Dealing with other people is probably the biggest part of most people's cognitive burden, though. And it's likely that the ability to make complex inferences when on one's own (solving a mathematical problem, writing a novel, or whatever) derives from the experience of communicating complex ideas through language.
I have a pretty close relationship with my dog and he has a fairly elaborate mental world, but his capacity for abstraction is limited. I taught him to find a ball that I had hidden or that he had dropped and forgotten about, and he has particular toys (including particular balls) that he knows are 'his' and which he doesn't like other dogs to play with, or that they are only allowed to play with within certain strictures (eg not taking it out of my dog's sight). I normally bring two identical balls for him to play with, and it turned out to be a lot harder to get him to go find the ball if he already had one on the ground - he would keep trying to give me the ball he had, and seemed unable to conceptualize that he could have a ball and not have a ball at the same time. Eventually he got the hang of this, but I have doubts about his ability to consider more than 2 states at a time, ie if I take him out to play with 3 balls and I don't see him having a ternary model of their location, but rather something along the lines of 'ball(s) I already have' and 'ball(s) I need to find'. Likewise he has a notion of pack hierarchy involving myself, himself, and several neighbors' dogs who he plays with regularly, but I think that's a fairly one-dimensional affair. Right now he knows it's raining when I open the front door and doesn't feel like walking around in it, but he'll still want to investigate the back door in the hope that the weather there might be different. He knows the diference between inside and outside (verbally as well as physically) but I'm not sure he has an abstract representation of a unitary outside.
EDIT: turns out playing with balls >> getting wet for the third time in 3 hours. Bang goes that theory.