Based on reading the comment threads here, it seems as though some folks are missing something important in this post. So, I’ll try to restate it differently in case that helps. Below, double-quotes are used to refer to the word, while single-quotes are used merely to highlight and separate tokens.
There is a mathematical formalism, which we can call “probability”, which does a good job of modeling various sorts of things, like ‘subjective degrees of belief’, ‘frequencies’, ‘volume’, and ‘area’.
‘Bayesians’ think that “probability” should refer to ‘subjective degrees of belief’. ‘Frequentists’ think that “probability” should refer to ‘frequencies’. One alleged problem with ‘Frequentists’ is that they seem to carelessly slip between ‘subjective degrees of belief’ and ‘frequencies’, due to the natural-language meaning of “probability”.
One suggestion proposed in the comment threads was to simply use “probability” to refer to ‘subjective degrees of belief’ as the ‘Bayesians’ would have us do, since we already have the word “frequencies” to refer to ‘frequencies’. I intuit that the OP’s objection to this suggestion is that it leaves us with no word for the mathematical formalism called “probability” above, which can apply just as well to ‘frequencies’, ‘subjective degrees of belief’, and many other things.
I intuit that the OP’s objection to this suggestion is that it leaves us with no word for the mathematical formalism called “probability” above, which can apply just as well to ‘frequencies’, ‘subjective degrees of belief’, and many other things.
Based on reading the comment threads here, it seems as though some folks are missing something important in this post. So, I’ll try to restate it differently in case that helps. Below, double-quotes are used to refer to the word, while single-quotes are used merely to highlight and separate tokens.
There is a mathematical formalism, which we can call “probability”, which does a good job of modeling various sorts of things, like ‘subjective degrees of belief’, ‘frequencies’, ‘volume’, and ‘area’.
‘Bayesians’ think that “probability” should refer to ‘subjective degrees of belief’. ‘Frequentists’ think that “probability” should refer to ‘frequencies’. One alleged problem with ‘Frequentists’ is that they seem to carelessly slip between ‘subjective degrees of belief’ and ‘frequencies’, due to the natural-language meaning of “probability”.
One suggestion proposed in the comment threads was to simply use “probability” to refer to ‘subjective degrees of belief’ as the ‘Bayesians’ would have us do, since we already have the word “frequencies” to refer to ‘frequencies’. I intuit that the OP’s objection to this suggestion is that it leaves us with no word for the mathematical formalism called “probability” above, which can apply just as well to ‘frequencies’, ‘subjective degrees of belief’, and many other things.
“Probability theory”