So, do you have an alternative? Which observations can be generalized? Which not? The experiment itself is an artificial construct, and what is viewed is abstracted from the context in which it naturally occurs.
Wow, that's a quite artificial differentiation.
In a laboratory, our sample may well be "a uniform distribution." But this does not allow us to say that all of nature is a uniform distribution (all possibilities equally probable, so that everything happens sooner or later, or has already happened in the past).
Could you - or the equally pinged AlamoGirl give an example for a uniform distribution on an unbounded space?
No. Could you? How would you get your mind around the idea of "an unbounded space?"