Mathematical probability is the fractional concentration of an element in a logical set. The word, probability, has the aura of the rationality of mathematics. Its synonym, chance, connotes a lack of rationale. The perfect deal is defined as four hands, each a flush of thirteen cards. Its probability is its fractional concentration and equals the probability of every other variant four-hand deal, namely one divided by the total number of variant four-hand deals. The probability is 4.474 x 10^(-28).
The following is an excerpt from the essay, “What is modern in the new atheism? – the inference of probability”, which was printed in the Delta Epsilon Sigma Journal, Volumes LVII Issue 2 (2012) and LVIII Issue 1 (2013). Links to the pdf files of the entire journal issues are:
Imposing an arbitrary extra-mathematical numerical limit on probability
This brings us to the most common error shared not only by Dawkins and his critics, but by many others. It is a variant of the argument of ‘the perfect deal’, which, due to its low probability, cannot be explained by chance. The argument goes by many names. Dawkins calls it ‘the problem of improbability’, by which he claims that the improbability of evolution in a one-off event is ‘far beyond the reach of chance’. The argument is that of ‘irreducible complexity’. Most complexities are explained by mathematical probability, but not those of a probability close to zero. The argument is also called the anthropic argument. In this form the argument claims that the combined probability of the various factors necessary for life on earth is so close to zero that the combination of factors cannot be due to chance.
The argument is based on the distinction between the connotations of the synonyms, chance and probability. Its general form is: The probability of this outcome is so close to zero that this outcome cannot be due to chance. The argument implies that chance is some numerical limit imposed from outside the mathematics of probability.
The argument is a mathematical self-contradiction. It states that the fractional concentration of this element in this set is so close to zero that it cannot be the fractional concentration of this element in this set. The problem of improbability, under whatever name, is a fiction. Dawkins’ thesis in The God Delusion is that there is no solution to the fictitious problem of the improbability of God, whereas Darwin’s theory solves the fictitious problem of the improbability of evolution in a one-off event.
It is a fiction. There is no finite limit to the number of elements in a set. Consequently, there is neither a positive lower limit greater than zero for the fractional concentration of a specific element in a set nor an upper limit less than one for improbability. For a set of n unique elements, the probability, 1/n, cannot be too close to zero to be a valid probability, nor can the improbability, 1 – (1/n), be too close to one. All numerical values of probability are of equal validity, irrespective of how close they are to zero.