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# Probability. You Keep Using That Word. I Don't Think it Means What You Think it Means.

posted Saturday May 26, 2018 08:00 AM ### Bo Bennett, PhD

Social Scientist, Business Consultant

### About Bo Bennett, PhD

We are always trying to make sense of things. One of the ways we do this is through probability, or the extent to which something is probable; the likelihood of something happening or being the case. We say things such as "it's probably going to rain tomorrow," "politician X is likely to do a better job," or "God raising Jesus from the dead is the best explanation of the data." These are just some of the different ways we can express the same general statement: "X is more probable than Y." Depending on the context, this can mean one of following:

1. Statistically, X is more likely than Y. This is an example of classical probability. It's referring to some calculable number between zero and one (zero being impossible and one being certain), which can also be expressed as a percentage.
2. To the person making the claim, X makes more sense than Y. This could be considered a casual usage of the term "probable" known as subjective probability. Nobody broke out a calculator and worked out the odds; they simply made an educated or observational guess based on several factors that we will explore below.
3. Even to the mathematician using Bayes Theorem, it could mean that given certain assumptions, X is more likely than Y. This is a statistical calculation. However, there is some guesswork that calls into question the accuracy of the conclusion.

So we have different usages of the term "probable." So what? This is no minor communication faux pas, especially in debate or discussion where the conclusion drawn from such a claim can result in public policy (as in politics) or even the threat of one's eternal misery (as in religion). We need to be precise in our language and know when others are not being precise in theirs. Without understand the basics of probability, we can come to some very wrong conclusions by some very seemingly persuasive arguments.

## Mathematical Probability vs. Plausibility

When we hear some claim such as "It's more probable that a god exists than doesn't exist" or "It's more probable that a god doesn't exist than does," we think mathematics. This is because virtually every child going through school has learned the about classical probability and how to calculate the odds of events when certain information is known. However, when people are speaking about something like the existence of a god, they aren't speaking about a valid statistical calculation; they're speaking about plausibility, or how believable the claim is given one's presuppositions, worldview, knowledge, understanding, and mental abilities. Where classical probability is an objective (same for everyone) statistical measurement about our shared reality, plausibility is an evaluation about one's subjective (personal) level of belief.

## Why We Can't Use Classical Probability For Complex Questions Such as the Existence of a God

To understand why the meaning of probability is different when calculating a roll of the dice from when calculating the existence of a god, we need a little refresher on classical probability.

The Probability of an Event Equals the Number of Favorable Outcomes Divided by the Total Number of Possible Outcomes

As far as mathematical formulas go, they really don't get much simpler than this. To figure the probability of any event we need to know just two things: 1) the total number of possible outcomes and 2) the number of favorable outcomes. So let's start simple. What's the probability that we will roll a "two" on a fair die? Because a fair die has six sides numbered one through six, the total number of possible outcomes is six. The number of favorable outcomes would be just one because there is one number two on a six-sided fair die. Now for the math part:

1 / 6 = .1666(repeating)

Now let's convert this into human language that most people understand and can easily conceptualize: we have a one in six chance on throwing a "two" using a fair six-sided die, or we can say about a 16% chance. With me so far? Congratulations! You passed the third grade! Now for the big boy and girl stuff.

## When Classical Probability Cannot Be Used.

Classical probability can only be used in situations where a) the number of possible outcomes is known and b) each outcome is equally likely. If we had a weighted die (one that cheaters use so a certain number comes up more often than others), we would still have a known number of outcomes (six for the one die) but each outcome would not be equally likely, so classical probability would not apply. If we were to calculate the probability that the next person would walk through a door is exactly six feet we would not be able to use classical probability. Not only is each outcome not equally likely (i.e., people are much more likely to be 5' 10" than two feet tall) but unless we know the height of the tallest person in the world and the shortest, we don't know the number of possible outcomes. But height is what is called a normal distribution, so getting an accurate probability using a different formula is not a problem.

