Is the Existence of God Probabilistic?

dice, probability

Is the existence of God probabilistic? It is if human intellectual knowledge is the inference of probability. This essay is intended (1) to acknowledge that yes is the answer of Richard Dawkins, the most prominent of the New Atheists, and (2) to establish that yes is also the answer of the Thomist philosopher, Edward Feser, a critic of Dawkins and the New Atheism.

What is Probability and What is “Probabilistic”?

Probability is the mathematical ratio of a subset to a set. Its numerical spectrum is 0 to 1. Anything having a probability between 0 and 1 would thereby be probabilistic. There are magnitudes of probability. However, the adjective probabilistic applies to all values within the spectrum between zero and one, irrespective of magnitude, just as does the noun probability. This is evident in the fact that every correctly calculated value of probability is just as valid a probability as every other. If one value of probability, in its valid range, deserves the adjective probabilistic, then every value does.

Consider these two numerical values of probability, greatly differing in magnitude, but which, in light of their validity, are both probabilistic. One is the probability of any playing card of a standard 52-card deck other than the three of diamonds. Its probability is 51/52, or 0.98, which is close to one. Another probability is the sequence of 52 unique elements, such as a set of playing cards. Its probability is 1/52!, or 1.24 × 10-68. Any card other than the three of diamonds, as well as any sequence of a deck, are both probabilistic. The former is not too close to one to be probabilistic. The latter is not too close to zero to be probabilistic. The definitions, the meanings, of probability and probabilistic should not be confused with emotion or with the prudence of placing a bet.

Dawkins’ Placement of Matters of Human Knowledge Within the Spectrum of Probability

Dawkins does not disparage perfectly valid values of probability by using the adjective probabilistic pejoratively. However, he does disparage values of probability close to zero by claiming they represent a “problem of improbability.”

Dawkins places the probability of the existence of God within the spectrum of probability near zero (The God Delusion, 113). The existence of God thereby exemplifies a “problem of improbability.” Similarly, he places near zero the probability of success of Darwinian evolution in a single large stage. The example he gives is the evolution of the mammalian eye in a single stage (p. 122). On the same page, he identifies the cracking of a combination lock by trial and error as presenting a “problem of improbability” if the probability of success of one trial of a single-stage trial is close to zero.

Dawkins claims that the mathematical “problem of improbability” can be solved in the latter two cases. The solution is replacing a single stage of evolution or a single-stage trial, each having a probability close to zero, with a series of sub-stages. The probability of each sub-stage is much greater than the probability of the single stage. Dawkins describes each sub-stage as “slightly improbable, but not prohibitively so” (p. 121). This mathematical solution to the “problem of improbability” — namely, a series of gradual sub-stages — could not be applicable to God because a staged progression to or development of God would be a self-contradiction.

It does not matter for the purpose of this essay that Dawkins’ demonstration regarding a series of sub-stages fails to show an increase in the probability of success as he claims, but instead does illustrate an increase in the efficiency of mutation by suppressing mutations. The contention of this essay is that probability is probabilistic irrespective of the magnitude of its numerical value. Probability cannot be denigrated as probabilistic or as embodying a problem of improbability based on its magnitude. The acceptance or rejection of probability as probability based on magnitude is emotional, not intellectual.

The basic philosophical implication of The God Delusion is that human knowledge is the inference of probability. Secondarily, judgments having a probability close to one tend to be true, while judgments that are closer to zero are “too probabilistic” and tend to be false. This philosophy of knowledge is shared by many of those who are advocates of Bayesian reasoning.

Feser’s Placement of Matters of Human Knowledge Within the Spectrum of Probability

In his critique of Dawkins, The Last Superstition: A Refutation of the New Atheism, Feser does not address Dawkins’ central argument for atheism. Dawkins begins his thesis, “Why there almost certainly is no God,” by emphatically stating, “The argument from improbability is the big one” (The God Delusion, 113). Yet Feser completely ignores Dawkins’ argument. It is as if Dawkins’ did not present his “one big argument” based on his mathematical solution to the “problem of improbability.”

When Feser uses the nouns probability and improbability, it is in noting that these concepts do not characterize human judgments of logical forms, such as the judgments of mathematics. Notably, Feser uses the adjective probabilistic to place matters of human knowledge other than logic within the spectrum of probability.

Feser’s placements within the spectrum of probability differ from those of Dawkins. Feser places mathematics at the upper endpoint of the spectrum, namely, at the numerical value of one:

Mathematical arguments start from purely conceptual premises and draw necessary conclusions.

The natural sciences are placed well within the spectrum. I infer near its midpoint:

Scientific arguments start with empirical premises and draw probabilistic conclusions.

Philosophical arguments, such as those that conclude that God exists, are close to, but not quite at, the endpoint of one. They are definitely within the spectrum between the endpoints of zero and one. In other words, they too, like scientific arguments are probabilistic:

Metaphysical arguments of the sort Aquinas is interested in combine elements of both of these other forms of reasoning: they take obvious, though empirical starting points and try to show that from these starting points, together with certain conceptual premises, certain metaphysical conclusions follow necessarily. (All three quotations: The Last Superstition, 82-83)

The Thomist Perspective

The fact that Feser, like Dawkins, places areas of human knowledge within the spectrum of probability, while excepting the non-empirical such as mathematics, attests to a philosophical principle common to both Feser and Dawkins: Human knowledge, with the exception of logic, is the inference of probability.

Thomist philosophy holds that human knowledge is not probabilistic. Human knowledge is not the inference of probability. Human knowledge is the understanding of the natures of things. This is so whether the objective of knowledge is nature at the level of being, nature at the level of substantial change, or nature at the level of the properties of material things, as evidenced by discovering the mathematical relationships inherent in the measurements of those properties.

Conclusion

Feser, in his book The Last Superstition, a Refutation of the New Atheism, gives an excellent general overview of Thomist philosophy, but fails in two points: (1) He does not address Dawkins’ “one big argument” against the existence of God, namely, Dawkins’ argument from improbability; (2) he contradicts Thomist philosophy on a major matter by concurring with Dawkins that human knowledge is the inference of probability. Feser concurs by pinning areas of human knowledge to the spectrum of probability, thereby characterizing human knowledge, notably philosophy with its proof of the existence of God, as probabilistic.

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