Do we know that anything exists unperceived? "Its true that I am what I am because everything else is not me. But it isn't true that nothing outside of me can change without me changing. In fact, this happens all of the time. When someone in India dies, do I - a person in the UK - change? Surely not. But then, it will not follow that if the paper ceased to exist I would change."
When you suppose that the paper stops existing when not being perceived, do you mean that the atoms that form the paper disperse so that they are not shaped in the form of paper anymore or do you mean that the atoms stop being atoms and do not exist anymore?
I am assuming that when you say that something stops existing you mean that the atoms that form that something stop existing, they are no more. When you say that someone in India dies, its atoms do not stop existing, they just assume another organization. However, if they stoped existing, everything would necessarily change since you are literally taking something out of existence.
Now, if you mean that the atoms that form something change their organization in space when you are not looking at such something, an action should be causing such change, and such action should be absent when you look at such something again, or the other way around. If this is the case, what do you think is causing such change?. Also, I believe this action should be an action that acts only on that which you do not see but does not act on that which you do see, or the other way around. Therefore, if you were the paper, such action should be acting on what is now your body (from the point of view of the paper) when you are not perceving the paper and should stop acting on your body when you hold the paper. So what I am trying to say is that: if the paper dissapears when you are not perceiving it you should also dissapear relative to the paper, dont you think? However, your shape remains constant.
Now, if you mean that something literally stops existing just because we are not looking at it, I do not believe, and I gave you the reason why this is hardly probable.