I would go back much farther (it is difficult for us to do so) than the
questions about whether certain quantities are human constructs. In the
evolution of western, scientific human thought the step out of the
"ocean" onto the "shore" was the very revolutionary idea that we should
seek some sort of understanding of phenomena by looking at the numbers
generated by (freely designed) measuring devices. I think this began
with Boyle, et al, in the 1600's. Prior to this, such a mode of
understanding was not even a part of human thinking. Since then it has
become the essential feature of every human invention which goes by the
name of quantitative science (and quantitative recreation, etc.).
We say all this too quickly and too glibly; we need to make a real
effort to appreciate what it was like before the notions of
quantification and measurement became part of "understanding".
I think that perhaps our root pedagogical problem is that many of our
students have never been led "ashore".