benignuman: We are working with different understandings of the concept of belief. I think yours generates a good framework of understanding, but I do not think it is sufficient. Also, I think your understanding of the nature of science as a whole (as laid out in the first paragraph of the OP) is not fully formed. This will factor in later.
One thing that important to tack onto this concept is that science is not determined by scientists. Science is a tool used to catalogue information, and scientists are people who use that tool. As with all tools, if the user does not properly understand the use of the tool, or insists on applying the tool to tasks it is inherently unsuited to, work done with the tool with likely be faulty. Science is very often touted as a way to get all the answers about the universe and such (which I expect is where axioms about physical existence and projected rules and laws come from), when in reality, science as close to a goalless process as possible. It is a means, not an end. If it has any end, it is only to be an efficient means. We create our own ends to give meaning to the enterprise, but those meanings are not intrinsic to science itself. And yes, due to the inductive nature of scientific inquiry, such subjectivity can lead to skewed conclusions. But at the end of the day, science is still fully capable of washing its hands of all that. The responsibility does not lie with the method itself.