The Doomsday argument, attributed to Brandon Carter, was described by John Leslie (1993, 1996). It is worth recalling preliminarily its statement. Consider then proposition (A):
(A) The human species will disappear before the end of the XXIst century
We can estimate, to fix ideas, to 1 on 100 the probability that this extinction will occur: P(A) = 0.01. Let us consider also the following proposition:
(Ā) The human species will not disappear at the end of the XXIst century
Let also E be the event: I live during the 2010s. We can also estimate today to 60 billion the number of humans that ever have existed since the birth of humanity. Similarly, the current population can be estimated at 6 billion. One calculates then that one human out of ten, if event A occurs, will have known of the 2010s. We can then estimate accordingly the probability that humanity will be extinct before the end of the twenty-first century, if I have known of the 2010s: P(E, A) = 6×109/6×1010 = 0.1. By contrast, if humanity passes the course of the twenty-first century, it is likely that it will be subject to a much greater expansion, and that the number of human will be able to amount, for example to 6×1012. In this case, the probability that humanity will not be not extinct at the end of the twenty-first century, if I have known of the 2010s, can be evaluated as follows: P(E, Ā) = 6×109/6×1012 = 0,001. At this point, we can assimilate to two distinct urns – one containing 60 billion balls and the other containing 6,000,000,000,000 – the total human populations that will result. This leads to calculate the posterior probability of the human species’ extinction before the end of the XXIst century, with the help of Bayes’ formula: P'(A) = [P(A) x P(E, A)] / [P(A) x P(E, A) + P(Ā) x P(E, Ā )] = (0.01 x 0.1) / (0.01 x 0.1 + 0.99 x 0.001) = 0.5025. Thus, taking into account the fact that I am currently living makes pass the probability of the human species’ extinction before 2150 from 1% to 50.25 %. Such a conclusion appears counter-intuitive and is in this sense, paradoxical.
(excerpt from) Franceschi P. An Introduction to Analytic Philosophy: Paradoxes, Arguments and Contemporary Problems, 2nd edition, March, 2010
Ambiguous images ▣ Arbitrary focus ▣ Bistable perception ▣ Complementarity relationship ▣ Conflict resolution ▣ Conflict resolution with matrices of concepts ▣ Conflict types relating to matrices of concepts ▣ Contrary relationship ▣ Courage ▣ Dialectical contextualism ▣ Dialectical monism ▣ Dialectical monism in Aztec philosophy ▣ Dialectical monism in Heraclitus ▣ Dichotomic analysis ▣ Dichotomic analysis applied to paradox resolution ▣ Dichotomous reasoning ▣ Disqualification of one pole ▣ Disqualification of the positive ▣ Doctrine of the mean ▣ Doomsday argument ▣ Dualities ▣ Dual poles ▣ Extreme opposition ▣ General cognitive distortions ▣ Instance of one-sidedness bias ▣ Liar paradox ▣ Matrix of concepts ▣ Maximization ▣ Mental filter ▣ Minimization ▣ Bistable cognition ▣ Omission of the neutral ▣ One-sidedness bias ▣ One-sided viewpoint ▣ Opposition relationship ▣ Principle of dialectical indifference ▣ Requalification into the other pole ▣ Reference class ▣ Reference class problem ▣ Reference class problem in philosophical paradoxes ▣ Reference class problem in the Doomsday argument ▣ Reference class problem in Hempel’s paradox ▣ Reference class problem in the surprise examination paradox ▣ Selective abstraction ▣ Sorites paradox ▣ Specific cognitive distortions ▣ Surprise examination paradox ▣ System of taxa ▣ Two-sided viewpoint ▣ Viewpoint of a duality ▣ Viewpoint of a pole