The Grand Coherence, Chapter 5: The Feedback Loop Between Worldviews and Evidence

This post is part of the book The Grand Coherence: A Modern Defense of Christianity. For all the links in the book, see this introductory post.

If I had to coin a name for the epistemology we arrived at in chapter 3, I might call it “evidence-constrained coherentism,” but I don’t really want to name it. At least, I’d just as soon have readers forget the name as soon as they finish this chapter. A name might suggest that we are talking about a special kind of thought and knowledge, when really we are talking about just plain old thought and knowledge in general. We are dealing with matters so general that naming them would be the business of specialists, and I am not a specialist. In a wise joke, one fish comments on how nice the water is today, to which another fish replies, “What’s water?” In the same way, evidence-constrained coherentism is so normal that it doesn’t need a name.

But as a fish with no name for water in general might want words for particular kinds of water, like muddy or hot or running, so I think natural language furnishes us with words for different kinds of evidence-constrained coherentism, such as (a) common sense, (b) the dogmas of the Church, sufficiently discussed in the last chapter as a style of learning and thinking and knowing, and (c) science and the scientific method, of which it is the business of this chapter to discuss the character and origins. But first, by way of comparison, let’s talk a little about common sense.

Common sense must, above all, settle most to all practically relevant questions somehow. To focus on this, it ignores impractical and speculative questions, or questions that go beyond everyday experience to cover strange or remote contingencies. It mostly believes what it hears, but can be skeptical when it hears things that go against intuition and/or experience. Standards of evidence are low in a way: people may accept and internalize claims as common sense rather uncritically. At the same time, there is resistance to novelty, reliance on intuition, and a repeated turning to collective judgment that makes it hard for new, untested claims to pass for common sense. People try not to accept things as common sense unless they think that they or others have lots of relevant experience supporting them. Common sense beliefs are promiscuously traded among people through casual conversation, so common sense is inhospitable to precision and exactitude, and to anything that has to be articulated carefully and at length. It has a preference for proverbs, that is, for short, pithy, memorable statements that can circulate easily. 

Coherence in the common sense domain is a rough and unrigorous affair. You can disagree with a proverb, but if two proverbs seem to have logically inconsistent ramifications sometimes— maybe “the squeaky wheel gets the grease” vs. “no good deed goes unrewarded”— then maybe you just don’t have the wisdom to use those proverbs right. Common sense can involve a lot of discernment, but it doesn’t encourage the refinement of critical thinking and careful logic. And while it highly values experience, especially the ordinary experiences of everyday life, individual and collective, it doesn’t encourage formal theory testing. It imputes a lot of authority to an inherited stock of wisdom, but regards that wisdom as partially inarticulate, with proverbs to signpost it rather than to fully explain it. Your own experience and other people’s stories help you understand what the proverbs mean.

Science, by contrast, distinguishes itself by precise statement of hypotheses and exact measurements, and is an elite affair, listening to experts rather than ordinary people. It studies, first and foremost, that which is perceptible to our senses, that which can be seen, heard, smelled, tasted and touched. At a more advanced stage, it deals with many things that are not directly, in themselves, in the normal course of things, sensorily perceptible, such as biological cells, atoms, electric and magnetic fields, or the centers of the earth and the sun, but it makes them accessible to the senses through special media, such as microscopes, or deduces their existence by reasoning from sensory experiences, as interpreted with the help of hypotheses about natural laws. In short, science studies matter. 

Only at an advanced stage, when it aspires to become a total theory of the world, does science begin to deal in mental phenomena internal to human beings, such as moods or morals, which are not intersubjectively observable. When it does so, it has to depart somewhat from characteristically scientific habits of thought such as precise statement of hypotheses and exact measurement and rigorous theory testing followed by rapid abandonment of theories in the event of predictive failure. That’s why  psychology and sociology feel less “scientific” to most people than natural sciences like chemistry and physics, and lack their authority. Worse, “scientific” studies of human phenomena like the mind and society sometimes introduce an unwarranted assumption that they are still studying mere matter, and human beings are reducible to atoms and energy, simply because the scientific materialist ideology requires it, even though that assumption rarely if ever contributes to the genesis of successful hypotheses. In English, there is a narrower natural language meaning of the word “science” that restricts the term to the natural sciences and ignores the social and human “sciences.” I prefer that usage.

