If I were asked to accept something on faith in a textbook, I'd... well, I'd consider it bunk. We can't truly know anything about the universe, but we can do our best, and our best involves discovering everything we can with the senses we have and the technology we can make.
I'll give an example. In my biology lab, we did a study on the evolution of antibiotic resistance in bacteria. We first took two microfuge tubes, filled both with equal volumes of Linden broth (a solution filled with everything E. coli needs to live), and placed a very small amount of ampicillin in one. We introduced (non-disease-inducing) E. coli into both and let the tubes sit for a week.
After the incubation period, we spread equal volumes of each culture onto two different agar plates, with four plates in total. One had only lysogeny broth (LB - another medium used to grow bacteria), and one had both lysogeny broth and ampicillin.
We waited another week for the bacteria to grow and counted the colonies. That's the key here - raw data. And that data was?
The non-ampicillin colony on the non-amp plate: too many colonies to count.
The amp colony on the non-amp plate: 290 colonies.
The non-amp colony on the amp plate: 32 colonies.
The amp colony on the amp plate: 206 colonies.
You don't need a chi-square analysis to know that's a significant effect, but we did one anyway. Again, numbers are needed. While the colony grown without ampicillin had very few survivors on the ampicillin plate, the colony grown with ampicillin, while it flourished less on the non-amp plate than the non-amp colony, was barely affected by the amp plate - a drop from 290 to 206, as opposed to one of too many to bother counting to 32. Conclusion? The ampicillin in the amp colony killed the non-resistant, leaving the resistant to flourish where they would normally be outcompeted by a strain that does not use precious energy to produce what would otherwise be an unnecessary enzyme.
And that is how we "know" things - by pure, raw observation, mathematics, and logic.
