Sometimes we think of faith as something optional, and something directed toward the supernatural. Not so. Faith is unavoidable, and faith directed toward the supernatural is a small part of all faith.

As for many discussions of faith, the starting point for my discussion of faith are the words of the (unknown) author of the Epistle to the Hebrews. Using William Tyndale’s translation with modern spelling, Hebrews 11:1 reads

Faith is a sure confidence of things which are hoped for and a certainty of things which are not seen. 

In my book, the more evidence we have to go on and the less faith we have to depend on, the better. That is, I disagree with the words the resurrected Jesus is reported to have said to a doubting Thomas (John 20:29, Tyndale):

Thomas, because thou hast seen me therefore thou believest: Happy are they that have not seen and yet believe.

Rather, happy are they who have much evidence to base their choices on. But choices–to act, or not to act–often have to be made when evidence is scarce. That is where faith comes in.

One might be tempted to think of faith as a Bayesian prior. But it isn’t that simple. In Bayesian decision-making, “prior beliefs” are left unexplained. But in the real world they come from different ways of responding to and reasoning about past experience. New data sometimes simply updates prior beliefs within the same paradigm, as Bayesian theory suggests. But other times, new data upends the thin tissue of reasoning and reaction that was crucial for the formation of those prior beliefs, resulting in a much bigger change in views than straightforward Bayesian updating would imply. And sometimes additional reasoning–in the absence of any additional data whatsoever–can dramatically change one’s views.

A simpler point is that what is prior to one set of events is posterior to earlier events. Putting both points together, faith is what one believes at a given moment in time, however one has managed to cobble together those beliefs.

In situations where one is willing to think of one choice as inaction, with costly actions having debatable benefits, one can distinguish between a “belief in nothing” that leads one to continue in inaction, and a “belief in something” that leads one to act. When proponents of action say “Have faith!” they are advocating a belief in a high enough marginal product of action to make it worth the costs. That is very much the perspective of the Lectures on Faith, which were once part of the Mormon canon, but now enjoy only semi-canonical status. (The full text of the Lectures on Faith can be found here.)  Let me quote a passage from the Lectures on Faith that has stuck with me, again modernizing the spelling:    

If men were duly to consider themselves, and turn their thoughts and reflections to the operations of their own minds, they would readily discover that it is faith, and faith only, which is the moving cause of all action, in them; that without it, both mind and body would be in a state of inactivity, and all their exertions would cease, both physical and mental.

Were this class to go back and reflect upon the history of their lives, from the period of their first recollection, and ask themselves, what principle excited them to action, or what gave them energy and activity, in all their lawful avocations, callings and pursuits, what would be the answer? Would it not be that it was the assurance which we had of the existence of things which we had not seen, as yet? Was it not the hope which you had, in consequence of your belief in the existence of unseen things, which stimulated you to action and exertion, in order to obtain them? Are you not dependent on your faith, or belief, for the acquisition of all knowledge, wisdom and intelligence? Would you exert yourselves to obtain wisdom and intelligence, unless you did believe that you could obtain them? Would you have ever sown if you had not believed that you would reap? Would you have ever planted if you had not believed that you would gather? Would you have ever asked unless you had believed that you would receive? Would you have ever sought unless you had believed that you would have found? Or would you have ever knocked unless you had believed that it would have been opened unto you? In a word, is there any thing that you would have done, either physical or mental, if you had not previously believed? Are not all your exertions, of every kind, dependent on your faith? Or may we not ask, what have you, or what do you possess, which you have not obtained by reason of your faith? Your food, your raiment, your lodgings, are they not all by reason of your faith? Reflect, and ask yourselves, if these things are not so. Turn your thoughts on your own minds, and see if faith is not the moving cause of all action in yourselves; and if the moving cause in you, it it not in all other intelligent beings?

Application 1: The Cognitive Economics of Human Capital

Let me apply this idea to Jill’s decision of whether to go to college and learn economics or not. Some consequences of college might be relatively easy to discern, such as the costs,  and if she is relatively well informed, the likely effect on her future wage. But what about the benefits learning economic analysis might have for her future decision-making? A tempting approach to analyzing Jill’s problem would be to think of her computing what her life would be like (or a probability distribution thereof) if she does go to college, as well as what her life would be like if she doesn’t go to college, compare the two to see which one she prefers, and make that choice. But in this case, Jill can't compute what her life will be like if she goes to college and learns economics because she doesn’t know now the analytical tools that could influence her life in critical ways if she does go to college and learn economics. In other words, she can’t make a fully rational choice (according to the demanding standards of most economic models) of whether or not to go to college without knowing the very things that she would be learning in college. But if she knew those things already, she wouldn’t need to go to college!  

