Self-referencing doomsday argument rebuttal

Self-referencing doomsday argument rebuttals attempt to refute the Doomsday argument (that there is a credible link between the brevity of the human race's existence and its expected extinction) by applying the same reasoning to the lifetime of the Doomsday argument (DA) itself.

The first researchers to write about this were P. T. Landsberg and J. N. Dewynne in 1997; they applied belief in the DA to itself, and claimed that a paradox results.

If the DA's lifetime is governed by the principle of indifference and the Copernican principle then based on the length of its current existence, and assuming that it is randomly drawn from a reference class of probabilistic speculations it is 95% certain that it will be refuted before the year 2500.

If the DA is not itself subject to these principles then its assumption that the human race's survival-time can be modeled using them appears to be a paradox (to Lansberg & Dewynne).

Alternatively, if the DA is subject to these presumptions, then as it is expected to expire (be refuted) earlier that its own prediction for the likely survival time of humanity there is a second paradox: The predictions of a theory concerning events to occur after it has been refuted (such as human extinction) are not logically meaningful. Conversely, if the DA survives until the end of human civilization (in the year 5000, say) then it will have dramatically beaten the odds against the expectations of the Copernican principle. This can create a paradox for an argument based on probability, as shown if future scenarios are broken into three groups:

The "quick extinction" in possibility 1 is considered fairly likely in those Doomsday arguments using the number of births as a reference class, but comparing like-for-like we should compare the length of time the DA survives before refutation with the length of time the human race survives before extinction. Therefore, J. Richard Gott's (temporal) DA is used to calculate the probabilities of the three scenarios above:

If the Doomsday Argument can apply to itself it can be simultaneously right (as a probabilistic argument) and probably wrong (as a prediction).

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