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Up Level (Evolution)
Fisher's Fallacies


In a fallacious argument, unchallenged for fifty years, Fisher (1) sought to make plausible, by analogy, his claim that natural selection increases probability. He wrote:-

 "In the writer's opinion, it was Darwin's chief contribution, not only to Biology but to the whole of natural science, to have brought to light a process by which contingencies a priori improbable are given, in the process of time, an increasing probability, until it is their non-occurrence rather than their occurrence which becomes highly improbable".

 For an example in which the probability of a man having at least one son is 5/8, Fisher considered "the prior probability that a hundred generations of his ancestry in the direct male line should each have at least one son. The odds against such a contingency as it would have appeared to his hundredth ancestor (about the time of King Solomon) would require for their expression forty-four figures of the decimal notation; yet this improbable event has certainly happened."

"The peculiarity of natural selection with which we are concerned is that it constantly modifies the frequency with which different types of organism come into existence, and consequently the probability of all types of organism which might appear, whether such types are actually in existence or not.The rate at which the probability is modified will not be as great as that illustrated by the continuance of the male line, but, with selective intensities of the order of 1 per cent the lapse of 10,000 generations will suffice to bring about changes of probability of the same magnitude."

On a first reading, I immediately felt uneasy because, if the argument were valid, one could obviously, by taking larger and larger numbers of generations, show that an event with arbitrarily small probability had certainly happened. and this seemed just too far-fetched to be credible. There must be a mistake somewhere. It then took me, however, several months to put my finger on the flaw in Fisher's argument:

Each 1st-generation man either is an ancestor of some 100thgeneration man (and so may be placed in a set "A", say) or isn't (set "B"). Let P denote the probability that a 1stgeneration man will have an unbroken 100generation male succession. Each 100thgeneration man necessarily had an unbroken male ancestral line to generation 1; therefore, his ancestor there must have had an unbroken male succession for 100 generations and hence, for him (an Aman), and, similarly, for all Amen, P = 1. (Clearly, P = 0 for all Bmen). For a man chosen at random from the 1st generation (an "R" man), P = e, where  0 < e << 1. To get the event that "certainly happened" (P = 1), Fisher correctly chose an Aman. To get his "improbable event" (P = e), Fisher should have chosen an Rman but, instead, mistakenly chose an Aman and consequently concluded (wrongly) that an "improbable event has certainly happened".

In fact, Fisher demonstrated neither that an improbable event has happened nor that a probability has increased. Astonishingly, Fisher made an elementary blunder in a probability argument!

In the same article (1), Fisher made a second important error: he conflated complexity and improbability. By quoting Darwin's statement about the problem of explaining the origin of organs as complex as the human eye, Fisher tacitly acknowledged that it was the generation of complexity that called for explanation. However, he did not mention complexity again but instead discussed the generation of improbability. Complexity and improbability are not synonyms, and the generation of improbability does not imply or require the generation of complexity. A single counter-example suffices to show this: with certain bacteria, random mutations occasionally produce mutants that are resistant to certain viral infections and so have selective advantage in their presence. But the mutants are simpler than their parents (2), so increases in adaptiveness and improbability in this case are associated with a decrease of complexity.

This single example shows that an increase in adaptivity does not entail an increase in complexity. The onus is therefore on the Darwinists to substantiate their conjecture that random mutations plus natural selection can lead to increases in complexity. To the best of my knowledge, they have not yet done so.

Here, FIsher used the old bait & switch ploy: having used complexity as bait, he immediately switched his discussion to adaptivity!

So, even if Fisher had shown that adaptiveness and natural selection generate an increase of probability (he didn't, in fact), this would not have met his purpose because he would still have needed to show that there was also an increase in complexity.



(1)  R. A. Fisher, in Evolution as a Process, J. Huxley, A. C. Hardy, E. B. Ford, Eds. (Allen & Unwin, London, 1954), pp. 91, 92.
(2) Lee Spetner Not By Chance (Judaica Press, New York, NY, 1997, 1998)  p. 141, paragraph 3.