Experiment #81 · Thought experiment

The Doomsday Argument

Anthropic reasoning about human extinction

Brandon Carter (1983); John Leslie; J. Richard Gott · 1983 · Anthropic reasoning, philosophy of probability

First published: B. Carter, Royal Society lecture (1983); J. Leslie, *The End of the World* (1996).

If you are a randomly-drawn human, you are unlikely to be among the first 5% — so the total number of humans is unlikely to be much larger than your birth rank suggests.

Treating yourself as a typical observer in the human population, you should expect your birth rank to be roughly median rather than extreme. If you are roughly the 60-billionth human, the total population is unlikely to exceed about a trillion — bounding humanity's future duration far below what naive extrapolation suggests. The argument is structurally identical to Sleeping Beauty and closely related to Bostrom's simulation argument; rejecting it requires rejecting either typicality or self-locating priors.

Formulation

Let N be total number of humans ever. Conditional on being human #n, infer P(N | n) via Bayes; with a flat prior in log N, expect N ≈ 20·n with 95% confidence. Hence doomsday relatively soon.

Compare this experiment

Dimensions Engaged

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Observer

Observer · Number: how should an observer reason about the size of their reference class?

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Time

Time · Extent: bears on the expected duration of human existence.

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Information

Self-locating information as evidence: does knowing your birth rank constrain population predictions?

Responses — How Schools Engage

Affirms / takes the bait 2

Multiverse Theory

Compatible with broader anthropic reasoning: the same self-sampling assumption that handles multiverse priors yields the doomsday verdict.

Simulation Theory

A close cousin of the simulation argument: both depend on typicality across populations of observers. Acceptance of one strongly motivates acceptance of the other.

Denies / rejects the premise 1

Logical Positivism

Anthropic typicality extracts cosmological conclusions from a probability measure no one knows how to specify. The argument is a methodological warning, not a positive thesis.

Reframes the question 1

Pragmatism

The argument's practical purchase is in motivating attention to existential risk; the specific probability claims are far less robust than the imperative to take long-tail risks seriously.

Holds it inconclusive 2

Naturalism

Live debate: depends on the right reference class and prior. Many naturalists treat the argument as a useful constraint on cosmology and risk reasoning without endorsing the headline doomsday verdict.

Analytic Metaphysics / Logical Atomism

A canonical battleground for self-locating priors: thirder-style reasoning supports doomsday; halfer-style reasoning does not.