[lxgr]

I think most philosophers would be fine with treating "there is no bear there" and "the amplitude of the probability density function of a bear is negligibly low there" as the same statement for this discussion :)

An entire bear spontaneously tunneling across a large distance or spontaneously forming out of vacuum fluctuations is really, really quite unlikely.

[dumbo-octopus]

Don’t confuse the event with the distribution. An event always either has or hasn’t occurred, no further statement can be made. It’s only in bulk that one can talk about distributions. But in this contrived anecdote, there is only one observation, one event.

[lxgr]

Some distributions are definitely relatively stable over time, so you can absolutely make predictive statements about the future given past observations.

That's true for both biological bear population dynamics and movement patterns and for quantum tunneling bears :)

[dumbo-octopus]

> you can absolutely make predictive statements about the future given past observations

Only if you accept that as true axiomatically.