III. Anthropic reasoning has issues with infinite worlds; D-SIA can fix this

Per LessWrong, philosopher Stuart Armstrong has found a critical flaw in how we reason about probability when dealing with infinite universes. Self-Indicating Assumption—the theory that you should adjust your beliefs based on how many copies of you exist in each scenario—works in finite worlds but fails completely in infinite ones. The math becomes undefined; you can't learn from observations at all. Armstrong proposes D-SIA, a distributional alternative that treats multiple agents as a continuous quantity rather than discrete counts. This fixes the paradoxes that plague traditional reasoning, and it matters if, as physics suggests, our universe is infinite.

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