Richard Dawkins: Falling Down Mount Improbable

Richard Dawkins’ identification of others as intellectually deluded concerning the existence of God is based on an argument that succumbs to the logical analysis reductio ad absurdum. Dawkins confuses addition with multiplication.

Richard Dawkins’ argument for the nonexistence of God is the central argument of his book, The God Delusion. He argues that there is no mathematical solution to the ‘problem of improbability’ of God, whereas there is a standard mathematical solution to those ‘problems of improbability’ that are solvable. He claims this standard is the solution to the improbability of Darwinian evolution, such as the evolution of the mammalian eye in a single stage. The answer is to replace a single probability stage with its probability equivalent, namely a series of substages. Dawkins claims this “breaks up” a “large” piece of improbability into “smaller” pieces.

All too often, proponents of opposing views fail to communicate because the critic ignores his opponent’s argument. However, this is not so if the critic’s argument is a reductio ad absurdum. In this argument, the critic claims to demonstrate that the premise of his opponent’s argument implies that which is obviously false and thereby demonstrates that the premise upon which the proponent’s argument is based must be false.

Dawkins’ Argument

In several of his essays or lectures, specifically, those dubbed “Climbing Mt. Improbable” (1991, YouTube Lecture 3, minute 4:30), Richard Dawkins definitively illustrated an increase in mutational efficiency in the scheme of Darwinian evolution when an equivalent series of substages replace a single large stage of evolution.

However, he claims to have demonstrated an increase in the probability of success of natural selection, not an increase in the efficiency of mutation. By claiming that the difference in the single stage and the series of substages is one of probability, Dawkins contradicts the justification for the replacement, the fact that the sequence of substages is equivalent to the large, single stage precisely in the equality of the probability of success of natural selection.

Dawkins’ argument succumbs to the critique reductio ad absurdum from two perspectives: improbability and probability.

From the Perspective of Improbability

In the 1991 Royal Institute Christmas Lecture “Climbing Mount Improbable,” Richard Dawkins considers the case of three mutation sites of six mutations each. He notes that subjecting the three sites simultaneously to nonrandom mutation would require a minimum of 216 mutations to ensure the presence of at least one copy of the mutation that can survive natural selection. That is a 100% probability of success. Dawkins calls the 216 nonrandom mutations “tries,” mistakenly thinking the probability of success is 1/216 and that the improbability is a large “piece,” namely 215/216. He views the six comparable nonrandom mutations of each of the three substages of the series as representing a probability of 1/6 and an improbability of 5/6.

The yield of improbability of ‘breaking up’ the large piece of 215/216 is, therefore, the sum of three pieces of improbability of (5/6)x(36/36) = 180/216 each, for a total yield of 540/216. The yield of 540/216 of the breakup is greater than the “large” piece of improbability (215/216) broken up. That is an impossibility. It is logically absurd. Of course, 540/216 or 2.5 also exceeds improbability’s range of definition, 0 to 1.

In The God Delusion, Dawkins claims that the series of substages “breaks up” a large piece of improbability into smaller pieces that are “slightly improbable, but not prohibitively so,” thereby freeing Darwinian evolution from what Dawkins identifies as “the problem of improbability.” His own numerical example proves him wrong. His analysis is based on addition, whereas his example is based on multiplication.

From the Perspective of Probability

A similar absurdity results when considering probability. If Dawkins were right, the small piece of probability of 1/216 would be broken up into three larger pieces of 1/6 each for a yield of probability of 1/2. Breaking a small part of something into larger pieces is absurd, not science or mathematics.

From Both Perspectives

To accept Dawkins’ explanation of what he perceives to be “the problem of improbability” of Darwinian evolution is to identify Darwinian evolution as absurd. If a consequence of a premise is absurd, so is the premise. The real problem is not one of improbability within Darwinian evolution. The problem is Dawkins’ misidentification of an increase in mutation efficiency. He misidentifies it as an increase in the probability of success of natural selection.

A Word of Praise for Dawkins

Dawkins’ failure to see the distinction between the efficiency of mutation and the probability of success of natural selection should not blind us to Dawkins’ significant contribution to our understanding of Darwinian evolution. Dawkins’ analysis indicates that Darwinian evolution is not a biological theory but a set of mathematical algorithms. This is evident in that his illustration of 3 mutation sites of 6 mutations each would be clearer if the illustration referred to three dice. Instead, Dawkins presents it as the three interdependent dials of one combination lock vs. the dials of three independent locks of one dial each.

Dawkins is correct in that comparing a single large stage to its series of substages is critical to our understanding of Darwinian evolution. Indeed, correctly recognizing that the role of sub-staging is to increase the efficiency of mutation while having no effect on the probability of success of natural selection is to build on the initiating work of Dawkins in recognizing Darwinian evolution as a set of mathematical algorithms in which a series of substages replace a single large stage.

Dawkins takes the first giant step toward understanding Darwinian evolution but then falls over.

Mutational Efficiency

In the 1991 Royal Institute Christmas Lecture “Climbing Mount Improbable,” Richard Dawkins, although oblivious to doing so, implies a mutational efficiency factor of 12 = (216 mutations)/(18 mutations) in favor of the series of substages compared to a single, overall stage for three mutation sites of 6 mutations each. His illustration of nonrandom mutation is at 100% probability of success of natural selection for both the single stage and the series of substages.

Random mutation cannot achieve a 100% probability of success of natural selection, in contrast to Dawkins’ analysis of nonrandom mutation with its 100% probability of success of natural selection. However, a similar advantage in mutational efficiency is achieved in favor of the series of substages at given values of success with random mutation. For a probability of 90.9% of success of natural selection, the single stage requires 516 random mutations, while the series of substages requires only 57. That is an efficiency factor of 9 = 516/57 in favor of the subseries.

Summary

If Dawkins were not oblivious to what he demonstrated, he would have taken a second giant step in our understanding of Darwinian evolution by recognizing the role of substages in increasing mutational efficiency. He would have also realized that his central argument in The God Delusion is not only false in the context of the probability of Darwinian evolution but irrelevant to the existence or non-existence of God.

The existence of God is a philosophical topic to which mathematics is irrelevant. Thus, Dawkins’ argument could be dismissed on that basis. Instead, it is more appropriate to delineate the errors inherent in Dawkins’ argument in the mathematical context within which he presents it. Such is meeting him on his chosen turf.

My Way Vs. The Way, Truth, and Life in Western Philosophy

In his Regensburg Speech, Pope Benedict XVI traced the exaltation of the will over the intellect since the beginning of that exaltation in Western philosophy in the late Middle Ages. That degrading of the human intellect has come to fruition in our day. Contemporary thought begins not with seeing the beauty of God reflected in the natures of created entities, which are the direct objects of human knowledge in our lives on earth. It begins by declaring that My truth is the conformity of the natures of things to be what suits My way, even if it means choosing death rather than life for others.

We have abandoned the knowledge of God as seen through creation and reinforced through revelation, which identifies Him as The Way, The Truth, and The Life. Some have abandoned human thought as seeking the truth of the natures of created things. Instead, they favor an analysis alleged to be an evaluation of probabilities, even though probability is solely of mathematical form, having nothing to do with the natures of entities.