In some of my lectures I start by talking a bit about the definition of juggling. This is not always without risk…
I give 4 examples of starting points to do so:
1 - look in a dictionary
2 - ask 10 000 people on the street and from that information define some kind of general, statistically based definition
3 - look historically at what juggling has contained
4 - ask yourself how you feel about it
They will all give different results.
So #1, Looking in a dictionary gives (IMO) a bit boring view, and #4 did not seem interesting because it can just be anything and different from every person.
I was very interested in the definition that #2 would give, and the reason is I am a juggler and if I say that to people, I would like to know what pops into their minds. If I am promoting a juggling show I want to know what that label communicates, what preconceptions it creates and what expectations there is likely to be.
I was also very interested in #3 which was the closest to some kind of tangible truth that could be argued and discussed.
To get more specifically into what @Tomgrinyer was scratching at, I am not sure i would say interaction is the same as manipulation. Is there a difference between interaction and manipulation in your case, or what was the need to use this word, rather than manipulation?
I would say a trapeze artist interacts with the trapeze, but not necessarily manipulates it. Sure there can be manipulation, but I think there are other aspects that are more present (traditionally). Personally, if someone created a trapeze act where they intended manipulation, I would not have a problem calling that juggling definition wise, although I could see problems in calling it that in terms of promotion etc.
Same thing goes for the chinese pole, that (generally) doesn't move at all, other aspects like movement of the body, are more present.
I think also we need to remember there can be things that could fall in several categories, such as dance and juggling, aspects of both things are often present.
I think there is a barrier between a discussion of the definition and how the word is actually used in language and conversation. I could probably argue that some things could be defined as juggling, when in discussion, I would not use that word to describe them, since it is likely that it would just cause confusion.
I think that there are some manipulation types that will be find more often in juggling (such as a cascade of three objects) than others, and therefore can be easier to connect to juggling. If I juggle a cascade of three kittens, I doubt no one would say I wasn't juggling?
But in a duet between two people doing contact improvisation with aspects of manipulation, this could perhaps also be called juggling, but it is a harder case to argue, and even harder to argue why such a label should be put on it when there already is one that communicates what they do. What can appear here is territorial pissing, rather than communication.
We probably need to accept conceptual juggling also as juggling, so if someone would create a piece that has no juggling but still clearly draws the mind to juggling.
To answer your question, how do we define "object"?:
In juggling, I would define the object as "the entity that is being manipulated".