In the context of a technological assay, such as a screening test for a disease, a false positive is a failure, but, if its frequency is low, it does not invalidate the utility of the assay. Such a case is a failure, but in one sense only partially so. In philosophy, a false positive, in the sense of being right for the wrong reason, is a complete failure. It is intriguing that today the same false argument is employed by both sides, pro and con, with respect to the existence of God. The stated conclusion of the one argument is true, the other false. But, the core of both arguments is invalid.

In his essay, “How Contemporary Physics Points to God”, Fr. Robert Spitzer states, “The odds against all five of the anthropic coincidences happening randomly is exceedingly and almost unimaginably improbable. Most reasonable and responsible individuals would not attribute this to random occurrence (because the odds are so overwhelmingly against it), and so, they look for another explanation which is more reasonable and responsible.”

Similarly, Richard Dawkins claims the problem that any theory of life must solve is how to escape from chance. Dawkins’ solution, within the context of evolution in a one-off event, is to increase the probability (pages 120-122, *The God Delusion*). He characterizes the odds of a billion to one, not as overwhelming, but as staggering, absurd and stupefying (page 138, *The God Delusion*).

Dawkins claims that the probability can be increased in the case of evolution by breaking up the improbability into smaller pieces (page 121, *The God Delusion*). Dawkins claims that this is not possible in the case of the improbability of God (page 113, *The God Delusion*). Appropriately, Spitzer does not consider this possibility in the case of the anthropic coincidences. However, both men envision the same problem, namely, that a value of probability is too close to zero for probability to be an explanation. Implicitly, if the value of probability were close to one, neither would object to probability’s serving as an explanation.

This is the same view as proponents of Intelligent Design, who consider biological complexities. Some are at sufficiently low levels of complexity for which the probability is close enough to one to serve as an explanation. Of course, the proponents of Intelligent Design are not interested in these, but in the occurrence of biological complexities that are irreducible, in the context of natural selection, to low levels of complexity. For these irreducible complexities, it is argued that the probability is too close to zero to serve as an explanation.

It is not their solutions or lack thereof, but the basic problem as they envision it, which is the focus of this essay. As envisioned by Spitzer in the anthropic coincidences by Dawkins, both in evolution in a one-off event and in the improbability of God, and by its proponents in the argument of irreducible complexity, the problem of improbability at its core is, “The probability of this outcome is so close to zero that it could not be due to chance.”

One might just as well say, “My chance of winning the lottery is so close to zero, that, if I did win the lottery, it could not be due to chance.”

One might just as well say, “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.”

Probability is the fractional concentration of an element in a logical set. It is a definition within the mathematics of sets.

The fractional concentration of this element in this set is the fractional concentration of this element in this set, no matter how close this probability is to zero. Most people would accept the stipulation that the top card of a shuffled deck simulates a probability of 1/52. Notice that the top card is in no way special compared to the other locations in the deck. This implies accepting the stipulation of the simulation of a probability of 1/52 for each card in the deck. Of course, this implies stipulating that the shuffled deck simulates a random sequence of 52 cards at a probability of 1.2 x 10^(-68). That is a probability of less than one in a trillion, trillion, trillion, trillion, trillion. The assent to the simulation of a probability of 1/52 by shuffling the deck is essentially assent to the simulation of a probability of 1.2 x 10^(-68). This is most appropriate because all values of probability are of equal validity over its range of definition, no matter how close to zero.

It should be apparent that there is no such problem as a ‘problem of improbability’. To reject or to accept probability as an explanation based on its numerical value is illogical. If probability is accepted at some value as an explanation, then at some other value it cannot be rejected as an explanation on the basis of its numerical value, irrespective of how close it is to zero. Similarly, the acceptance of probability as an explanation is not bolstered by a value of probability closer to one.

The concept of a problem of improbability, i.e. a problem due to the numerical value of probability within its range of definition, is meaningless. Dawkins unwittingly clarifies the issue by identifying some values of probability within its range of definition as ‘prohibitive’. Of course, the prohibition cannot be inherent in the mathematical definition itself. The prohibition is simply by fiat of the one who envisions the problem, where the problem is in fact his own fiat of prohibition. There can be no solution because there is no problem. The discussion of sets and subsets at the Mad Tea Party makes more sense than a discussion of sets, which proscribes numerical values of mathematical probability within its range of definition.

