Indexical uncertainty is irreducible subjective uncertainty induced by anthropically expecting to be in more than one possible future world.

Suppose you are an AI and shortly 2 instances of you will see "Hello green world" and 3 instances will see "Hello red world". If you are a conscious AI, then you should anticipate seeing a green world with 40% probability, and a red world with 60% probability, and this subjective uncertainty is irreducible because it reflects an objective state of affairs where different versions of you see different things. To obtain full knowledge of this state of affairs obtaining later is to be left with subjective uncertainty now about "what I will see happen next".

On the Many-Worlds Interpretation, quantum uncertainty is irreducible because it is indexical uncertainty; the amplitudes in configuration space diverge into blobs of different measure, and we find ourselves in all blobs, somehow with a weight proportional to the measure of amplitude inside our blob.