So to summarise in pop Bayesian terms, akin to "don’t be so sure of your beliefs; be less sure when you see contradictory evidence." :

1. There is always evidence; if it looks like the contrary, you are using too high a bar. (The plural of 'anecdote' is 'qualitative study'.)
2. You can always give a guess; even if it later turns out incorrect, you have no way of knowing now.
3. The only thing that matters is the prediction; hunches, gut feelings, hard numbers or academic knowledge, it all boils down to probabilities.
4. Absence of evidence is evidence of absence, but you can't be picky with evidence.
5. The maths don't lie; if it works, it is because somewhere there are numbers and rigour saying it should. (Notice the direction of the implication "it works" => "it has maths".)
6. The more confident you are, the more surprised you can be; if you are unsure it means you expect anything.
7. "Knowledge" is just a fancy-sounding word; ahead-of-time predictions or bust!

ETA:

1. Choosing to believe is wishful thinking.