By becoming a scientist yourself you can’t solve the problem of circularity. You can forget about it and just join the culture of experimentation and believing in results. Science is like Communism – it works as long as everybody buys into it. If someone refuses to buy into it, it reverts back to Capitalism or the free, unregulated production of knowledge that “works.”

Two things make a scientific theory successful: (a) it provides deep, satisfying explanations for the state of the world, and (b) it makes good predictions about the future. These are in theory separable, but to the extent they are separated, most scientists focus on (b). Whether or not a scientific theory correctly predicts the future is not a matter of opinion. It either does or it doesn’t.

You are right, though, that there is some circularity here. The scientific method is provably the best method of producing theories that do a good job of predicting the future precisely because that’s at the core of the scientific method. Why evaluate theories in terms of their ability to predict the future? Why not prefer theories that are most intuitively correct? No reason. Science can only tell us about the state of the world, not about which parts of the world we should care about.

I’ve got a fully expanded post on these issues here.

How do we know that facts are “facts” and hard facts are hard facts? Only because a scientist told us so. But how do we know that his assumptions are still valid? The reason some scientists get nervous is because they often know that there’s an ascertainment bias going on all the time. For science to thrive and ignorance to subside, science needs to establish a meaningful dialogue between the social and the hard sciences, between sciences and humanities, between sciences/humanities and religions, etc., so that both parties constantly cross-check each other’s claims and translate them into each other’s “languages.” This dialogue shouldn’t turn into a sticky compromise but a well-regulated mutual commitment to respect each other’s territory.

The same danger as awaits science has already befallen Christianity with its miracles: apparently, they used to be abundant shortly after the emergence of Christianity and in the middle ages but now it’s hard to come across a single one. And some branches of Christianity don’t need them to maintain their integrity.

As long as researchers know that, things are ok, but when you see the numbers being plugged in R or whatever, ugh. Meta-studies in particular. We must use statistics in science, it is the right tool, but I think the subject should be taught in place of calculus in HS and undergraduate.