This is wonderful, you have identified the crux of the conflict. And identifying conflicts is a great thing. We each have a different understanding of how science works. At the root of it, it’s a cases of Popperian Epistemology vs Bayesian Epistemology.

This is how I understand Bayesianism.  Bayesianism works on a spectrum, on one end I don’t see a problem with it, on the other end it breaks. One end includes finite problems, like probabilities of winning in poker, the other end,  we introduce new unpredictable things into the game (this is our reality), and Bayesian induction can’t work.

People who don’t know about Poppers refutation of Bayesian Induction, or don’t understand it. They will not like or grasp the worldview stated above.

We are looking at science through a different lens, philosophy, or if you prefer, worldview.

Take the name of this forum for example, one’s view of science effects their understanding. Each sees the same thing but understands it differently:

LessWrong.com

Popperian- “Less Wrong” means, we eliminate errors from our best ideas, to better ideas,
 

Bayesian- “Less Wrong” means, one finds credible evidence to justify or prove that we are more right.

Using Bayesianism to influence ones worldview is more popular, just look at the downvotes this Post is getting here. I also came from the same Bayesian based common-sense worldview. But, my learning has brought me to understand that Poppers theory is better. It explains more about understanding reality. But I could be wrong.

Popper on probabilities:

Popper spent a lot of time explaining probabilities and problems of induction.

If you are interested here is reference to some of his writing on the matter:
https://stanford.library.sydney.edu.au/archives/sum2016/entries/induction-problem/

And here he proved mathematically how probabilities are impossible:

https://sci-hub.3800808.com/10.1038/302687a0

Thank you for posting your comments. I hope more people have helpful criticism, then I can correct my errors. Downvotes don’t do much for me. I would rather learn where I’m going wrong.

Please correct me if I’m wrong, but doesn’t Bayesian induction claim we can be more confident we are right based on more evidence?

The method I have come to understand comes from Karl Popper, which is, we improve our knowledge through conjecture and criticism (the elimination of errors from our best held knowledge). Not by the probability of being closer to truth.