Sacred Probabilities — Part I

In the first of a three-part series on the theological implications of economic probability, Economist Philip Pilkington examines Pascal’s Wager.

Probabilities have not been given their theological due.

Augustin Pajou, “Pascal studying the cycloid” (The Louvre, 1785)

This is understandable, as probabilistic reasoning has long been thought to be a subfield of mathematics and, outside of Biblical numerology, mathematics seems to have little to say about theological questions. To think this, however, is misleading at every level, from root to branch.

It is a misunderstanding that has actively been peddled by the promoters of probability theory itself. Many of the promoters of probability theory are themselves mathematicians and they are often in the business of selling their skills to either researchers in other fields or even to companies and governments – modern day haruspices, reading the omens of the entrails at court. Needless to say, the marketing for such activities is much easier if the practice can remain cloaked in the language of mathematics and science.

The scientific proponents of contemporary probability theory typically think of probabilities as being objective entities.

Take the example of a coin.

Provided that the coin is balanced, there is a 50% probability of flipping a heads and a 50% chance of flipping a tails. Scientific proponents of probability theory think of this as being an objective, almost material relationship not unlike the exertion of Newtonian force on an object. Sometimes they will refer to subjective probabilities, also known as Bayesian probabilities, but this is just a method for increasing the accuracy of a given probability as more evidence becomes available. The probability is still seen as a sort of objective entity.

The alternative view was laid out in John Maynard Keynes’ now sadly neglected 1921 book A Treatise on Probability. Keynes did not treat probabilities as objective entities but rather as an assessment of a proposition rather than the as the assessment of an event. So, when we look at a coin toss, the probability does not apply to the coin toss itself, but rather our judgment of it. When we say: “The coin toss will produce heads,” it is this proposition that is being assessed in terms of probabilities. This brings probabilities out of the realm of actual objects and into the realm of our epistemological capacities. Probabilities, for Keynes, are a species of inductive argument of the sort discussed by the likes of Leibniz, Berkeley, Hume, and Kant.

It is at this point that probabilities become theologically interesting. In what follows we will examine three different cases of probabilities being of theological interest.

The first is the well-known case of Pascal’s wager in which probabilistic argument is deployed as an argument for the existence of God, although as we shall see, it goes beyond this. We will explore this in Part I.

In Part II we will move onto the second topic. This is the far less well-known of Bayes’ argument in favor of miracles. Here we will see that one of the main mathematical formulations in modern probability theory, Bayes theorem, was developed by a Presbyterian minister to argue against those, like Hume, who were sceptical of the possibility of miracles.

Finally in Part III, we will explore a novel argument that probability theory is highly relevant to the question of Extra Ecclesiam nulla salus (no salvation outside the Church) and the related matter of the specific conditions of salvation.

Put less academically, and more surprisingly, in three parts this essay argues that probability theory can shine light on that most difficult of theological questions: will my actions and beliefs damn me to an eternity in Hell?