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Dawkins Is More than Zeal

January 20, AD2014


Oftentimes the new atheists, including Richard Dawkins, are dismissed as offering nothing new, but simply expressing an evangelic fervor in spreading atheism. This could not be further from the truth in the case of Richard Dawkins. He has made a fundamental contribution to modern philosophy in the area of human knowledge; epistemology. By identifying human knowledge as the inference of mathematical probability from material reality, Richard Dawkins has laid the philosophical cornerstone of modern relativism.

Dawkins’ major contribution to modern philosophy

According to Dawkins all design, i.e. all intelligibility, has as its source, the human mind. It is only in human artifacts that material reality displays intelligibility. Material reality itself is irrational. The complexity of material reality merely gives the illusion of human design, i.e. intelligibility. The fountain of this complexity is mathematical randomness, the probability of which can be inferred from material reality. Mathematical randomness renders material reality irrational in itself. However, that randomness can be humanly organized by means of the human logic of mathematics. It is the inference of mathematical probability that renders material reality knowable and subject to scientific investigation. Because the individual human mind is the sole source of intelligibility, the individual human is the sole arbiter of everything. Viola, modern relativism.

The irrationality of material reality does not eliminate causality according to Dawkins, because mathematical probability is causality. It is in explaining the cause of biological speciation that Dawkins elaborates his philosophy of causation as mathematical probability. Dawkins’ argument is a counterproposal to the argument of Intelligent Design. Intelligent Design identifies biological speciation as complexity irreducible to probability, to randomness, i.e. to chance. According to Dawkins (The God Delusion, page 119-121) the possible explanations of the riddle of improbability of biological complexity are not design and chance as proposed by the proponents of Intelligent Design. Rather, the alternatives are natural selection and chance.

Proponents of Intelligent Design, in viewing design and chance as alternatives, identify causality as all or nothing. In such a scheme, causality is a discrete variable of 1, a complete explanation, or 0, i.e. chance and no explanation at all.

Dawkins claims that natural selection changes causality into the continuous variable of probability, ranging from 0 to 1. He notes that the evolution of a complex biological organism such as the mammalian eye in a one-off evolutionary event would be so improbable as to be a matter of chance and “no sane biologist ever said that it was” (The God Delusion, page 120). However, natural selection solves the problem of improbability by replacing a single, large stage with small sub-stages in which natural selection terminates each sub-stage, keeping it small. Thereby, natural selection increases the numerical value of probability of each sub-stage. Natural selection “breaks the improbability up into small pieces. Each of the small pieces is slightly improbable, but not prohibitively so”. (The God Delusion, page 121)

In this manner natural selection increases the probability of evolutionary success. Natural selection modulates the amplitude of causality. Causality is not a discrete variable of absence equal to 0 or presence equal to 1. Causality is a continuous variable, which has a range of amplitude from 0 to 1. Causality is not yes or no. Causality is mathematical probability, shades of grey. In Darwinian biological evolution, natural selection modulates the amplitude of mathematical probability, the amplitude of causality.

Dawkins’ philosophy does not explain away causality as does the philosophy of Hume. Hume essentially denied causality as simply a habit of human expectation. Hume identified causality as the human habit of associating sensual impressions as sequences, where such sequences are happenstance outside of the human habit leading to expectation of the sequence.

Dawkins does reject the traditional notion of causality, but as all, in contrast to nothing, which is chance. In accord with tradition, Dawkins rejects chance as an explanation. Dawkins does not reject causality. He refines it as having amplitude. He refines causality as mathematical probability, which varies in magnitude and which can be inferred from material reality. Indeed, according to Dawkins such inference is the very mode of the human understanding of material reality. In Dawkins’ philosophy, causality is characterized by degree. It is the degree or amplitude of causality, which is inferred from material reality as mathematical probability.

Dawkins’ philosophy and atheism

In the perennial philosophy, the existence of God is the conclusion of an argument based on the inherent intelligibility of material things. More than that, the very concept, the very definition of the word, God, originates in the conclusion of that philosophical argument. The conclusion is not, therefore, God exists. The conclusion is, therefore, unlike material things, which do not explain their own existence, though otherwise fully explicable in their intelligibility, there must exist a being whose intelligible nature and existence are identical; this being we call God. If material reality is not inherently intelligible, then there is no argument. Then the word, God, has no definition, and there is no being to be so named.

