I don’t understand what this “probability theory can only be used...” claim means. Are they saying that if you try to use probability theory to model anything else, your pencil will catch fire? Are they saying that if you model beliefs probabilistically, Math breaks?
I think they would be most likely to describe it as a category error. If you try to use probability theory outside the constraints within which they consider it applicable, they’d attest that you’d produce no meaningful knowledge and accomplish nothing but confusing yourself.
Can you walk me through where this error arises? Suppose I have a function whose arguments are the elements of a set S, whose values are real numbers between 0 and 1, and whose values sum to 1. Is the idea that if I treat anything in the physical world other than objects’ or events’ memberships in physical sequences of events or heaps of objects as modeling such a set, the conclusions I draw will be useless noise? Or is there something about the word ‘probability’ that makes special errors occur independently of the formal features of sample spaces?
I think they would be most likely to describe it as a category error. If you try to use probability theory outside the constraints within which they consider it applicable, they’d attest that you’d produce no meaningful knowledge and accomplish nothing but confusing yourself.
Can you walk me through where this error arises? Suppose I have a function whose arguments are the elements of a set S, whose values are real numbers between 0 and 1, and whose values sum to 1. Is the idea that if I treat anything in the physical world other than objects’ or events’ memberships in physical sequences of events or heaps of objects as modeling such a set, the conclusions I draw will be useless noise? Or is there something about the word ‘probability’ that makes special errors occur independently of the formal features of sample spaces?
As best I can parse the question, I think the former option better describes the position.