Probability is solely a matter of mathematical logic. Material simulations of the mathematics of probability, such as dice and playing cards, are visual analogies. The logic, which the material simulations are employed to visualize, is not inherent in the nature of the material employed. This is in contrast to the measurable properties of material things, which properties are inherent in their natures and which are the subject of science.

Alice, the Hatter, the March Hare and the Dormouse held a reasonable and responsible discussion of sets and subsets. The Hatter, e.g. noted, “You might just as well say, ‘I see what I eat’ is the same as “I eat what I see’!” Fr. Spitzer, Richard Dawkins, the proponents of the argument of irreducible complexity, et. al. are not reasonable and responsible in citing outcomes which cannot be attributed to random occurrence ‘because the odds are so overwhelmingly against it’.

It would be reasonable and responsible for Spitzer, Dawkins et. al. to reject low values of probability as an explanation, not because the odds are overwhelming, but because mathematical probability is never the explanation of anything, irrespective of its numerical value. They, and we, merely have to be consistent by also rejecting intermediate and high values of probability as an explanation.

Though one may define an unimaginably low value of probability, its significance is solely logical and therefore cannot buttress an argument about the existence of anything. An argument pro or con the existence of God, based on probability, is an argument in which the premises address purely logical concepts. Existence, or lack thereof, cannot be the conclusion of a purely logical argument. Mathematical probability, which numerically characterizes the composition of logical sets, has nothing to do with the existence of anything.

Those who base their arguments, pro and con, about the existence of God on the ‘problem of improbability’, do not have the recourse of going back to the drawing board of mathematics. The discussion of the relationships of logical concepts does not lead to a conclusion about existence. They do have the recourse of reviewing the principles of Aristotelian-Thomism: The characteristics of everything within our experience is explained by the nature of that thing. Nothing within our experience explains its own existence or that of another.

Outside of the context of mathematical sets, probability expresses a person’s degree of certitude: ‘That statement is probably true.’ Statistical probability is a hybrid of mathematical probability and personal certitude. It details a commonly accepted convention for expressing the degree of personal certitude in the mean of measurements based on assumptions of the distribution of measurements about their mean.

Also, it is philosophy which underpins both the proof of the existence of God and the validity of science, including modern physics. If modern physics pointed to God, it would be by a circular argument, namely: Philosophy justifies modern science which justifies philosophy. This is not to deny that the beauty of science is a specific case within the general argument of beauty for the existence of God.

## 13 thoughts on “The Odds on the Existence of God”

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Stacy Trasancos“The prohibition is simply by fiat of the one who envisions the problem . . .” Yes! I remember being perplexed at the way Intelligent Design theorists use probability theory to prove God’s existence, but I couldn’t express it the way you do so well. In research, probability is a tool to assess your data, as you said, it’s a way to gauge certainty about a conclusion and a way to identify where there are factors you still need to account for. But to feed data, get an outcome, and then use it as proof of existence is circular.

Jeff_McLeodThis is a brave article and of course 100% true. It is not even controversial. You are articulating what is crystal clear to anyone born before 1900.

To readers who were born after 1900, Bob is issuing a stern warning. Probability is not the explanation of ANYTHING.

I am right now looking at an anthology called

The Probabilistic Revolution>on my bookshelf, the series contains an entire section devoted to how “probability” came to be seen as an explanatory cause, as in Darwinian natural selection.At age 21 I was very impressed with this argument. At age > 50 I laugh to myself: is there ANY theory that could NOT be ratified as true if we allowed “statistical improbability” as an efficient cause?

Bill SDoes it seem virtually impossible that all this came about by chance? Yes it does. It seems most likely that there is some sort of teleological mechanism that some would call Intelligent Design. Then it seems that the Intelligent Design implies the existence of an Intelligent Designer which is a tribal god with a chosen people and a son who suffered and died to atone for the disobedience of the first humans and who is present in consecrated bread and wine.