Science, i.e., natural science, deals in what is intersubjectively observable, and consequently it is often able to efficiently establish consensus through proof, so it doesn’t need to silence debate by fostering a culture of deference and agreement. On the contrary, it can often afford to encourage maximum critical thinking and questioning of authority, the better to incentivize participants to design experiments that will settle disputed questions once and for all. Science is not a take-it-or-leave-it affair. It is always learning, always open, in principle, to challenge, and stands ready, at its best, to take all comers, to answer all critics, to refute all skeptics, or if it fails to do so, gracefully and gratefully to change its mind. 

A historical example will help to illustrate the character of modern science, while also showing more or less how it began. Along the way, I’ll show how the birth of the Scientific Revolution exemplifies the kind of Bayesian rationality I’ve been describing.

Throughout the Middle Ages, a model of the cosmos prevailed according to which the earth was at the center, or we might say the bottom, for “down” meant “towards the earth,” of the universe, uniquely prone to chaos and decay and sin. That sad state of affairs reigned up to the orbit of the moon, in the “sublunary” part of the cosmos. Beyond the moon, it was different. All was perfection and light up there, among the heavenly bodies, which moved in a sublimely orderly manner described by the ancient Ptolemaic system, compiled by the astronomer Claudius Ptolemy (c. 100-170 AD). This cosmology was imaginatively brought to life in the Paradiso of Dante Alighieri (c. 1265-1321). C.S. Lewis (1898-1963) explained the medieval model of the cosmos, along with its origins and history, in his book The Discarded Image. 

The medieval cosmology owed as much to Greek philosophy as to the Bible. It is certainly not biblically mandated. It even retained traces of Greek mythology, with the planets having their own spheres in a cosmic hierarchy and retaining some of the character of the pagan gods they had been identified with. Nonetheless, it was felt to harmonize with Christian theology. The doctrine of the Fall, for example, was physically inscribed into the form of the cosmos, with fallen nature below the moon, sinless immortality above it.

But in late medieval and early modern times, the old model began to sustain a number of blows. First, improved observation of the heavens even with the naked eye started to reveal that the movements of the heavenly bodies didn't perfectly fit the Ptolemaic model. Astronomers kept refining the Ptolemaic system in ways that made it fit the facts better, but also made it more complicated. Eventually, Copernicus (1473-1543) showed how the movements of the heavenly bodies could be explained more neatly and accurately if you start from the assumption that the sun, not the earth, was at the center of the universe. So a long contest between the “heliocentric,” or sun-centered, and the “geocentric,” or earth-centered, cosmologies began. 

Then the telescope appeared, with Galileo (1564-1642) as the recognized inventor though he had forerunners, and it became possible to look at the heavenly bodies as if up close. And it turned out that they were not perfect at all, as had long been assumed, but had bumpy, irregular surfaces! That's not directly relevant to the heliocentric vs. geocentric debate, but it's indirectly relevant in a very important way. For the medieval cosmology had posited a major discontinuity at the orbit of the moon, and that makes more sense if the earth and the sublunary realm are spatially distinct. Place the sun at the center, and make the earth and planets its satellites, and it becomes very odd, to the point of implausibility, that the earth is governed by different rules, such that its tendency to chaos and decay and sin are unique. 

Before the telescope, the distinction between sublunary chaos and celestial perfection seemed empirical. The sun, moon and stars seemed to display a sublime perfection in their movements and forms that couldn't be found on earth. But when the telescope revealed irregular surfaces on the planets, it became more plausible that a single system of uniform laws governed the whole cosmos, including the heavens, and astronomers and physicists began to work out what those laws were, culminating in the cosmic system of Isaac Newton with his laws of motion and gravitation. Along the way, unfortunately, Galileo got in trouble with the Catholic Church, and was famously interrogated by the Inquisition, forced to recant from his embrace of Copernicus’s heliocentric universe, and placed under house arrest for the rest of his life, becoming Exhibit A in the supposed war of science and religion, which is why the episode is famous.

