertainty
The squiggles on the paper are our representation of this probability—they are “probability”, not probability, if you like.
no, probability, or I assume you really mean rationality, is the void
Bayes is just playing with squiggles on paper. If when you interpreted bayes, you found some claim, which seemed to not work, you would have to abandon bayes, or be irrational.
The squiggles on the paper are our representation of this probability.
What probability where? If you start by saying degree of belief is probability, and then show that degreeo f belief is probability, I am not impressed. You can call them “the representation” instead of calling them “the theory” if you want. And you can use “is” instead of model if you want. And you can even use “probability” instead of “degree of belief”, though I suspect that may all get rather confusing quickly. But do realize that every reason you give for saying that probability is degree of belief, a frequentest can give for saying that probability is frequency.
“Probability” is a really stupid noun, kind of like “red-hood”, or “emergence”. Notice how in the actual theory, we only ever talk about the probability of something. “Probability” is a function, not an object. Ask yourself: “what IS probability?” really probe, and you’ll find that that is a stupid question. The right question would have been, “what does probability return given an argument?” The answer is that it might return the rational degree of belief of a proposition, the frequency of a predicate out of a finite population, the frequency of a value out of an infinite amount of trials, the volume of a space, the area of a shape, or even the length of a line. All of these are consistent with the komologorov axioms.
no, probability, or I assume you really mean rationality, is the void
Bayes is just playing with squiggles on paper. If when you interpreted bayes, you found some claim, which seemed to not work, you would have to abandon bayes, or be irrational.
What probability where? If you start by saying degree of belief is probability, and then show that degreeo f belief is probability, I am not impressed. You can call them “the representation” instead of calling them “the theory” if you want. And you can use “is” instead of model if you want. And you can even use “probability” instead of “degree of belief”, though I suspect that may all get rather confusing quickly. But do realize that every reason you give for saying that probability is degree of belief, a frequentest can give for saying that probability is frequency.
“Probability” is a really stupid noun, kind of like “red-hood”, or “emergence”. Notice how in the actual theory, we only ever talk about the probability of something. “Probability” is a function, not an object. Ask yourself: “what IS probability?” really probe, and you’ll find that that is a stupid question. The right question would have been, “what does probability return given an argument?” The answer is that it might return the rational degree of belief of a proposition, the frequency of a predicate out of a finite population, the frequency of a value out of an infinite amount of trials, the volume of a space, the area of a shape, or even the length of a line. All of these are consistent with the komologorov axioms.