That is what some people believe. I’m ok with an intelligent designer of some sort but I don’t see any connection of it with Yahweh, God, Allah, Jesus, Buddha, Krishna, Zeus or any other imagined deity.

Bob DruryFrom my perspective, if I allow chance as an explanation in one instance, I cannot deny its being the explanation in every other instance. No value of probability within its range of definition is invalid nor is it more or less valid than another. My understanding of the Intelligent Design Argument is that probability is acceptable as an explanation in some instances, but not in really complex instances. It seems to me that you, Bill, are identifying a teleological argument as Intelligent Design. This would be perfectly acceptable except for the fact that the term, Intelligent Design, has been pre-empted by an argument based on probability.

Bill Sif I allow chance as an explanation in one instance, I cannot deny its being the explanation in every other instance.All things are subject to chance and to the laws of nature. If I fire a gun into the air, the bullet will return base on the law of gravity. There is also a chance that it will strike someone. A person firing into there air should know the bullet will land somewhere and has to take into consideration the possibility that someone might get struck by it at random.

Bob DruryWhen we use the words, such as chance and random, in that context, we are simply admitting our ignorance of the causal factors involved. We are not referring to mathematical probability as does the argument called Intelligent Design and the algorithm of Darwinian evolution or as was I in my earlier reply.

Bill SWhen we use the words, such as chance and random, in that context, we are simply admitting our ignorance of the causal factors involved.Of course there are causal factors in a person getting hit by a bullet shot up in the air. But it is still a random occurrence happening to the person by sheer chance. The person shooting in the air is the primary causal factor. It is just a random event like the asteroid that wiped out the dinosaurs and made it possible for mammals to take over the planet.

Bob DruryCommunication depends on the definition of words. In my post I defined mathematical probability as the fractional concentration of an element in a logical set. In this context randomness refers to the method of defining the probabilities of new logical sets on the basis of the probabilities of a source set. This is the context of use by the persons I cited in the post. In material simulations of mathematical probability, such as rolling dice, we equate our ignorance of the forces to

which the dice are subjected to randomness. Similarly, in casual conversation, when we are not discussing mathematics and when we are ignorant of the causal

factors of an event we admit our ignorance by characterizing the event as random. By use of the word, random, in your reply aren’t you referring to

ignorance of at least some of the causal factors of an event? That is what I would mean by saying that an asteroid’s hitting the earth was a random event. If

I said a person was shot by sheer chance I would mean that I was impressed by the multitude of factors, some known, some unknown, each of which was necessary to the result.

Bill Swhen we are not discussing mathematics and when we are ignorant of the causal

factors of an event we admit our ignorance by characterizing the event as

random.

I understand that. What do you say to those who believe that God controls every event whether it is an asteroid hitting the earth or a person struck by a falling bullet?

Bob DruryAristotle delineated four causes of material things and of material events. No one has yet one-upped him. They are the formal, material, efficient and final causes. Typically with respect to asteroid hits and people struck by falling bullets, we would be analyzing the proximate causes of these events. God, of course, is none of these proximate causes. However, the analysis of causality is not exhausted by the sole consideration of proximate causes. Within efficient causality, besides proximate efficient causes there must be an ultimate, yet immediate, cause of the very existence of every finite entity. A being, whose nature is only logically distinct from his existence, is the only possible explanation of the existence of the entities within our experience. It is in this ultimate sense, not in a proximate or material sense, that God is said to be the cause of all things.

God identifies himself to Moses as I Am, Who Am. He instructs Moses to tell the people that he was sent as a messenger to them by I Am. Jesus of Nazareth claims, “Before Abraham came to be, I Am.” Although Aristotle identified God as pure act, that concept of God was not as lucid and not as emphatic as that expressed in what a tribe of nomads claimed to be a revelation to them.

Bill Swhat a tribe of nomads claimed to be a revelation to them.That is the hardest thing to accept. That the intelligence behind all that is appeared in a burning bush and lead a chosen people out of captivity.