Is There a Probability for the Universe? New Thoughts about the Anthropic Coincidences

The heavens declare the glory of God; and the firmament sheweth his handywork. Day unto day uttereth speech, and night unto night sheweth knowledge. There is no speech nor language, where their voice is not heard.”
—Psalm 19 (KJV)

“It is a strange fact, incidentally, that religious apologists love the anthropic principle. For some reason that makes no sense at all, they think it supports their case. Precisely the opposite is true. The anthropic principle, like natural selection, is an alternative to the design hypothesis. It provides a rational, design-free explanation for the fact that we find ourselves in a situation propitious to our existence.”  
—Richard Dawkins, The God Delusion


The illustration above is a diagram of the “Triple Alpha Process” describing the nuclear synthesis of carbon-12 nuclei in giant stars from three helium nuclei (alpha particles).   It’s one of those “special” events or features that are called “anthropic coincidences.”   These anthropic coincidences, regarded as unlikely events  (low probability events, but see below) are the basis for the  “Anthropic Principle,”that our universe is finely tuned to support carbon-based life. It’s known in several versions ranging in acronym form from Weak Anthropic Principle (WAP), to the Strong Anthropic Principle (SAP), the Christian Anthropic Principle (CAP) and, not least, the Completely Ridiculous Anthropic Principle (you do the acronym).

My interest in this was reignited by Bob Drury’s fine post about why it’s not correct to use probability arguments about the Anthropic Principle, fine-tuning of the universe.   Many believers in God argue that when the Anthropic Coincidences are combined, the exceedingly small joint probability of them happening together supports the proposition of a creating God.   As I will try to demonstrate below and as Bob Drury pointed out, this reasoning is incorrect.

Nevertheless, I also believe that these anthropic coincidences help us to believe in God. I take the point of view of the psalmist  in Psalm 19,  quoted above: “The heavens declare the glory of God.”   I’ll argue that if probability is taken as a measure of the degree of belief (how much you would be willing to bet on the truth of a proposition), then it can be applied to the Anthropic Coincidences to support belief in a creating God.


I’ve discussed the Anthropic Principle in several other posts on this blog:   Philosophic Issues in Cosmology 6The Theology of Water,  and Are We Special: The Anthropic Coincidences.  The arguments presented in these posts can be classified as shown below.   The categories listed are discussed in greater detail (with examples) in the linked posts and references given therein.

  • Features of the universe–e.g. space dimensionality 3; the mass/energy content of the initial universe that enabled expansion but not immediate collapse; uniformity in very early universe;  size;
  • Finely tuned values for fundamental physical parameters–e.g. the mass difference between proton and neutrons that enables stability for nuclear processes; the carbon-12 excited state energy that by resonance enhances the probability of carbon-12 nucleus formation from a rare collision of three He nucle (see figure and linked referencei;
  • Nature of physical laws–e.g ratio of electromagnetic force to gravitational force; inverse cube force law for gravity; quantum mechanical laws that enable chemical bonding and (see below) the special properties of water;
  • “Accidental” geo-astronomical features–e.g. tilt of the earth’s axis enabling life-friendly climate, unusually large moon shielding earth from asteroid and meteor collision.

It must be emphasized that there are many more instances of such fine tuning–parameters for which the values have to lie between narrow limits to enable a life-supporting universe, and many more examples of geo-astronomical and chemical features.    George F.R. Ellis, in the reference linked above, specifies general conditions that must obtain for a universe to contain life as we know it.


Ellis points out a major objection to using probability arguments for the existence of the universe: the universe is a single datum—probability arguments are generally applied to samples from larger collections for which we have information about variability (if one holds a “frequentist interpretation” of probability, as below).  For example, if you’ve examined 20,000 crates of oranges and found 100 crates containing bad oranges, you’d be justified in putting a probability of  100/20,000 or .005 in finding a bad orange in the next crate.   But if you’ve only come across one crate of oranges, then it’s speculation to put a probability on finding a bad orange.  (But see below.)

Another error one finds is that some apologists list a string of fine tuning examples (call them a,b,c,d…x),  and then use the argument that P(a,b,c,d…x) = P(a) P(b) P(c)P(d)…P(x).  They say that the probability of the total set is the product of the probabilities for each member  of the set. This would be true if the events were independent, in other words if what happened for one event did not depend on what happened for another.¹  Such independence will not necessarily hold. Consider, for example, the properties of water that are life-friendly:

  • thermodynamic–high freezing and boiling points, high specific heat, etc.;
  • physical –surface tension, low specific gravity of ice, maximum density of liquid water at 4 deg C.

