Easy to answer: Apply the Popper test to whatever statement you would like to make. If it is unfalsifiable, it's nothing more than empty babbling.
hahaha
I, too, once thought like you
Until I realized that statement undermines its own truth
Now I rave, babbling, through philosophical... youth
I can't rhyme worth shit
Anyway. The problem with the assertion that "only statements whose truth-value can be experimentally determined are valid statements" is that it doesn't satisfy its
own criterion for validity. And once you start saying "some but not all unfalsifiable claims are okay," you're just scrambling to fix a sinking ship. You can say that the philosophical question has no readily apparent
utility, which is true, but... then again, the same might have been said about various theoretical physics ideas, and look where relativity and QM have gotten us.
Also: the world will die a heat death, right? That's what we think? So once everything in the universe is no longer capable of motion or change, does time
actually stop? Or does it just stop for all intents and purposes? And is there a difference?
(The heat death is just an illustrative example: if I had to make it more abstract, I'd say something about whether truth is a fundamental metaphysical quality or property, or whether it is instead tied more strongly to
something I can't define or figure out right now but that probably has to do with observation, but I prefer the more koan-like route of questioning.)
As for logical positivism, I'd say it makes sense as a social
constraint on validity (it's not useful to present a non-verifiable claim), but not as a conceptual definition of validity. Except that maybe those mean the same thing. I'm not sure.
That also ties into the many-worlds QM thing I like to consider: do we go with "we can no longer see it, therefore it is not there" or "the equations describe the universe splitting apart into multiple, mutually-unreachable parts, so the other part is still there" (awful physics explanation, good enough for a philosophy discussion at 10:50 PM)?