Maybe I don't understand your argument but it sounds like to me you would think that 3 feet long is societally determined because you need a social system to define what 3 feet is and create measuring tapes and whatever but that would make every metric socially constructed. It only works based off a different definition of what socially constructed means thqn I intended in my post so I could try to nail down a better definition or if you want you could suggest to me clearer words in the future but I'm loathe to get into a semantic argument here.

Edit: TL;DR by my understanding your definition of societally determined is so broad as to not really be very meaningful.