What about our god question? Let's try to use classical probability here. Unlike a coin that is either heads or tails, "god" isn't one side of a two-sided fair coin. To remove any theistic or atheistic bias you might have regarding the existence of a god, let's consider the following: What's the probability that a pink unicorn named "Chester" exists who poops rainbows? Let's say that he either exists or doesn't exist (two total possible outcomes). But does this mean that Chester has a 50/50 chance of existing? Not necessarily. Technically, we don't know the liklihood of each event so we can't use classical probability. The same goes for the god question. This is why classical probability won't work here or in any similar situation where there is no known value to each possibility, including the existence of the paranormal and the probability of miracles.

## What About Bayes Theorem?

Bayes Theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. Although this is a mathematical formula, the probability calculated is highly depended on a subjective figure. To give you an idea what I mean, in 2004, Stephen Unwin published a book titled The Probability of God: A Simple Calculation That Proves the Ultimate Truth. Using Bayes Theorem, and being 95% confident in God's existence before the calculation, Unwin calculated God's existence at 67%. His prior belief in God greatly influenced the numbers he used in his prior probability calculations. In a review of Unwin's book, atheist and skeptic Micheal Shermer used the spreadsheet provided by Unwin to calculate the existence of God as well, but he plugged in different numbers as prior probability and came up with the existence of God at 2%. This means that although Bayes Theorem might be a valid way to calculate probability for topics such as the existence of God, it is highly unreliable.

By now, it should be clear that when we are talking probability outside situations where the number of possible outcomes is known and each outcome is equally likely, what we really are talking about plausibility, which is the equivalent of "this makes more sense to me." But Bayes Theorem is still quite useful as it requires us to consider each claim that may lower or raise the probability. It is especially useful when the initial assumptions or prior probabilities are agreed upon. If nothing else, applying Bayes Theorem is a useful exercise in critical thinking.

## Understanding and Plausibility

Imagine the year is 300 AD. You are living in a pre-scientific age—in a time before people knew how diseases spread, when people thought the earth was the center of the universe and the universe was believed to be tiny, when there was no method to date the earth, when evolution was unheard of, and before the genome was mapped that showed our genetic similarity to other living organisms on earth. When comparing the probabilities of a natural alternative vs. a supernatural alternative, the lack of understanding in a natural alternative would make the supernatural one more plausible and thus, more subjectively probable. Fast forward about 1700 years. The level of understanding we have today about the natural world is far greater than the understanding we had in 300 AD. But let's not give credit where credit isn't due. "We," collectively speaking, have this understanding, but the level of understanding that any individual has varies greatly. What we find is that the understanding of naturalistic explanations to questions where supernatural explanations are commonly proposed is strongly correlated with not believing in any gods. One such piece of evidence for this is the fact that by one study, 83% of Americans in the general public say that they believe in God, where that number is just 33% among scientists—those with precisely the kind of understanding of naturalistic explanations to which we are referring.

## Comparative Probabilities.

Before you write off probabilities as being useless when debating gods or the supernatural, we can make good use of probability when comparing options, even when the probability of each option is unknown. Recall Chester, our pink unicorn who poops rainbows. By logical necessity, we know that just a unicorn existing is more probable than Chester existing. Otherwise, we would be committing the Conjunction Fallacy, which is the assumption that more specific conditions are more probable than general ones. Similarly, we can say that "magic" is more probable than any god, since "magic" (defined as the power of apparently influencing the course of events by using mysterious or supernatural forces) is just one of the many necessary aspects of any god. Comparative probabilities work with unknown outcomes only when one of the outcomes is a more general condition of the others. So while this may be useful when comparing whose god is more likely to exist (hint: the more generic god), it doesn't help when comparing the existence vs. non-existence of a god.

Don't be misled when discussing probabilities. In discussions of gods and the supernatural, "more probable" often means just "more plausible" to that person given his or her presuppositions, worldview, knowledge, understanding, and mental abilities. If you find yourself claiming that something is more probable than something else, look at your own reasoning and see what it is you actually mean. Look at where your subjective point-of-view is affecting the probability. Probability theory is great for many purposes, but calculating the probability of the supernatural is not one of them.

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