If Dawkins is right, that human knowledge of material reality is the inference of mathematical probability, then we should all be atheists. If mathematical probability is inferable from material reality, then material reality is not intelligible. There could be no argument for the existence of God. Then, atheism is true. Atheism would not be the disbelief in God, but the contention that the word, God, has no existential definition.

What do some of Dawkins’ critics propose?

Some agree in principle with Dawkins that mathematical probability can be inferred from material reality. They simply do not follow this to its logical conclusion that material reality is therefore fundamentally irrational. Madrid and Hensley (The Godless Delusion, p 130) identify inductive reasoning as the inference of probability. Similarly, Hahn and Wiker (Answering the New Atheism, p 22) identify mathematical probability as inferentially characteristic of the material processes affecting genetic variation.

In contrast, in The Last Superstition, A Refutation of the New Atheism, Edward Feser does not mention mathematical probability even once. He does not address the philosophical implications of the inference of mathematical probability. Feser completely ignores the thesis of The God Delusion, namely that whereas there is a mathematical solution to the improbability of evolution in a one-off event, there is no mathematical solution to the improbability of God. Instead of addressing the philosophy of the new atheism, Feser ably refutes versions of atheistic philosophy much older than that of the new atheists, while giving an excellent summary of the perennial philosophy of Aquinas and Aristotle. Feser’s book is a very worthwhile read for what it does address, in particular the exposition of Aristotle’s four causes of material things, namely the material, the formal, the efficient and the final. These are key to understanding Dawkins’ philosophy.

The crux of Dawkins’ philosophy

Of the four causes, the source of formal and final causality is the human mind, which expresses such causality in material artifacts. Because mathematical probability can be inferred from material reality, there can be no formal or final causality in material reality.

Of the four causes, only material causality is inherent in material reality as the principle of individuation. All material things are of the same nature, differing from one another in their individuality, which subjects them to mathematical probability.

Mathematical probability is not fundamentally the fractional concentration of an element in a logical set. Rather it is the efficient cause of material events. More importantly it is the efficient cause of the very existence of things and thereby the sufficient explanation of their existence. Mathematical probability is the probability of coming into existence.

The Aristotelian solution

Material reality is inherently intelligible in its formal, efficient and final causality. Its formal and efficient causality is the source of measurable properties, which in their intelligibility are mathematically related and the subject of scientific investigation.

Material causality is the principle of individuation which renders material things countable. The individuality of a material thing cannot be separated from its measurable properties. The mathematics of probability, which concerns solely the individuality of logical elements, can be applied to material reality only analogically.

The jargon of mathematical probability in its use of words such as event, outcome, occurrence and result, connotes coming into being. Nevertheless, in reference to material reality, probability has nothing to do with existence and everything to do with human ignorance, i.e. limited human knowledge, including limited scientific knowledge. Probability characterizes knowledge, not reality.

The mathematics of probability involves the formation of other logical sets based solely on the probabilities of a logical source set. Although the elements of the logical sets may have IDs which indicate their possession of measurable physical properties, it is only their logical membership in sets due to their individuality that matters. The IDs are purely nominal tags. It is only in logic that the measurable properties of a thing can be divorced from its individuality. Consequently, the mathematics of randomness, in which only individuality is relevant, cannot be inferred from material reality.

The mathematics of probability applies to logical elements and logical sets. The nexus which permits the analogy of probability by material simulation is the purposeful human ignorance of the causality of selection. For example, the roll of dice is viewed as random by identifying randomness as the human ignorance of the physical forces, which non-randomly determine the actual outcome in each roll. The mathematics of probability may be employed to compensate for human ignorance at the level at which randomness is posited.

The Aristotelian understanding of the four causes recognizes material reality to be inherently intelligible, rendering the mathematics of experimental science inferentially possible. In its further understanding of the material cause as the principle of individuation, it recognizes mathematical probability as analogically, not inferentially, applicable to material reality.

