Let me throw in what might be a useful term: “unobservable”.
Take, for example, the standard deviation of a time series. We can certainly make estimates of it, but the actual volatility is unobservable directly, we can only see its effects. A large chunk of statistics is, in fact, dedicated to making estimates of unobservable quantities and figuring out whether these estimates are any good.
Another useful term is “well-defined”. For example, look at inflation. Inflation in general (defined as “change in prices”, more or less) is not well-defined and different people can (and do) propose various ways to quantify it. But if you take one specific measure, say in the US a particular CPI and define it as a number that comes out of specific procedure that the BLS performs every month, then it becomes well-defined.
Just to nitpick, the standard deviation of a time series is not even well-defined unless we know that the series is stationary. In Shalizi’s words, “if you want someone to solve the problem of induction, the philosophy department is down the stairs and to the left”. If it were well-defined (e.g. if the time series were coming from some physical process with rigidly specified parameters), it would be just as observable as the mass of the moon, i.e. indirectly. That would fit my criteria for a “true number”.
I guess that for me a “true number” has to be a well-defined number that you can measure in multiple ways and get the same result, so inflation is out because it’s not well-defined, and CPI is out because it’s just one method of measurement that doesn’t agree with anything else.
Let me throw in what might be a useful term: “unobservable”.
Take, for example, the standard deviation of a time series. We can certainly make estimates of it, but the actual volatility is unobservable directly, we can only see its effects. A large chunk of statistics is, in fact, dedicated to making estimates of unobservable quantities and figuring out whether these estimates are any good.
Another useful term is “well-defined”. For example, look at inflation. Inflation in general (defined as “change in prices”, more or less) is not well-defined and different people can (and do) propose various ways to quantify it. But if you take one specific measure, say in the US a particular CPI and define it as a number that comes out of specific procedure that the BLS performs every month, then it becomes well-defined.
Just to nitpick, the standard deviation of a time series is not even well-defined unless we know that the series is stationary. In Shalizi’s words, “if you want someone to solve the problem of induction, the philosophy department is down the stairs and to the left”. If it were well-defined (e.g. if the time series were coming from some physical process with rigidly specified parameters), it would be just as observable as the mass of the moon, i.e. indirectly. That would fit my criteria for a “true number”.
I guess that for me a “true number” has to be a well-defined number that you can measure in multiple ways and get the same result, so inflation is out because it’s not well-defined, and CPI is out because it’s just one method of measurement that doesn’t agree with anything else.