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"The Fixation of Belief" (Champaign cover)

This is a rewriting of C.S. Peirce’s earlyish essay “The Fixation of Belief,” published November 1877 in Popular Science Monthly. It’s the first of a series of six essays, collectively titled “Illustrations of the Logic of Science.” It’s presumably written for a lay audience, so is simpler than his specialist papers, but I think it still benefits from a cover version.

A what? About these covers.

TL;DR

Belief produces habit. Habit is a rote reaction to particular circumstances. Acting from habit feels pleasant (or at least a normal part of the daily routine).

Doubt interrupts habit. Doubt is unpleasant. The response is to resolve the doubt – to use some process of inquiry to either confirm the belief, adjust it, or replace it. The end result is a reentry to the “ground state” – the pleasant experience of exercising a habit.

Inquiry ends when doubt ceases, which has no firm connection to whether a truth has been established.

The process of inquiry we dub “science” is not new. People use it every day. But because of the increasing complexity of the world, we need the method of science to be used more often and with more awareness and skill.

I

Let’s say that reasoning is an umbrella term for all the processes of converting claims that you believe into new claims that you now also believe. There are many types of reasoning. For example:

To continue to get our definitional ducks in a row: deductive reasoning is guaranteed to (or at least advertised to) turn true premises into true conclusions. (Note the shift of focus from belief to truth.)

Logic is a kind of reasoning that looks only at the form of an argument. Consider this guiding principle of Boolean algebra:

IF (A or B) is true, 
THEN A is true, OR 
     B is true, OR 
     both are true.

It works regardless of whatever A and B are claiming. (This abstract meaning of “logic” is usually traced back to Aristotle.)

Starting with Aristotle, deductive logic meant syllogisms. The most famous syllogism is:

  • All men are mortal.
  • Socrates is a man.
  • Therefore, Socrates is mortal.

Technically, that should be written with every sentence starting with “All”:

  • All men are mortal.
  • All entities in the single-element category “Socrates” are men.
  • Therefore,
    All Socrates-type entities are mortal.

You can summarize this as having the form AAA (All-All-All). Technically, it has the form AAA-1, but I don’t want to get into what the number means. Here’s a syllogism of the form EAE:

  • No reptile has fur.
  • All snakes are reptiles.
  • Therefore,
    No snake has fur.

I don’t know why the letter E was chosen; presumably it’s the first initial of some Latin word. (We’re now way past the time of Aristotle and in the long era of scholastic clerics who did all their work in Latin.)

Given handy mnemonics like AAA and EAE, medieval scholastics of course decided to hide them in Latinate names. So AAA is “Barbara.” “BArbArA.” Get it? And EAE is “CElArEnt.” Not to be confused with “CElArOnt,” which uses a “Some” (O) instead of a “No” (E).

I struggle to understand the mind of someone who thinks saying a name from which an acronym can be deduced is better than just saying the acronym. Perhaps it’s a gatekeeping or hazing ritual. Consider the following sentence, which I encountered on page 21 of a philosophy text: “All forms of inference […] may be reduced to Barbara.” Who’s Barbara‽ There’s no clue that it’s a syllogism’s nickname. The word “syllogism” doesn’t even appear until page 56. Grr.

There are 24 such “categorical” syllogisms, one disjunctive syllogism, two kinds of hypothetical syllogism, and one way of chaining syllogisms together. Even with all those, there are many valid arguments that can’t be expressed in syllogism form, but people were stuck with syllogisms until the latter part of the 1800s, when people like Boole (1854), de Morgan (1860), and Frege (1879) developed better and more powerful notations and derivation rules.

When Roman and medieval European logicians taught logic, they focused on these 27 ways of going from premises to valid conclusions. And what of the premises? How do you know they’re true? – They’re true if the relevant authorities say they’re true.

It was not until the 1200s that Roger Bacon gave experience (rather than announced axioms) a central role. It is only experience, he said, that generates new knowledge. He included in “experience” not only the physical world, but also “interior illumination,” which allows one to reason to the correctness of, say, the doctrine of transubstantiation of bread into flesh during the Eucharist. That is, this was only a small step toward what we nowadays think of as science.

Working in the 1600s, the other Bacon (Francis) developed a doctrine that experience is subject to verification and examination, shifting the focus to inductive reasoning…

Important: Inductive reasoning isn’t the same as the mathematician’s “proof by induction, which is actually a form of…sigh… deductive reasoning. In contrast, inductive reasoning means the process of observing the same property in many entities of a class, thereby coming to believe it a property of all entities in that class.

Inductive reasoning caught on in science. But there were doubts. In 1739, Hume argued induction has no particular connection to truth, and was so convincing that he threw everyone into a tizzy that probably only peaked in the first half of the 20th century.

However, in everyday science, problems with induction happen seldom enough, and controllably enough, that we welcome induction into the halls of logic.