Note: In addressing the improbability of evolution in a one-off event, Dawkins correctly identifies the mathematical framework of Darwinian evolution as cycles of an algorithm of mathematical probability and of the discriminate filtering of the generated random numbers. However, he gets the mathematical details wrong.  Read more here.

© 2014.  Bob Drury.  All rights reserved.

Photography: See our Photographers page.

About the Author:

Bob Drury is retired. He has been fascinated with the reasonableness of the Faith since his junior year in high school in the mid-20th century for which the religion text was entitled, “Faith and Reason”. That fascination has continued throughout his education in philosophy, math and science. In his essays he hopes to share that fascination with others. Read more at his website, They Have No Wine.

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  • Camila

    Hi Bob,

    This was interesting. I am currently taking a philosophy course and we are covering the Thomistic/Aristotelian proves of God.

    You say “If Dawkins is right, that human knowledge of material reality is the inference of mathematical probability, then we should all be atheists.” I don’t get this. Why should this be so? If I apply the principles I have learned so far (early in the course) I would say something like this…

    The fact we can have any inference of mathematical probability is proof positive that there are various beings in existence. None of which can explain its own existence. All beings are caused causes or we might say inferred inferences, right? So even if there was only 1 inferred inference, or even 1 very simply mathematical probability that is enough to prove that there must have been some ‘other’ being who is not a caused cause or inferred inference; that is there must bee an uncaused cause or an uninferred inference, if you will. Even if we don’t want to call this being ‘God’ yet we must conclude this. Since otherwise it would only be another caused cause and another inferred inference in the long (or short) chain of caused causes or inferred inferences, correct?

    At some point this chain was not and then it was. Even if all be a mathematical exercise – the very fact we can ‘observe’ such a reality makes the point there IS a reality….. And IF there is any reality we can easily apply Aristotle’s and Thomas’ solution.

    Am I being too simplistic?

    • We agree that a relationship among material things cannot be inferred without inferring their existence. We differ in our appreciation of the mathematics of probability.
      Science is the discovery of the mathematical relationships inherent in the measurable properties of material reality. These relationships are inferred from material reality. Such inference cannot be true of probability, because the relationships of probability apply only to elements which have no
      measureable or other characteristic properties.
      Probability postulates that the only characteristic of an element is its individuality. It can be counted. All other characteristics, although denoted by the nametags of the elements, are essentially non-existent. In probability, God, a mountain, each of two tigers and a paperclip are logically equal. These five elements merely belong to four different logical sets. The
      mathematics of probability cannot be inferred from reality, unless the
      characteristics by which we know material reality are meaningless. Probability concerns only logical elements of logical sets. The above set of nouns does not designate existing things within the context of mathematical probability. The set of nouns does not differ in probability from the set: A, B, two C’s and D.
      In the science of gravity, a mountain, two tigers and a paperclip are reduced to mass. However, mass is characteristic of these material things as material, not as logically equal individuals.
      I would not resort to series and chains of causality in
      proof of the existence of God.

    • Camila

      Let me see if I understand. What you are saying is that reality could simply be a result of the probability of atoms coming together and then ceasing to come together and perhaps rearranging itself again. In the context of eternity I suppose that millions of years is but a tiny fraction of time so what we perceive as a long time, say for example 1 year (any unit of time would work here really) is so small next to infinity. The tiger or the paper clip or me for that matter is just the result of a probability? We can translate this concept to ‘mathematical probability’ into numbers – who cares whether this number becomes me or a tiger or the paperclip, the point is that it is just a single event in the infinite number of probabilities.

      If the above is correct; I don’t understand how God can be another probability. The definition of God is not compatible with probability.

    • Camila

      Further, if we must abstract logic from reality – what use is there in that?

      Unless we deny that matter is not – and we imagine all is but an idea – a mathematically probable idea – then would the atheist say that even the idea of ‘me’ as I know myself to be also be the result of mathematical probability?

    • Camila

      How does mathematical probability explain altruism?

