Richard Dawkins on Understanding Fractions

Bob Drury - Dawkins

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Are you English? Richard Dawkins gave the correct answer: It’s a matter of degree. You’re as English as the fractional concentration of Englishmen among your ancestors. No matter what fractional concentration of your ancestors is English, that fraction plus the fractional concentration of non-Englishmen among your ancestors equals one.

Richard Dawkins has used this arithmetic as a stick to rap the knuckles of those who disagree with him. Funny thing, it turned out to be a sledge hammer with which he hit himself smack between the eyes. By the valid analysis in his essay, The Tyranny of the Discontinuous Mind, Dawkins established the inanity of the thesis of his book, The God Delusion. Its thesis is that whereas there is a solution to the problem of improbability of evolution in a one-off event (i.e. happening only once), there is no solution to the problem of the improbability of God. However, his essay demonstrates that the problem of improbability, as a concept, is illogical.

In his essay, The Tyranny of the Discontinuous Mind, Dawkins says some people can’t see the continuity of the degree of ethnicity as well as the continuity of degree in other variables. Dawkins labels such people as having a Discontinuous Mind. Persons of a discontinuous mind insist that such variation is black and white, differing in kind, not degree. One such person of a discontinuous mind might say that anyone whose fractional concentration of English ethnicity is less than 25% is not English. Dawkins points out, such a person has chosen an arbitrary point of discontinuity in the continuous spectrum from 0 to 1 to divide the spectrum of ethnicity into a dichotomy, demarcating two different kinds when in fact there is only one kind differing in degree.

Who could have such a \”Discontinuous Mind\” and make such a blunder of seeing a dichotomy of kind, when there is only a continuous spectrum over the range of 0 to 1, where values differ only in degree? How about Professor Richard Dawkins himself? The focus of his book, The God Delusion, is the problem of improbability. If one understands fractions as correctly explained by Dawkins in the case of ethnicity, then there can be no problem of improbability to be discussed by Dawkins in the case of improbability.

Just like ethnicity, probability is a fractional concentration over the range 0 to 1, where values of probability differ in degree, not kind. However, Dawkins sees values of probability as differing in kind. According to Dawkins there are two kinds: values of probability that are scientific explanations and values of probability that are insane chance.

Probability is the fractional concentration of an element in a logical set. The probability of heads is one-half because that is the fractional concentration of heads in the set of heads and tails. The probability of any of the six faces of a die is one-sixth. A probability can be any value over the range of 0 to 1. A probability plus its improbability equals one.
The arithmetic complement of probability, namely improbability, has the same range of definition, 0 to 1. Any two values of probability differ from one another by degree, not kind. Likewise, any two values of improbability differ from one another by degree, not kind.

In the \”Discontinuous Mind\” of Richard Dawkins, there is a problem of improbability with Darwinian evolution in a one-off event such as the evolution of the mammalian eye in a single cycle of random mutation and natural selection. That improbability is so close to 1 that it is far beyond the reach of chance. Chance is not a solution to the problem of improbability and no sane biologist ever said that it was. The problem is how to escape from chance. Chance is the problem which must be solved. The problem is solved by breaking the improbability up into small pieces, each of which is slightly improbable, but not prohibitively so (The God Delusion, pages 119-122).

In other words, there is an arbitrary value of improbability close to 1, which demarcates a discontinuity in the range of definition of improbability. This point of discontinuity divides the spectrum into black and white, into a segment of the range of improbability that is a scientific explanation and a segment close to 1, where improbability is not a scientific explanation, but is insane chance. Values below the point, which was arbitrarily established by the Discontinuous Mind, are of the non-prohibited kind. They are scientific explanations. Values greater than the point are of the prohibited kind. They are scientifically inexplicable chance. Dawkins’ philosophically whimsical identification of a discontinuity trumps the logic of the arithmetic of degree not kind for the variable, improbability.

The fact is that Dawkins is right about ethnicity and the principle of continuity, which is the theme of his essay, The Tyranny of the Discontinuous Mind. However, Dawkins is wrong in The God Delusion because its thesis violates this valid principle. Due to the principle of continuity, The God Delusion’s problem of improbability is logically indefinable. The God Delusion is a not a book arguing in favor of the non-existence of God. It is a book arguing in favor of the existence of a non-existent problem in the logic of arithmetic, which Dawkins now admits is illogical in his essay.

Either his book is illogical or his essay is illogical. Either improbability is of two kinds, which are separated from one another by a point of discontinuity within its range of definition according to the book or, according to the essay, any two values of improbability over its range of definition of 0% to 100% differ from one another by degree not kind.

A longer version of this essay is posted on my website here.

© 2013. Bob Drury. All Rights Reserved.

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3 thoughts on “Richard Dawkins on Understanding Fractions”

  1. Any argument for a deity is, deistic, even if scientists conceded that much (there is no evidence for an intelligent beginning to our universe) this get’s you exactly as close to Catholicism as it does Islam or the Flying Spaghetti Monster.

    Ramen, may his noodly appendage touch you too.

  2. Pingback: Richard Dawkins on Understanding Fractions - CATHOLIC FEAST - Every day is a Celebration

  3. There seems to be a shift to the continuous mind in the field of psychiatry. For example, the new DSM-5 will group all of the subcategories of autism into a single category called autism spectrum disorder (ASD). This will eliminate the previous separate diagnoses of autism – including autistic
    disorder, Asperger’s disorder, childhood disintegrative disorder and
    pervasive development disorder. I think the black and white way of thinking today can be seen in extremist views that are making the news, like the assertion that we must choose between 100% national security and 100% personal privacy. Dawkins probably didn’t do well with the metric system and decimals. Very interesting.

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