Francis Bacon’s use of induction and experience was crude, and scientists continually improved upon it. Indeed, each major advance in scientific theory is also an advance in science’s toolbox of guiding principles. For example, the theory of gases introduced uncertainty and probability into science. Unlike Newton, Clausius and Maxwell did not require exact knowledge of the position and velocities of all the entities in a system to calculate its future: they could use statistics.

Similarly, Darwin’s controversial theory explained how chance variation could lead to new species. Whether or not Darwin’s theory is true is not at issue here. The point is that his method worked. You can hardly argue that his guiding principles didn’t lead him to a new claim about the world.

II

Suppose you use a tarot deck to make a new claim about the world. You can present that process in an if-then form like “Because I believe in A, B, and C, it follows that I should believe in this new idea, D.” But it would be better to present it as:

  • I believe in A, B, and C.
  • AND my guiding principle (the tarot) suggested claim D.
  • AND I trust that guiding principle.
  • THEREFORE I believe in D.

Contrast that with this:

  • I believe that all men are mortal and that Socrates is a man.
  • AND, using the “Barbara” syllogism as my guiding principle, I must conclude Socrates is mortal.
  • AND I believe syllogisms are ampliative (turn valid premises into new valid conclusions).
  • THEREFORE I believe Socrates is mortal.

The reasoning has the same form. Which of these arguments you accept depends on which of the tarot or Aristotle you prefer as your guiding principle. There are reasons to prefer the latter:

  1. Almost no one disbelieves in syllogisms, but lots of people disbelieve the tarot.
  2. A syllogism works the same way whoever’s wielding it (unlike a tarot deck).

As another example of a guiding principle, consider a rotating copper disk placed between the poles of a magnet. It quickly comes to rest. From that, we conclude the same will happen for all copper disks. That’s according to the guiding principle that what’s true of one copper disk will be true of another whenever the two differ in only irrelevant characteristics like thickness or diameter.

However, it would be riskier to conclude, from this experiment, that magnets will have the same effect on rotating brass disks, because the differences between brass and copper seem likely to be relevant. (And, indeed, the behavior of brass differs.)

For the most part, we reason well, especially when it comes to what you might call practical or basic or routine matters. If on a high ledge, you simply cannot convince yourself that stepping off it will result in your being wafted gently to the ground. (At least, not more than once.)

That’s unsurprising. If Darwin is right, you’d expect that natural selection would produce creatures whose reasoning processes become ever more “tuned” to the realities of the physical world (or their particular umwelt).

However, as the world and our understanding of it grow more complicated, the failure rate for our habitual guiding principles will increase. We’ll need to adopt better ones to continue to thrive. What those are is the topic of the next essay. In the meantime, let’s look more carefully at the result of reasoning: belief.

III

Click to expand in a new tab.

Pretty much every day with nice weather, you’ll find me typing on my laptop outside the University of Illinois Bookstore. Of the many round tables available, I believe the one shown on the right is the best one to sit at. If asked, I can list my reasons. For one thing, there’s only one adjacent table, which halves the chance of having someone VERY LOUD having a distracting conversation within earshot.

As a result, when I walk up to the patio, I’ll choose to sit at my favorite table, provided it’s empty. But “choose” is really the wrong word here. I don’t evaluate all the tables I see and decide which is the best. I simply perceive that “my” table is empty and sit there out of habit. Evaluating my options happened when I formed my belief; thereafter, it’s rote rule-following (unless something jars me out of my rut).

All beliefs bring with them habitual behavior. If you believe that nice guys finish last, you’ll habitually behave not-nicely in any situation where you perceive you might finish last. You may reason about how best to be not-nice, but you won’t reason whether you should be not-nice. You just habitually protect yourself from others.

By analogy, you no more decide to act on a belief than you decide to salivate when you smell (or think of) your favorite food.

But beliefs can change. Consider the classic Mitchell and Webb “Are we the baddies?” sketch, a story of belief, doubt, and changed belief.

In the beginning of the sketch, the one SS officer (“Hans”) believes the Nazis are the good guys, so he calmly plans for an upcoming Soviet assault. The unnamed second character, however, is worried that they (the SS division) might be the “baddies.” He clearly finds this doubt uncomfortable, so he enlists Hans in reasoning about the problem. They use the guiding principle “People obsessed with symbols of death are bad.” The evidence shows the principle applies, so a new belief replaces the old. And the new belief is associated with its own rule for action: if you find yourself among baddies, run away!

In contrast to belief, which produces calm, doubt produces a kind of irritation. This irritation (unlike the calm of belief) provokes reasoning, which ends when a new belief is attained (or the old one is reaffirmed). And now habit takes over.

IV

Belief and doubt are something like interoception: a perception of the state of one’s body (in this case, of the brain). A state of doubt is something like hunger: it impels you to replace the unpleasantness with the pleasant feeling of fullness. This has some implications.