Let's try to make sense of this history using evidence-constrained coherentism.

Let proposition A be: “The universe is spatially divided into a celestial realm, where perfection and good order and eternal life reign, and a sublunary realm, where things are ever pulled downwards, and good order is perpetually being eaten away by chaos, decay and death.”

In the Middle Ages, people had high confidence in A. The evidence they could see was constantly confirming it. In the heavens, they saw a sun and moon perfectly round, and the stars and planets following their courses with perfect reliability. On earth, things were always rather unpredictable. The best laid plans went oft awry. And all living things died in due course, living order giving way to rotting chaos. Dropped things fall on earth, but the stars don't fall.

But how perfectly did the stars follow their courses, really? That depends on what those courses were. To be explicable and predictable, they must follow rules of some sort. But what were the rules? The rules of the Ptolemaic system kept turning out to be subtly wrong. And then the rules of the Copernican system turned out to be right. The planets move as if they are orbiting the sun. At the practical level, that's the best way to predict their positions, for purposes of navigation, say, or calendar design. So let's formulate that into a theory.

Let proposition B be: “The planets, including the Earth, orbit around the sun.”

Proposition B was suggested by astronomical evidence and is continually confirmed by it. But now we have a problem, because propositions A and B are apparently inconsistent. If the earth is orbiting around the sun, there can be no spatial division of the universe into celestial and sublunary. One solution is to deny A. But that leaves all sorts of phenomena desperately unexplained. If there is no celestial vs. sublunary partition of the universe, why don't the stars fall the way dropped objects do on earth? Why doesn't the earth fall into the sun? Why don't the stars exhibit irregular and chaotic conduct the way things always seem to do on earth? Why don't heavenly bodies have imperfect, accidental shapes, like things on earth? Why does the earth keep moving around the sun, not slow down and stop like moving things do in our experience? The best way to save all sorts of commonsense knowledge would be to deny B, conceding at most that the planets seem to move around a stationary sun. So let’s reformulate it that way.

Let proposition B’ be “The planets move as if they, and the Earth, orbit around the sun.”

Now we can set up the world’s response to Copernicus‘s discovery as a Bayesian updating event. 

Let’s assume that by 1550 or so, B’ is an established fact, which people have to come to terms with. They must therefore update their confidence in the medieval cosmology from some P(A), their prior belief, to P(A|B’), a new belief adopted in light of the Copernican movements of the planets. 

To apply Bayes’ Law, they also need some value for P(B’|A) and P(B’|~A). P(B’|A) is the probability that the planets would seem to move as if they orbited the sun, if the medieval cosmology were true and they actually orbited the earth. A low value seems appropriate, say 5%. P(B’|~A) is the probability that the planets would seem to orbit the sun if the medieval cosmology is false. It’s not clear how to assign that, so let’s call it 50%. 

If P(A) is 80%, P(A|B’) is 80%*5% / (80%*5%+20%*50%) = 28.6%. 

But if P(A) is 99%, P(A|B’) is 99%*5% / (99%*5%+1%*50%) = 90.8%

This shows why, if two believers in the medieval cosmology, one tentative and one staunch, encountered Copernicus’s discoveries, the tentative one might be convinced of heliocentrism, and abandon the medieval cosmology, while the staunch one would remain convinced of the medieval model. The differences in this example comes from subtle differences in their prior state of confidence in the medieval cosmology. It could also come from different feelings about just how unlikely it would be for planets in a geocentric world to move in a seemingly heliocentric way. One way to put it is that people might vary in how impressed they were by the pattern that Copernicus saw. 

Those who abandoned the medieval cosmology at this stage would have found themselves lacking a coherent worldview. Without the celestial vs. sublunary partition of the universe, they would have no idea why the stars kept moving, or why they didn’t fall. And the heliocentric theory’s claim that the earth was moving rapidly through space must have struck many as wildly counterfactual. Why don’t we feel the movement then? Why is there no permanent wind? Why do dropped objects fall straight down instead of the earth moving under them as they fall? Until Isaac Newton (1643-1727) formulated his laws of gravity and motion, these questions lacked good answers. Some might be induced by critical reflection to return to the medieval cosmology as they contemplate all the bewildering ramifications of abandoning it.