These properties all depend on the very unusual capacity of protons in a H2O molecule to form strong hydrogen bonds to oxygen atoms in other H2O molecules.   And that hydrogen bonding capability arises from quantum mechanics and the physical nature of electrostatic attraction.    So it is one feature, not many, for which a probability should entered. .And how do you assess the probability of quantum mechanics giving rise to hydrogen-bonding?


“But is it probable that probability brings certainty?
—Blaise Pascal, Pensees 496

I’m going to try a different approach, using probability as a measure of belief. (I apologize to those professional statisticians and mathematicians who will possibly be offended by my presumption.)   The approach is my take on Richard Jeffrey’s Subjective Probability.

Let’s start with a different definition of probability, based on strength of belief.   Consider the following examples for betting on a horse race.   You overhear a trainer telling a pal that “the next race is fixed for Trump’s Nag to win, with odds of 9/1”.    You bet $10,  expecting to win $90.    The defined probability, working from the odds ratio, is  1/(9+1) = 0.10.    The probability of losing your bet is then 1- 0.10 = 0.90.    The expectation value² is 0 = 0.10 x 90 + 0.90 x(-10).

The next step is to consider conditional probability, that is how the probability of an event depends on a linked event.   Let A represent the event that a stock price rises to $100.   Let B represent the event that information about the possible rise of the stock is given.    Then the conditional probability is denoted as p(A|B), the probability of event A given that event B occurs.   Note that there is no causal relation implied here–it’s only a matter of evidence.

Now to the meat of the matter.   Let F represent the proposition  “the universe is fine-tuned for carbon-based life to exist“;  G: “God exists“;  N: “God does not exist (or that “Naturalism= materialism” accounts for everything).    Then

  • p(G | F)  is a probability, a degree of belief, that F —> G, i.e. fine-tuning is evidence for the existence of God;
  • p(N | F)  is a probability that fine-tuning implies that God does not exist;
  • p(F | G) is the probability that if God exists then He can fine-tune the universe;
  • p(F | N) is the probability that a fine-tuned universe would occur in the absence of God;
  • p(G) is the probability—the degree of belief—that God exists;
  • p(N) is the probability—the degree of belief—that God does not exist.

Then straightforward manipulation³ yields

 P(G | F)) = [ P(G) ] [ P(F | G) ]
 P(N | F)      [ P(N) ] [ P(F | N)]

     1                     2             3

Term 1 is a likelihood ratio for degrees of belief: the ratio of “belief strength that fine-tuning implies the existence of God” to “belief strength that fine-tuning  implies no God;”  term 2 is a likelihood ratio,  “belief strength in God” to “belief strength in no God (naturalism);”   term 3 is a likelihood ratio “belief strength that God, if He exists, would create a fine-tuned universe to support life” to “belief strength that naturalism/materialism would yield a fine-tuned universe.”

Now certainly term 3 is a number much greater than 1, even if the exact value is indeterminate.   The value for term 2 will depend on the individual–for a Christian martyr, it would be a huge number;    for Richard Dawkins or Lawrence Kraus it would be a very small number.

Here’s the point: the value you impute to term 1, the likelihood ratio for belief that a fine-tuned universe is evidence for the existence of God, will be greater than  1 if you are not a hard core atheist.    If you’re agnostic—if you think that it’s a 50/50 proposition that God exists—then certainly fine tuning should convince you that God exists.   If you’re a strong believer in materialism/naturalism (Dawkins or Kraus), then term 2 would be small enough to swamp term 3, even if the latter is very large.

So the upshot is that if you do believe in God or if you’re an agnostic, fine tuning can be evidence for God’s creating hand.   If you’re an atheist—this will not be sufficient evidence.   And we come again to Grace given by the Holy Spirit as the mechanism for faith.


¹Further, if you do this with a large number of events, it will certainly not lead to useful information.   Consider a series of 50 independent events, each of which has a probability of 0.9.   Then the probability for all the events happening together is 0.9 ^ 50 = .0052. which is small, even though the probability for the events individually is large.

²The “Expectation Value” is the value you’d expect to get over a very large number of trials. For example, if you bet $1 on a single spot showing showing up on a toss of a fair die (six sides), and would get $3 if it did show up, then your expectation value would be (1/6) x $3 + (5/6) x(-$1) = -$1/3, a losing proposition.  (And the House always sets payoffs so that the expectation value for you is negative.)

³Consider p(F and G), the probability that both F and G occur (or that both F and G are true propositions).   Then a form of Bayes’ theorem is  that
p(F and G) = p(G | F) p(F) = p (F | G) p(G);

similarly p(F and N) =  p(N | F) p(F) = p (F | N) P(N);

Take the ratio of the two expressions.