  1. Unless forced to continue, we end inquiry when the feeling of doubt goes away, not when we’ve met some external standard of evidence. We all sometimes stop short, believe things that we don’t really have enough evidence for.

  2. Descartes rather famously resolved to doubt everything, found he couldn’t doubt that he was a thinking being, and built his philosophy on that axiom. Less known is that Descartes resolved never to feel hungry again, and he never did.

    OK, that last part isn’t true. But neither is the first. Saying you’re doubting everything isn’t the same as actually doubting everything. Pretend doubt won’t launch an inquiry that will really challenge your beliefs.

  3. If someone believes differently than you, you should first find a way to instill legitimate doubt, then argue for your position. Otherwise, you’re just arguing for the fun of it (which Descartes did, which a lot of people do).

V

The method of tenacity Doubt is unpleasant, and inquiry is work, so it’s not surprising that people cling to their beliefs. One popular way is to avoid anyone and anything that might raise doubts. Bonus points if you can make the avoidance emotional, so that just being in a situation that might prompt doubt instead prompts revulsion and contempt. Call this method of producing fixed beliefs the method of tenacity.

The method of authorityBut that’s an unstable strategy. As a social species, we simply cannot avoid letting other people’s opinions affect our own. Unless we’re all to become hermits, fixing a belief – keeping doubt away – has to be a collective effort. The fixed belief has to become a societal belief: taught in schools and thereafter constantly reiterated. Teaching, advocating, or even expressing contrary beliefs must be socially costly. If that’s not enough, well, history shows us that massacring those who believe wrongly is at least temporarily effective at ensuring they won’t poison the mind of the true believer.

Call this method of fixing beliefs the method of authority. Yes, changes in belief will still occur, but they’ll be slow enough and small enough to be barely perceptible in one person’s lifetime. The method of authority works far better than the method of tenacity.

But no authority has yet been able to keep its populace ignorant of other societies, be they present or past. Sure, most people won’t learn much about other societies, and, if they do, they’ll shrug and believe that those people have different beliefs because they’re inferior or bamboozled. But history tells us you can’t prevent doubt-inducing thoughts like these:

The logico-deductive method Such people will decide that they need a better way of arriving at beliefs than just listening to authority. Perhaps what we should do is engage in free discussion and free inquiry and let that push us toward better beliefs, ones in harmony with nature. Such discussions will always revolve around reasoning through consequences of a priori axioms. Call this the logico-deductive method.

There’s a history of how well it works. Consider cosmology. It’s easy to create a system that is “agreeable to reason.” But how well does that system work outside the bounds of a priori reasoning? Plato reasoned himself into a belief that the ratios of the distances between planets had to be the same as the ratios of the lengths of musical instrument strings that produce harmonious chords. How do you judge between Plato’s theory and Kepler’s early theory that the orbits are determined by the ratios of regular solids? It comes down to which of the two is more agreeable to your reason.

This makes the fixation – the reaffirmation – of belief a matter of taste, and taste is notoriously variable. So philosophy has endlessly vacillated between thinking matter generates mind (materialism) and mind generates matter (idealism). The logico-deductive method doesn’t seem effective in causing diverse people’s beliefs to converge. Certainly not as effective as the method of authority.

The method of scienceSomething better than the previous three methods is needed. The one herein proposed is the method of science, which depends on an “external permanency,” a reality that is unaffected by what we think about it. Moreover, that reality must be accessible to anyone (unlike, say, a mystic’s intuitive grasp of the nature of external reality.)

Now, one might object that first we must prove that reality exists before trying to make use of it in reasoning. That proof can’t be made using science – it’s circular to prove reality exists by using a method that assumes reality exists. So we have no choice but to fall back on a gentle version of the method of authority to justify our belief in reality. That is:

  1. There isn’t anyone who really doubts reality, any more than Descartes could succeed at doubting everything. So there’s social proof for the method of science.
  2. Everyone already uses the method of science to solve a great many problems of daily life. In such cases, the method is only abandoned when the person involved can’t see how to apply it. More social proof.
  3. The scientific method has an impressive track record at creating and solidifying new beliefs. Even if there isn’t really a reality, should we care? The scientific method works.

The method of science depends on these assumptions:

  1. There are real things. Their natures are entirely independent of our opinions about them.
  2. Those realities affect our perceptions according to regular laws (what one might call reality’s fixed habits).
  3. Different people have different relationships to external objects, and so perceive differently, but our understanding of the laws of perception allows us to reason about how things really are.
  4. Anyone with enough experience who spends enough time reasoning about observations will be led to the same conclusion, a.k.a. the Truth.

The remaining essays will dive deeper into the method of science, seeking to present it as a repeatable process. In the meantime, some closing thoughts.

