I was impressed with the lucidity of an essay at Strangenotions.com attributed to one, Chana Messigner (http://www.strangenotions.com/venn-diagram/). She was identified as graduating from the University of Chicago, having majored in mathematics and soon to commence teaching mathematics in high school. I now believe such a person to be purely fictitious.

The essay critiqued the proposal that science and religion cover disparate areas of human knowledge and therefore, by definition, cannot be in conflict. She noted that there are indeed areas of overlap. There would be no means of reconciling even apparent conflicts between science and religion, if the two disciplines have mutually exclusive epistemologies in accord with the premise that they cover disparate areas of knowledge. The epistemological basis of science is admittedly empirical evidence and obviously rational. The epistemological basis of religion is apparently faith and seemingly arational. In the absence of a common epistemology, any conflict must be resolved in favor of science.

This lucid essay was followed by an interview of the alleged Chana Messinger conducted by Brandon Vogt (http://www.strangenotions.com/messinger/). In it the interviewee claimed to be an atheist since reading *The God Delusion *by Richard Dawkins. A college math major can certainly be an atheist, but not by having read *The God Delusion*. That book is chock full of mathematical errors some of which are hilariously comical. Here are two.

The core argument of The God Delusion is that there is a mathematical solution to the improbability of evolution in a one-off event, but there is no mathematical solution to the improbability of God. When Dawkins discusses probability in the context of evolution, he is referring to mathematical probability, the fractional concentration of an element in a logical set, where the range of its definition is zero to one. When he discusses probability in the context of the existence of God, he is referring to the subjective numerical ranking on a scale of zero to one of an individual’s subjective certitude of the truth of a premise. Dawkins’ argument is based on equivocation in use of the word, probability.

Dawkins thinks his argument is mathematical. The mathematical probability of God is nearly zero and the mathematical probability of non-God (the improbability of God) is nearly one. However, when he “take(s) the idea of a spectrum of probabilities seriously” (p 50, *The God Delusion*), he rates theism at a probability of one, i.e. 100%, and atheism at a probability of zero! Throughout the rest of his book it is the other way round. The central thesis of his book is that the improbability of God is nearly 100% and the probability of God is nearly zero. Apparently in the rest of the book, in which he argues in favor of his thesis, Dawkins is not taking “the idea of a spectrum of probabilities seriously”.

More hilariously, having identified theism at a probability of plus one, he places its opposite, atheism, not at minus one, but at zero. Consequently he has no place in his spectrum for agnosticism, which should be zero, half-way between the plus one ranking of theism and the opposite ranking of atheism at minus one. When Dawkins realizes that there is no place for agnosticism in his spectrum, he says that if it is practical agnosticism, it can be shoehorned it in at +0.5. Dawkins identifies agnosticism in practice as having a middling opinion on the existence of God. The midpoint +0.5, is labeled a ‘temporary zero in practice’. However, he says this won’t do for agnosticism in principle. Agnosticism in principle would be the claim that the existence or not of God is humanly unknowable or that the premises, that ‘God exists’ and that ‘God does not exist’, have no meaning. Dawkins, to his credit, refuses to identify +0.5 as a ‘permanent zero in principle’. Even after discussing the fact that there is no true zero (no permanent zero in principle) in his spectrum of zero to one, poor Richard could not figure out the reason why. He doesn’t realize that his spectrum lacks a true zero due to his high school level mathematical blunder of identifying zero as the opposite of plus one.

Dawkins’ spectrum of probabilities has nothing to do with mathematical probability or with the objective truth or falsity of the premises. It is a scale for expressing the degree of certitude of one’s personal opinion. Perhaps Dawkins should be excused, because it is not easy to keep these distinctions clearly in mind due to the terminology employed. When Dawkins refers to the improbability of God, he considers it comparable to the improbability of the assembling of a Boeing 747 by a hurricane sweeping through a junkyard. (p 113, *The God Delusion*). Such improbabilities have nothing to do with mathematical probability or objective truth. These improbabilities do not identify a logical set of elements in which one or more of the elements is tagged ‘God’ or tagged ‘Assembling of a Boeing 747 sweeping through a junkyard’. In context, these probabilities apply solely to a scale for ranking the certitude of one’s personal opinion of the truth of premises. Yet, Dawkins claims, “I can’t get excited about personal opinions” (p 108, *The God Delusion*).