    • Jeff_McLeod

      Mathematical probability does NOT explain altruism. Altruism is an improbable thing in a universe that tends toward entropy.

      It’s almost as if a REMNANT preserves the order of things, right? This is what the prophets said, right? Read the prophets in the Old Testament. There is a remnant that survives, despite the trends of the universe. The remnant, against all odds, fulfills the divine plan.

    • Jeff_McLeod

      I should add, from a strict probabilistic viewpoint, anything is possible, right? I on the other hand am coming from a maximum likelihood point of view where we ask what is the most LIKELY explanation for the explained data. From THAT viewpoint, there is no explanation of altruism. It is utterly unlikely under the hypothesis of random fluctuation around a norm of self-interest could “explain” altruism. You simply can’t say that altruism is just as expected as a stock market crash.

      Others might argue that altruism, while unlikely, is still empirically possible under the hypothesis of random fluctuation.

      You can’t really argue “explanations” from probability. ANYTHING is explained by Kolmogorov’s probabilities, right?

      What you CAN argue is the likelihood of outcomes. And this, I submit, is where altruism is a most unlikely event.

    • Camila

      Well, what I was thinking is whether in the world of probabilities there is any way to argue for a kind of cause and effect. My computer is just as a probable outcome as my phone as my dinner; and all at the same time.

      As I pondered, I think altruism is more of an anti-thesis to natural selection as suppose to the probability line of thought. In the survival of the fittest mentality, altruism makes no sense – even less when it serves for the purpose of saving a more inferior being.

      And by inferior I mean with lesser possibility or likelyhood of reproducing itself or that if it were to reproduce would inherently carry less desirable traits.

    • Camila


      After my last post what came to my mind is Christ’s word to Peter “He (Jesus) said to them, “But who do you say that I am?” Simon Peter said in reply, “You are the Messiah, the Son of the living God.” Jesus said to him in reply, “Blessed are you Simon son of Jonah. For flesh and blood has not revealed this to you, but my heavenly Father.”

      In other words, at its extreme, if we reduce reality to a mathematically probable scenario, where it would be possible to conclude that God does not exist, then Jesus’s word are amazing here. For flesh and blood can fathom God’ non-existence so a human (flesh and blood) affirmation that God exist can ONLY be done by Divine intervention – the infusing of the theological virtue of faith.

      This whole thing proves that faith can not be produced by the human mind, but must be given from God to a soul humble enough to ask for it.

      This is absolutely amazing if we think about it. Jesus’s words are truly stunning!

    • Jeff_McLeod

      I wholeheartedly agree with you comment! Jesus is saying, my gosh, Simon Peter, what you said is most improbable, and yet you are spot on!

      It is stunning as you say!

    • Camila

      I like how you said this.

    • I have to apologize for being so obscure. What I hoped to convey was that mathematical probability is purely logical having nothing to do with existence, real beings, material
      events or time. Probability is the fractional concentration of a logical element in a logical set. The mathematics concerns the definition of new logical sets in terms of the probabilities of an arbitrary, logical source set. In randomly forming a new set of one card from a deck of fifty-two, what is the probability of its being the three of diamonds? The IDs of the elements are purely nominal. Whether an element is tagged ‘God’ or ‘Playing Card’ has no relevance to the mathematical relationships, nor to the real things from which the tags may be stolen. It is people like Dawkins, who mistake thought for reality by claiming that mathematical probability is characteristic of real things, can be inferred from real things and is the efficient cause of the existence of things (though he doesn’t use the philosophical terminology, efficient cause). Admittedly and perhaps unfortunately, the jargon of the mathematics implies that probability is an efficient cause. You may find of interest:

    • Camila


      Your post was very interesting, and it was an interesting discussion. Thank you for your patience, nothing to apologize. I found it most relevant considering the class I’m taking. I’m fascinated by all this.

      You say “it is people like Dawkins, who mistake thought for reality” – I think this is a common problem; in my opinion.

      God bless you Bob.

    • Camila

      I’m still thinking about our conversation. The more I think the more I realize just how Dawkins’ ideas are crazy. So just as this world ‘as we know it’ could possibly be an outcome so too any combination (even ridiculous combinations like me being in the middle of the dinosaur era drinking hot cocoa and watching tv)…..