VI (skippable)

Enter heavy-handed irony mode

That’s not to say that the other three methods don’t have some advantages.

  1. The logico-deductive method excels at giving rigorous arguments for favored conclusions. Hellooooo, US Supreme Court. It’s always pleasant to know that you were right all along.
  2. The method of authority is inevitable, and it is also inevitable that it will be used to suppress beliefs the authority considers dangerous. Persecution of such beliefs produces social peace and a calm life (for those not persecuted).
  3. The method of tenacity is the best of all. It produces decisiveness. No effort is spent questioning goals; all effort is spent achieving them. Those who practice tenacity often are brilliant successes.

Exit heavy-handed irony mode

Those who think beliefs should coincide with facts will have to give up some of the advantages of the other methods, because there is nothing in those methods that forces the reasoner to grapple with facts.

Someone who does grapple with facts may find them leading in uncomfortable directions, and many people will be tempted to cease the effort and retain their old, accustomed beliefs. Such a person is in a sorry state of mind indeed.

The last paragraph of the essay is what my wife would call “flowery,” and I find it unlikely I could successfully put it into a modern style. So here it is, verbatim.

Yes, the other methods do have their merits: a clear logical conscience does cost something—just as any virtue, just as all that we cherish, costs us dear. But we should not desire it to be otherwise. The genius of a man’s logical method should be loved and reverenced as his bride, whom he has chosen from all the world. He need not contemn the others; on the contrary, he may honor them deeply, and in doing so he only honors her the more. But she is the one that he has chosen, and he knows that he was right in making that choice. And having made it, he will work and fight for her, and will not complain that there are blows to take, hoping that there may be as many and as hard to give, and will strive to be the worthy knight and champion of her from the blaze of whose splendors he draws his inspiration and his courage.

Commentary, 149 years later

  1. This essay is more about the psychology of belief than the philosophy of science. But remember that psychology had only recently forked off from philosophy to form its own discipline. (You can say psychology started with Fechner in 1854 , when Peirce was 15, or when Wundt founded the first specifically psychological laboratory in 1879 – two years after the publication of Peirce’s essay.)

  2. As a matter of psychology, a flip of the switch between belief and doubt that prompts immediate action seems less likely than a gradual accumulation of doubt that finally reaches the threshold of doing something about it. Peirce knew the neuroscience of his day. But that science was extremely crude and speculative. They knew neurons existed and not a whole lot more. Neural activation thresholds were unknown. Peirce was hampered because contemporary models of how the brain works were… not how the brain works. I speculate this is because he’s grafting the spectrum of doubt-shading-into-belief onto the traditional philosophical binary of false/true. In general, Peirce prefers triads (like his semiotics of sign/object/interpretant – coming up) or a continuum modeled after the number line (in dialogue with Cantor).

  3. On the other hand, Peirce is very taken with the idea of surprise, of the external world providing an “interruption” or “intrusion” that requires a “brute reaction” which, in this case, would be commencing inquiry. (I bet that he, like me, was prone to epiphanies.) So maybe minor doubts that don’t spur immediate inquiry don’t count.

  4. As a computer programmer, I naturally think “how would one implement this?” when encountering any theory of How Things Work. Peirce’s theory is way too sparse. There’s no way that just one belief applies to a situation. At the very least, many other beliefs will come into play when applying the “nice guys finish last” habit. I don’t know if anything is lost by the simplification, but it bugs me.

  5. Following Peirce’s original, I wrote noncommittally about whether Darwin got it right. Darwin’s Origin of the Species was published only 18 years before Peirce’s essay. (Peirce was 20 at the time.) Peirce, influenced by his teachers, was originally skeptical of Darwinian evolution, but he later became a huge fan to the point where processes of chance, evolution, and selection became central to his thought.

  6. Indeed, Peirce developed an “evolutionary cosmology.” That’s what I was alluding to when I wrote “Those realities affect our perceptions according to regular laws (what one might call reality’s fixed habits).” Peirce speculated the universe was originally highly disordered, but chance combinations of… something… developed “useful” habits that solidified into natural law, in a process that might finish only when everything is lawlike and deterministic. Crazy talk, but I can’t help but think of the currently respectable theory of the “inflationary universe” where laws like electromagnetism didn’t exist until suddenly they did. “Above a temperature of around 1015 K, the electromagnetic and weak interaction had not yet separated, and the gauge bosons and fermions had not yet gained mass through the Higgs mechanism. This is sometimes referred to as the electroweak epoch. As the universe’s temperature continued to fall, below 159.5±1.5 GeV/kB, electroweak symmetry breaking happened.” – Wikipedia So I haven’t decided if Peirce is being a crackpot or not. The Darwinian revolution spurred a lot of people to speculate on evolutionary cosmology. Nowadays, the anthropic principle seems to have taken its place.