A probabilistic discussion by mathematician Michael Ikeda and astronomer Bill Jefferys argues that the traditional reasoning about intelligent design from the presence of fine-tuning does not properly condition on the existence of life, and is also based on a incorrect reversal of conditional probabilities (in an example of the
prosecutor's fallacy), which in this form erroneously claims that if fine-tuning is rare in naturalistic universes, then a fine-tuned universe is unlikely to be naturalistic. (In this context, "naturalistic" is taken to be synonymous with "not intelligently designed".)
They offer a proof that indicates one should in fact draw the opposite conclusion: the presence of fine-tuning actually argues
against intelligent design. Their main theorem under the assumptions that
1 our universe exists and contains life (L),
2 our universe is "life friendly" (F), and
3 life can exist in a "naturalistic" (N) universe only if that universe is "life-friendly" (N&L ⇒ F), while life might exist in a "designed" universe even if it is not "life friendly"
states that, given our universe contains life (L), the probability that our universe is naturalistic, P(N|L), is less than the probability that our universe is naturalistic given that it is also fine-tuned, P(N|L&F) = P((N|L) | F). (That is, adding the assumption of fine tuning
increases the probability that our universe is naturalistic, given that we know our universe contains life.) Thus, they argue ironically, supporters of intelligent design should try to prove that our universe is
not fine-tuned. The philosopher of science Elliott Sober makes a similar argument.