    • I agree, but I would like to make a couple of distinctions. Mathematical probability is concerned solely with logical elements in logical sets. The ID tags of the elements in sets are appropriately nouns, like heads and tails, not actions like being, drinking and watching. The jargon often implies action like the probability of rolling a seven with two dice. However, that probability of 1/6 is static. It refers to the number of sums equaling seven in the logical set defined as the sums of the mutations of two sets of the integers one to six. The only ‘action’ is the definition of a static, new
      logical set based on the probabilities of static, logical source sets. Dawkins thinks mathematical probability has to do with actions and coming into being,e.g. the probability of a hurricane’s assembling a Boeing 747 by sweeping through a junkyard. That doesn’t define a set of elements, even a set of one element. Anyone may rate his certitude of such an ‘event’ on a scale of zero to
      one. However, such probability refers to personal certitude of the truth of a proposition and has nothing to do with mathematical probability or even the objective truth of the proposition. Such confusion is the basis of much of Dawkins’ argumentation. In contrast to mathematical probability, the mathematical relationships evident in the measurements of material properties are evidence of the order inherent in material reality. However, we are led to seek such mathematical relationships through science because we are already philosophically aware of the orderliness of created material reality. See “Science Was Born of
      Christianity” by Stacy Trasancos. (Note: The last two posts on my blog concern the distinction between probability and density.)

    • Camila

      Thanks Bob. I appreciate your willingness to converse with me.

  • Patti Maguire Armstrong

    Some of my relatives are turning to atheism. The problem is that they have closed the door on God and attack all arguments that lead to him. At this point, prayer is going to have to bring those walls down. Thanks for such an intellectual article on atheism.

    • Prayer is surely the answer, especially the Mass. What surprises me is that we have seemingly squandered our centuries old patrimony in just three generations. It has not been a gain of understanding, but its loss.

  • leogirl87

    I think these “new atheists” have seen one too many sci-fi films.

  • Jason Fairfield

    Any good books that you recommend to help me better comphrehend this discussion, my background in philosophy is rather weak.

    • Feser’s book is a good introduction to the perennial philosophy
      of Aristotle / St. Thomas and the four causes, the material, the formal, the
      efficient and the final. Feser also offers a good critique of much of older, modern philosophy. Does anyone else have a suggestion?

      Part of any problem you may have is my not explaining things clearly enough. My essay is trying to point out how the mathematics of probability does not consider what a member of a logical set is in itself. Rather the mathematics only considers things as individuals. That is fine in this area of pure mathematics, where the properties of elements are irrelevant. Only individuality is relevant. However, this particular area of mathematics cannot
      be applied to real things except by analogy. We can’t separate the individuality of a real thing from what it is in itself. Here is where Dawkins parts company with the perennial philosophy. Dawkins claims that ‘vegetables are our cousins too’; that humans don’t differ from ‘a lemon’ by any ‘essentialist absolute’.
      In other words we are all individuals of the same kind and the mathematics of probability applies directly to everything. We, carrots, ants, humans, are all just individual elements.

      In the perennial philosophy, each material thing is a composite of two principles, matter and form. Form is general. It is the what of what a thing is. We are both humans among billions of humans. We don’t differ from one another in our humanness. We are both human, not because we differ in our substantial or essential form, but because the other principle of our compositeness is a principle of individuation, namely matter. Our
      intelligibility derives solely from our form, not from the principle of individuality. However, our substantial form is expressed in and through our

      The principle of individuality, i.e. matter, has no intelligible content. In this we concur with Dawkins. However, for Dawkins individuality is the only thing that counts (pun intended) because individuality is the essence of material things. A human is a lemon, except for individuality. The mathematics of probability considers only individuality. Thus, according to Dawkins we can infer mathematical probability from material reality, which inference is our very knowledge of material reality. Dawkins’ philosophy is the foundation of much of current modern thought, e.g. explaining our universe as a probability among multiverses. We can’t ignore Dawkins’ philosophy of probability or dismiss it offhand as trivial, as nothing new.

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