But the idea that you can describe this with a single scalar number and then treat this number as a real physical quantity that features in models and theories is obviously complete nonsense.
It’s not obviously complete nonsense. It’s obviously part nonsense and part sense, and without further argumentation it’s not obvious how large a part nonsense and how large a part sense.
Just because a quantity is defined in a rather arbitrary way, that doesn’t mean it carries no information. You can take the position that an informal analysis would incorporate the same information and do it better, but you’d have to actually compare the biases inherent in these two approaches. (I haven’t read the Morgenstern book that you’ve linked; maybe it does so.)
It’s not obviously complete nonsense. It’s obviously part nonsense and part sense, and without further argumentation it’s not obvious how large a part nonsense and how large a part sense.
Just because a quantity is defined in a rather arbitrary way, that doesn’t mean it carries no information. You can take the position that an informal analysis would incorporate the same information and do it better, but you’d have to actually compare the biases inherent in these two approaches. (I haven’t read the Morgenstern book that you’ve linked; maybe it does so.)