Diaspora, by Greg Egan.

This book is set 1000 years in the future, and humanity has split into three seperate forms: consciousness in a virtual landscape called a polis, consciousness in a robot body called a gleisner, and humanity as it has always been, called a flesher. At the beginning of the story, an orphan virtual consciousness (Yatima) is created and released into the polis. It must grow up, and self realize individuality to become marked as a full citizen of that virtual landscape.

Here is the end of that introductory section.

…

(pg. 32)

Before the asteroid could coincide with the fourth citizen’s icon, the orphan jumped back to its friends.

Inoshiro was furious. “What did you do that for? You ruined everything! You baby!”

Blanca asked gently, “What did you see, Yatima?”

“The rock jumped a little. But I wanted people to think… it wouldn’t.”

“Idiot! You’re always showing off!”

Gabriel said, “Yatima? Why does Inoshiro think you flew with the asteroid?”

The orphan hesitated. “I don’t know what Inoshiro thinks.”

The symbols for the four citizens shifted into a configuration they’d tried a thousand times before: the fourth citizen, Yatima, set apart from the rest, singled out as unique – this time, as the only one whose thoughts the orphan could know with certainty. And as the symbol network hunted for better ways to express this knowledge, circuitous connections began to tighten, redundant links began to dissolve.

There was no difference between the model of Yatima’s beliefs about the other citizens, buried inside the symbol for Yatima… and the models of the other citizens themselves, inside their respective symbols. The network finally recognized this, and began to discard the unnecessary intermediate stages. The model for Yatima’s beliefs became the whole, wider network of the orphan’s symbolic knowledge.

And the model for Yatima’s beliefs about Yatima’s mind became the whole model of Yatima’s mind: not a tiny duplicate, or a crude summary, just a tight bundle of connections looping back out to the thing itself.

The orphan’s stream of consciousness surged through the new connections, momentarily unstable with feedback: I think that Yatima thinks that I think that Yatima thinks…

Then the Symbol network identified the last redundancies, cut a few internal links, and the infinite regress collapsed into a simple, stable resonance:

I am thinking –

I am thinking that I know what I’m thinking.

Yatima said, “I know what I’m thinking.”

Inoshiro replied airily, “What makes you think anyone cares?”

For the five-thousand-and-twenty-third time, the conceptory checked the architecture of the orphan’s mind against the polis’s definition of self-awareness.

Every criterion was now satisfied.

…