I just checked "An Introduction To Philosophical Analysis" by John Hospers (p. 527 I think) regarding a discussion in that book about: do things exist un-perceived/ un-observed/ un-experienced?
What the author seems to conclude is that obviously science etc. can say nothing about that which it cannot observe, other than to offer "a best explanation" of things. For example several observations of a table might suggest "a best explanation" that there really is a table.
It seems that no matter how much coroborating evidence there is for an object or event existing "while no-one is looking"; people/ scientists/ etc. fill the gap in the data with the best looking "explanation", that the object or event is really there when no one is looking.
There is this story of someone saying to someone else: "the street light goes out when you shut your eyes but is on again when you open them"- (presuming no warm-up needed for that light) you might ask how is one person going to prove the light is on when they have their eyes closed? (presuming they place a barrier across their eyes so no light leaks through eyelids)
You may return to a bath with running tap and argue the best explanation as to why the bath became full in your absence is that the tap was really running when you were not looking.
Your knowledge of the bath tap scenario might be regarded as limited by the data you have actually interacted with. The rest might be regarded as reasonable speculation, projecting from the known data a workable idea about the unknown data.
Seems more than reasonable though.
Knowledge might be regarded as not just limited, but "limit" itself; so "knowledge" as "constraint", as the finite-ness or boundedness inherent in the existence of an object.
I agree that "meaning" involves context, so involves wider relationships ("meaning" might even translate into "mass" and into "probability density of finding an intersection of a bunch of other stuff").
2 cents there. Speaking of cents: have to reduce my involvement in this forum unfortunately (i-cafe fees).