Of his many other blunders in math, another hilariously comical one is his claim that a big piece of improbability can broken up into smaller pieces (p 121, *The God Delusion*). That means that the complementary little piece of probability is thereby broken up into bigger pieces! Tied into this is his inability to see the distinction between an increase in the probability of success of natural selection and an increase in the efficiency of random mutation. That, however, is a more subtle mathematical error than indicating that a little piece of probability can be broken up into bigger pieces.

Mathematical probability is the fractional concentration of an element in a logical set. The probability of the total of elements in a set is one. A set may be divided into nested subsets. Consequently, the probability of one for the entire set can be broken up into smaller probabilities, which can be broken up into smaller probabilities corresponding to the nested subsets. A deck of playing cards would serve as an example. The probability of a card is 52/52 = 1. The thirteen probabilities of rank, each of 1/13, add up to one. That doesn’t hold for the thirteen improbabilities of rank, each of which is 12/13. Nested within rank, the probability of rank and suit is 1/52. These four probabilities of 1/52 within each rank add up to 1/13. In contrast, the probabilities with which Dawkins is dealing in Darwinian evolution are factors which are multiplied to form a product, the overall probability. They are not parts which are added to form a sum, the whole probability. Darwinian ‘pieces’ of probability don’t add up. Similarly, their product can’t be broken up into bigger ‘pieces’. Of course, I should not refer to Darwinian ‘pieces’, but rather to Dawkinsian ‘pieces’ of probability and Dawkinsian ‘pieces’ of improbability.

Except for those who plan to teach biology to university students and/or philosophy to the general public, high school students should learn:

1. The opposite of +1 is -1, thereby defining a range of which the mid-point is 0.

2. The arithmetic operations of addition and subtraction are distinct from those of multiplication and division.

3. The word, probability has several disparate meanings two of which are:

a) **The fractional concentration of an element in a logical set.** The probability of rolling 7 with a pair of dice is a material analogy of the mathematical concept of probability, i.e. the fractional concentration of 7’s, among the logical set of integers consisting of the sums of the outputs of two random numbers generators to the base, 6. That is a probability or fractional concentration of 6/36.

b) **The ranking by an individual of the certitude of his opinion of the truth of a premise.** For example, consider the premise ‘Grant is buried in Grant’s Tomb’ and its negative form, ‘Grant is not buried in Grant’s Tomb’. Let these have ranks of +1 and -1, respectively. An individual may then express the certitude of his opinion of the truth of these premises. Typically this would consist of two ranks, one for each premise. One individual may be fully convicted that Grant is not buried in Grant’s Tomb. He would place one of his two ranks at -1 for full conviction of the truth of the negative form of the premise and the other at 0 for the null conviction of the truth of the positive form. An individual who was half persuaded by each premise, would place one rank at +0.5 and his other at -0.5. An individual who had no interest and, therefore no opinion, would place both his ranks at 0, indicating temporary indifference in practice. Another individual, who claimed that both premises lacked meaning, would place both his ranks at 0, indicating permanent indifference in principle.

I can readily believe in the existence of an Oxford University Professor of biology as incompetent in high school mathematics as the author of *The God Delusion*. I cannot believe in the existence of a clear headed essayist named Chana Messinger, who graduated college as a math major and yet who found *The God Delusion* something other than a comedy of mathematical errors. Chana is purely fictitious.

For other mathematical errors by the author of *The God Delusion*, see earlier posts on this web site as well as (http://deltaepsilonsigma.org/media/delta-epsilon-sigma/DES_Winter_2010.pdf), “Richard Dawkins’ problem of improbability in *The God Delusion*: A valid argument for atheism or an error in mathematics?”

For an assessment of the central philosophical concept of the new atheism, see Part 1 (http://deltaepsilonsigma.org/media/delta-epsilon-sigma/1DES_Journal_FALL12F.pdf) and Part 2 (http://deltaepsilonsigma.org/media/delta-epsilon-sigma/Volume-LVIII-Spring2013-Number1.pdf) of “What is modern in the new atheism? – The inference of probability”.