For the next stage in this history, let proposition C be: “The heavenly bodies have imperfect, irregular surfaces like the earth.” 

A historian of science could say more than I can about whether proposition C was articulated frequently or at length before Galileo’s telescope. But it would surprise me if it was. Often, many of the implications of a worldview or theory remain largely tacit, until surprising evidence prompts people to articulate what they always thought but rarely said. But it’s my impression that P(C|A) would have been low, say 1%, for believers in the medieval cosmology. Let P(C|~A) be 50% for the sake of argument. Then, when Galileo’s telescope reveals the irregular surfaces of the planets, the following Bayesian updating event might occur.

P(A|C) = 90%*1% / (90%*1% + 10%*50%) = 15.2%

In this case, a rather strong believer in the medieval cosmology, who had considered it 90% likely to be true, would be persuaded to abandon it by what the telescope revealed. The surprise of irregular planetary surfaces would disrupt the old tales of celestial perfection and weaken the whole cosmology. 

But we want to understand, in Bayesian terms, how the discovery planetary imperfections affected belief in heliocentrism, and for that, we'll need to reformulate some of our propositions, because Propositions A and B, the medieval cosmology and Copernican heliocentrism, seem logically incompatible, since part of the medieval cosmology is the spatial centrality of the earth in the universe. Yet people were able to entertain heliocentric theories and evidence when the medieval cosmology was still prevalent. To understand how, it will be helpful to articulate some proposition A’ could be defined, which preserves the part of the medieval cosmology that isn’t directly contradictory to heliocentrism, while being agnostic about geocentrism vs. heliocentrism. It might look something like this:

Proposition A’: “The universe is divided, though not necessarily in a persistent spatial way, into a celestial realm, where perfection and good order and eternal life reign, and a sublunary realm, where things are ever pulled downwards, and good order is perpetually being eaten away by chaos, decay and death.”

Such clumsy reformulations are often resorted to in order to keep alive a theory that people still rely on to understand the world, even though it has sustained some damage from adverse evidence. Logically, P(A'|A) is 100%, since A' consists in a subset of the content of A, so A logically implies A', but not vice versa. Evidence that would defeat A need not defeat A'. Yet A' is less coherent and intuitively appealing than A, since it seems odd that a celestial vs. sublunary division of the cosmos is maintained if is not persistently spatial.

Thanks to the reformulation, P(B|~A’) (as a reminder, Proposition B still refers to the claim that the planets, including the Earth, orbit the sun) need not be zero. Heliocentrism and this reformulated version of medieval cosmology could both be true. But it seems unlikely because they are still a very odd fit. By contrast, if A’ is abandoned, and the belief that the universe is divided into celestial and sublunary is given up, then heliocentrism has a pleasing simplicity. 

How, in this case, would the evidence of planetary imperfections from Galileo’s telescope affect belief in heliocentrism? We can think of it as a two-step Bayesian updating process.

The first step would be to update on A' given C. We can characterize the surprise that Galileo and his contemporaries must have felt upon seeing, or hearing about, the imperfections in the heavenly bodies, by saying that P(C|A'), or the likelihood that there would be imperfections in the heavenly bodies given the prevailing belief in a celestial vs. sublunary distinction, was very low, say 0.1%. By contrast, only simplify the universe into a more continuous place comprehensively governed by a consistent set of natural laws, and imperfections in the planetary bodies would seem very probable. In other words, P(C|~A') is high, say 95%.

So when an age in which the old medieval cosmology still held a certain grip on European minds, so that prior belief P(A') in the celestial vs. sublunary distinction, though not measurable, must have been fairly high, the revelations of the telescope triggered a major Bayesian updating event for those clever enough to think things through. Given P(A') of 80%:

P(A'|C) = P(C|A')P(A')/(P(C|A')*P(A')+P(C|~A')*P(~A')) =  0.1%*80% / (0.1%*80% + 95%*20%) = 0.41%

In words, planetary imperfections were so unlikely in a universe divided into celestial and sublunary, and so likely in a universe leaving such a division, that telescope evidence decisively dispelled the medieval cosmology. 

