Why are introspective verbs used for data in programming?

Just guessing / offering personal opinion... such words would rarely make sense in source code.

What would a function called "believe" do?

I can imagine such function names in, say, artificial intelligence projects, but even there used (probably) in a loose way. I suspect few web applications or iPhone games or flight control programs would be doing any "believing", real or imaginary.

Of the words you suggested, "sense" seems most likely to appear in real use, as robotic software and such may be literally accessing sensors.

Also, the last thing we need is more confusing language that gets in the way of absolute beginners realizing there's no ghost/consciousness/intentionality in the machine.

Indeed, unless you were doing, say, work on some scientific survey about people's beliefs, or whether school children understood a passage, or a game where these are literally mechanics, or something like that, i'd even be loathe to suggest ever seeing those as either function names or as variable names.

Its bad programming style 101 to give your variables/functions names that have some kind of cognitive connection/bias in people's minds apart from the function they actually serve in the code, and those are some pretty loaded words in most cultures...

The verbs aren't choosen at random. They are almost all a write-word (write, set, create, put, save, update, dump, clear, reset, print, append, ...) or a read-word (read, get, ensure, load, check, ...). But the verbs you list doesn't fall into either category. Think of what it would mean to command someone to "believe!" it doesn't make sense (to a non-sentient entity anyways!). "print!" otoh, is perfectly understandable.