Faith has always been a perplexing topic for me. The definitions we hear in church, and in the scriptures seem to come up short. Furthermore, faith is almost always accompanied by a discussion of knowledge and belief. But faith is generally what is defined in the scriptures, and we typically just accept the colloquial meanings of knowledge and belief.
Our Concept of Faith
We typically turn to two scriptural sources for understanding faith. In Hebrews 11:1 we read:
Now faith is the substance of things hoped for, the evidence of things not seen.
Additionally, in Alma 32:21 it says:
And now as I said concerning faith – faith is not to have a perfect knowledge of things; therefore if ye have faith ye hope for things which are not seen, which are true.
In Mormonism I think we have a hard time reconciling faith in large part because of our scriptures coupled with the “faith” it requires to believe our foundational truth claims. For example, why doesn’t God just come down to all of us and show us an “unmistakable witness” such that everyone “knows” beyond doubt that he is God? Furthermore, rather than a prophet expounding God’s plan, he himself could give it to us so we “knew” it came from him. From The Book of Mormon we have several examples where such “knowledge” was quickly turned to doubt and sin. We use these examples to show that such “knowledge” doesn’t produce the faith required for salvation. Many Mormons will argue that if such manifestations occurred it would be too easy to “know” the truth and faith would no longer be required (which we know is unacceptable since faith is required for salvation). As a sidenote, I’d like to point out the irony that most members “know” the church to be true, which, according to this reasoning means faith is no longer required for most members.
This feels tragically flawed to me. Did Joseph Smith have faith? I think so, yet he ostensibly saw God and Jesus Christ many times and surely “knew” beyond a reasonable doubt that they existed. Was Joseph somehow at a disadvantage because he had actually seen God? Was his faith destroyed by his “knowledge”? Why was Joseph’s vision acceptable, not destroying his faith, but a “sign” would not be acceptable because it would destroy faith?
The situation gets even worse. When someone expresses doubt in the church’s truth claims, they are often labeled as lacking faith. This may feel (to the doubtful individual) like an accusation of being too weak to accept things on faith. Or perhaps that the individual must check their logic and reasoning at the door in order to have the faith necessary for salvation. It marginalizes those who have different thresholds of faith, belief, and knowledge, and elevates those who have faith no matter how ridiculous the claims may be. This type of sentiment may also be responsible for the cultural notion that the widow who sacrifices her last dollar to tithing, rather than buying food for her children is somehow more righteous/spiritual/faithful than one who would not. Examples of faith are couched in terms of individuals who appear to act irrationally to a non-LDS third party observer.
Stochastic processes are processes that are non-deterministic. In other words, they are random, or based on probability theory. To fully elaborate on this theory we need some definitions (I apologize to the mathematics averse, but please bear with me as it will give us some powerful tools to discuss some very important topics):
- Random variable: a random variable is neither random, nor a variable (crazy I know). Rather it is a function (a mathematical function). A random variable maps the possible outcomes of a random event to a set of unique numerical values. For example, a random variable for a fair two-sided coin might be X=1 (if heads), 0 (if tails).
- Probability Density Function (PDF): the probability density function describes the relative likelihood for the outcomes of a particular random variable. An example of this could be a regular “bell curve” distribution describing how a group of students performed on a test. We may also refer (with an abuse of notation) to a PDF as a distribution. (NOTE: for the mathematically inclined, I am intentionally blurring the lines between discrete and continuous random variables. Additionally, for simplicity sake I am merging the concepts of probability density function and probability distribution, though they are in fact different)
- Frequentists: frequentists interpret probability as a measure of probability of an event in a large number of trials. For example, if I tell the frequentist that the probability of landing on either heads or tails of a fair two-sided coin are 1/2 the frequentist may reason as follows: since the probability of landing on either heads or tails is 1/2, that means if we toss a coin a certain number of times, I expect that half the time it will land on heads, and the other half on tails.
- Bayesians: bayesians interpret probability in a more subjective manner using probability as a measure of personal confidence. If I tell the bayesian the same information he/she may reason as follows: since the probability of landing on either heads or tails is 1/2, and I had to place a bet on what the outcome of one specific coin toss might be, I have no reason to have more confidence in the coin landing on one side over the other. Therefore placing my bet on heads is just as good as tails.
- Let A be an event or outcome (doesn’t matter what it is), P(A) is the probability of said event occurring.
- Mean (describes a PDF or distribution): let us loosely define this to be “the most probable event or outcome.” It could also be simply an arithmetic average, but the first definition is better for my purposes. In reality, the mean is the expected value of the random variable where expected value has a precise mathematical meaning analogous to the concept of the center of mass in classical mechanics.
- Standard deviation (describes a PDF or distribution): let us loosely define standard deviation as the variability from the mean. Often the standard deviation is an indication of how confident we should be in the mean. The proper definition is the square root of variance. Variance is the second central moment of a real-valued random variable.
- A normal distribution (Gaussian distribution, or bell curve): a normal distribution is the one you are all most likely familiar with – a regular bell curve.
- The prior distribution: our distribution of confidence before we add any data (may be a uniform distribution, indicating all things are equiprobable).
- The posterior distribution: the distribution of confidence after accounting for all the data.
Using Stochastic Theory
Stochastic theory allows us to quantify our uncertainty in various processes. This relies heavily on the bayesian concept defined above (for now let’s forget about the frequentists). Bayesians use probability to describe their confidence in a certain event or outcome. Let’s walk through an example:
Let’s suppose I have a class of 30 students. I am going to give them the same exam I gave a similar group of students 5 years ago. From my previous class the results yielded a very nice bell curve (normal distribution) with a mean of 75% and a standard deviation of 2. If I am to predict how well a single student will perform (ignoring all other extraneous information), I might say, with a fair amount of confidence, that the student will score a 75%. The small standard deviation gives me this confidence.
Conversely, let’s consider the same scenario, only this time the previous resultsyielded a bell curve with a mean of 75% and a standard deviation of 10. This time, I might be much less confident in predicting a student scores a 75%, but I still would predict a score of 75%.
We can see that a combination of the mean, and standard deviation, in this example, gives us a mechanism for predicting a student’s score as well as evidence for assessing our confidence in that prediction.
Faith as Confidence
The tools of stochastic theory give us a method of modeling and understanding our confidence in various outcomes or events. I propose a new mechanism for understanding and discussing faith, knowledge, and belief – namely the bayesian notion of confidence. I think this has several major advantages:
- It levels the playing field and creates understanding. We no longer have to argue over the semantics of faith, knowledge, or belief. We can shift the argument to what really matters – the evidence.
- It admits all forms of “evidence” including personal spiritual manifestations and allows each individual to weight the evidence as he/she sees fit. That “evidence” can then easily be incorporated into the confidence distribution.
- It removes the tendency to label. That is to say, it would be acknowledged that those who doubt truth claims have different weights attached to certain pieces of evidence. We might argue over the proper weighting one ought to give to a certain piece of evidence, but one’s weighting does not make him or her more or less faithful, just different.
- It is intuitively satisfying and generally describes human behavior. I don’t think I’m really elaborating on anything that most of you don’t already know or have thought about. I’m just spelling it out more clearly and hopefully giving you some technical tools for visualizing it.
- The only definition of irrational is not acting in accordance with one’s confidence. Even those who act according to a “whisper from the Holy Ghost” against their better judgment are seen as rational since they clearly weight the “whisper from the Holy Ghost” more than their judgment.
In part two of this post I will walk through an example of how I think this theory enlightens the faith discussion, levels the playing field, and accurately describes what we really mean when talking about faith, knowledge, and belief.