Is the outsider not needed for this line of reasoning to work assuming that the total number of people doesn't change? All the 100 blue eyed would commit suicid

Is the outsider not needed for this line of reasoning to work assuming that the total number of people doesn't change? All the 100 blue eyed would commit suicide after a hundred days after the creation of the island since they work out they have blue eyes. I think the main challenge in this puzzle is the lack of assumption on what kind of reasoning the islanders are capable of doing and what the initial conditions are.