The Handbook of Contemporary Behavioral Economics: Foundations and Developments, page 343 points to the more general conundrum of which Jill’s problem is an example:

The inability to formulate an optimization problem that folds in the cost of its own solution has become known as the “infinite regress problem,” with Savage (1954) appearing to be the first to use the regress label.  

Application 2: The Cognitive Economics of R&D

Another good example of the infinite regress problem is the decision of which lines of research to pursue. The issue is stark in a decision of whether or not to undertake a research project in mathematical economic theory. There is no way to make a fully rational decision according to the demanding standards of most economic models because the most economic models assume that information processing (as distinct from information acquisition) comes free, but the issue is precisely whether one’s own finite thinking ability will allow one to find a publishable theoretical result within a reasonable amount of time. Therefore, one must make the decision according to a hunch of some sort–or in other words, by faith. The analogy that makes one believe that a proof might exist is not itself the proof, and may fall apart. But that analogy makes one willing to take the risk. Except in cases where undecidability of the sort that shows up in Goedel’s theorem comes into play, the only fully rational probability that one could find a proof would be either 0 or 1, because one would already know the answer. But that just isn’t the way it is when you make the decision. You have some notion of the probability you will be able to find a proof–a probability that by its nature cannot have a firm foundation, yet still guides one’s choice: faith.

Application 3: The Cognitive Economics of Economic Growth

Growth theory faces a similar problem. It would be a lot easier to form a sensible probability distribution for future technological progress if one actually knew the technology already. Someday, economists studying the economics of other planets under the restriction of Star Trek’s (often violated) Prime Directive of non-intervention may be able to do growth theory that way. But we 21st century economists must do growth theory in ignorance of scientific and engineering principles that may be crucial to future economic growth. It would be nice to know the answers to questions such as how hard it is to make batteries more efficient, for example, or whether theoretically possible subatomic particles that could catalyze fusion exist or not. (My friend, theoretical physicist James Wells, has worked on the theory. The right kind of heavy, but relatively stable negatively charged particle could do it by taking the place of electrons in hydrogen atoms and making the exotic hydrogen atoms much smaller in size.) If it were all just a matter of getting experimental results, the economic model might be standard, but what if just thinking more clearly with the evidence one already has could make it possible to get to the answer with one decisive experiment instead of an inefficient series of 100 experiments. 

Just as with the standard approach to human capital, we often look at technological progress from the outside, in a relatively bloodless way: a shifter in the production function changes. But the inside story of most technological progress is that in some sense we were doing something stupid, but now have stopped being stupid in that particular way. I say “in some sense” because–while our finite cognition is painful–it is possible to be smart in recognizing our cognitive limitations and making reasonable decisions despite having to walk more by faith that we would like in making decisions that depend on technologies we don’t yet know exist.

Application 4: Locus of Control

A central life decision is whether to attempt to better one’s life by making an effort to do so. Information acquisition and learning how to process information are themselves costly, so the initial decision of whether to do the information acquisition and other learning that are a logical first step must be made in a fog of ignorance. Some people are lucky enough to have parents who instill in them confidence that effort to gain knowledge, learn and grow will be well rewarded in life, at least on average. It is good luck to have that belief, because it seems to be true for most people. But believing that it is true for you–that your efforts to better your life will be rewarded–must be an act of faith. For you are not exactly like anyone else. And even knowing that most people are similar in this regard is a bit of knowledge that might cost you dearly to acquire if you are not so lucky to as to have your parents, or someone else you trust tell you so.

If you decide that it is not worth the effort trying to better your life, you will not collect much evidence on the marginal product of effort, and so there will be precious little that could provide direct evidence to change your mind. In such a low-effort trap, it will not be hard evidence about your own marginal product of effort that switches you from believing in an external locus of control (outside forces govern outcomes with little effect of own effort) to an internal locus of control (own efforts have an important effect on quality of outcomes). If you escape the trap of believing in an external locus of control, it will be by believing some kind of evidence or reasoning that is much less definitive.

Conclusion

I do not believe in the supernatural. So for me, faith is not about the supernatural. Yet still we must walk by faith. Walking by the light of evidence is better, but such is not always our lot.

Not only must we sometimes walk by faith–whether we like or not–so must others. It matters what kind of faith we instill in those around us, to the extent we have any influence.

To me, faith in progress and human improvability–both individually and collectively–is a precious boon. It is not enough for us to have that faith. Many are caught in what I believe to be the trap of believing they can not better their lives. I believe it is important for them to have faith in progress and human improvability as well. If you believe in progress and human improvability as I do, let us together seek for better and better ways of transmitting that faith to those who do not yet believe.