The next step is to update belief in heliocentrism on the new disbelief in the celestial vs. sublunary distinction, i.e. to determine P(B|~A'). We're interested in people still unconvinced, prior to the revelation of planetary imperfections by the telescope, by the well-known successes of Copernican heliocentrism in explaining the movements of heavenly bodies. So prior belief in heliocentrism P(B), despite some favorable updating, would still be low enough to indicate nonbelief, e.g., 20%. We also need prior beliefs for P(~A'|B), the prior odds of there being a celestial vs. sublunary cosmic division under heliocentrism, which should be relatively low because it's so odd, e.g. 10%, and P(~A'|~B), the prior odds of there being a celestial vs. sublunary cosmic division without heliocentrism, which should be higher, e.g., 90%. When the telescope evidence refutes the medieval cosmology, the following Bayesian updating event occurs:

P(B|~A') = P(~A'|B)P(B)/(P(~A'|B)P(B)+P(~A'|~B)P(~B)) =  90%*20% / (90%*20% + 10%*80%)=69%

In words, before the telescope, the continuing persuasive force of the medieval cosmology weighed against Copernican heliocentrism because heliocentrism fit very awkwardly at best with a long-standing distinction between celestial and sublunary realms that seemed to be very helpful in explaining the world. When the telescope revealed the imperfection of heavenly bodies, it was evidence against the celestial vs. sublunary division of the universe, and thereby removed a major objection to the Copernican solar system, preparing the way for its acceptance. Here we glimpse the feedback loop between worldview and evidence. Our worldviews shape what evidence we find credible, and how we interpret our observations. But evidence, in its turn, affects what worldviews we invest our belief in, sometimes in very dramatic ways.

In great confrontation between Galileo and the Inquisition, the biblical warrant provided by the Inquisition for its view was extremely flimsy. That they had to quote Psalm 104:5, which in a poetic flight of praise for God and His world remarks that God has set the earth on its foundations and it “shall not be moved,” is a reminder of how little the medieval cosmology owed to scripture from the beginning. The real evidence for geocentrism was empirical. Of course the earth is stationary! Look at it! The Inquisition demanded that Galileo supply evidence for his extraordinary claims. Lacking it, they thought, he shouldn’t have written it so confidently, implying a knowledge he didn’t possess. 

But what did they mean by evidence? A good theorist can carry inference from evidence very far. The evidence for heliocentrism was that the observed orbits of the planets conformed to what they would be if they and the earth orbit the sun, and also, that the irregular surfaces of other planets disproved the medieval cosmology and pointed to uniform natural laws extending beyond the sublunary into the celestial realm. For a genius like Galileo, that was enough, even if the lumbering minds of old clerics couldn’t attain such flights of insight.

Eventually, Isaac Newton completed the Copernican revolution with his great laws of motion and gravity. The claim in Newton’s first law of motion that an object in motion stays in motion unless acted upon is, prima facie, contradicted by all human experience. We see things in motion always slowing down and stopping unless some force keeps moving them. Only in the heavens do we see things like planets and comets and moons persist in a changeless motion. Newton saw that the heavenly pattern expresses the law, while earthly experience is a special case affected by air resistance and friction but not contradicting the law. Newton’s service to astronomy lay not in observation but in supplying a unifying theory that explained with a swift simplicity all the many observed phenomena. But he did more, for he also unified the physics of heaven with the physics of earth, thus achieving a dazzling grand coherence for the laws of nature and the order of the universe. Copernicus and Galileo left much to be explained. Newton explained it. They posed a riddle that Newton answered.

