Yes, this would happen if you take an unbounded function and simply map it to a bounded function without actually changing it. That is why I am suggesting admitting that you really don't have an infinite capacity for caring, and describing what you care about as though you did care infinitely is mistaken, whether you describe this with an unbounded or with a bounded function. This requires admitting that scope insensitivity, after a certain point, is not a bias, but just an objective fact that at a certain point you really don't care anymore.