I think the topic of measuring productivity is a little more nuanced than what you think.
Something could be unmeasurable (unquantifiable), but comparable. Consider a contrived example: Two cars start a race at an unknown time - you are allowed to watch the end of the race. Which ever car finishes first is faster (on average, more fast). However, since you don't know when they began, you cannot measure their average speed.
I think a great deal of the headaches concerning productivity is comparing it between people and trying to put an exact amount on it. It is quite possible to say that one would be more productive in one environment vs another. Sometimes it is quite clear (I am less productive if I have a broken hand) and sometimes not so clear (not being in an office makes me more productive,... maybe).
Something could be unmeasurable (unquantifiable), but comparable. Consider a contrived example: Two cars start a race at an unknown time - you are allowed to watch the end of the race. Which ever car finishes first is faster (on average, more fast). However, since you don't know when they began, you cannot measure their average speed.
I think a great deal of the headaches concerning productivity is comparing it between people and trying to put an exact amount on it. It is quite possible to say that one would be more productive in one environment vs another. Sometimes it is quite clear (I am less productive if I have a broken hand) and sometimes not so clear (not being in an office makes me more productive,... maybe).