First of all Popper and Deutsch don't discard induction entirely. They just argue against induction as a source/foundation of knowledge. 

Now one comment on the Bayesian endevour: As a laymen mathematician I have little authority in saying this, but isn't it obvious that a probability calculation fails if the absolute value is infinite?

I was there at the beginning of the lesswrong movement and this emphasis on probabilistic thinking is new to me. Bayesianism also is blacklisted under my personal philosophical firewall for being gameable by social engineering. Maybe you should run a virus & threat protection scan on yourself. Are you easily computing seemingly unnecessary stuff when someone gives you input? Are attributing your own work to others after observing a 'statistically larger' set of similar ideas? Maybe this is malware? Restart once and reinstall popperian critical rationalism which is resistant to most of these things.