Today, the Darwinian revolution in biology is often compared to the Copernican revolution in cosmology. Certainly, there are resemblances. Both are audacious simplifications of the world. Both disrupted a previously existing worldview that was more comprehensive, in terms of the range of experiences of which it gave some account or explanation, than what they offered in its place. Thus, Copernicus said the earth was moving, but didn’t explain how it could then seem stationary. Likewise, Darwinism says people evolved from particles, but doesn’t explain how then they can have consciousness. Copernicus and Darwin both challenged forms of exceptionalism, Copernicus, an exceptionalism of the earth, Darwin, an exceptionalism of life and of man, in favor of more fundamental and universal principles. Galileo’s telescope eventually provided empirical evidence against the exceptionalism of earth that Copernicus challenged, and thereby supported him, and Newton finally articulated the laws that explained and unified the Copernican cosmos. But the Darwinian revolution has never had its Galileo or its Newton. Human exceptionalism remains as empirically robust as ever, and Darwinism has never explained consciousness. We will see in the following chapters why it never can. Not all simplifications of the world are true.

We could apply this kind of analysis to many episodes in intellectual history. Like the way the careful analysis of combustion by 18th-century chemists detached the identification of chemical elements from the traditional, intuitive categories of air, fire, earth and water, and led to the proliferation of newly-identified elements that were eventually organized into the periodic table of Dmitri Mendeleev (1834-1907). Or the way an experiment by Albert Michelson (1852-1931) and Edward Morley (1838-1923) disproved the existence of ether and forced a crisis on physics that was resolved only with the theory of relativity of Albert Einstein (1879-1955). Or the way Adam Smith (1723-1790) discerned new kinds of order in economic life and wrote them down in The Wealth of Nations, persuading the world of the beneficence of competitive market equilibrium, and laying the foundations of classical economics and of the 19th-century golden age of laissez-faire capitalism. Or the way classical economics, after a long though far from unchallenged hegemony, was dramatically discredited by the Great Depression, paving the way for John Maynard Keynes’ (1883-1946) prescriptions for macroeconomic management in a social democracy, and also for the rapid advance of communism and fascism. Or the way the theory of evolution of Charles Darwin (1809-1882) revealed a persuasive alternative to Aristotelian teleology for understanding apparent purpose in the biological world. And so forth.

In all these historical episodes, there are two recurring causes of change. First, there are surprising events or discoveries, new evidence that defies expectations and discredits old ways of thinking. Like Galileo’s telescope, and what it revealed about the planets. Second, there are theoretical triumphs that fit disparate known facts into newly discerned patterns. Like Copernicus’s heliocentrism and Newton’s laws of gravitation. Other great theorists on the order of Isaac Newton were Adam Smith, Charles Darwin and Albert Einstein. Sometimes the great discoverers were also great theorists, like Lavoisier (1743-1794). Other great discoveries were accidental, as when astronomers Arno Penzias (1933-) and Robert Wilson (1914-2000), in 1965, found something interfering with their radio wave experiments that turned out to be, not pigeon droppings as they first thought, but rather, the cosmic background radiation predicted by Big Bang theory, thus settling the question of the origins of the universe! 

It’s all part of the great feedback loop between worldview and evidence. Our minds are constantly being flooded with experiences, mental and sensory, many or most of which are evidence of nothing and leave no impression, because they are uninterpreted and irrelevant. But some experiences relate to theories that we have about the world, sometimes supporting and  confirming and illustrating and exemplifying them, sometimes challenging or contradicting them. It takes a worldview to give evidential significance to experience. Often our worldview helps us interpret experience. It makes things matter. It makes us notice things. The way we characterize and remember things is shaped by our worldview. But then experience, in turn, shapes our worldview, reinforcing some beliefs and undermining others. Our worldviews are also shaped by critical reflection, and sometimes we are forced to change our minds because we notice contradictions among our beliefs. Failures of coherence may occur because experience has forced us to update some of our beliefs, in ways that disrupt the logical harmony of our belief system as a whole. When we have to reformulate our generalizations in order to restore consistency, this should leave us somewhat less confident in them, though it helps somewhat if we remember enough past data to test them on it. But new theories should heighten our curiosity to test some of the new predictions that our new theories make. As we learn and grow like this, less of our experience is left uninterpreted and irrelevant. More and more things make sense. All of these patterns apply to cultures as much as or more than to individuals. Individual people all do some independent learning, but pick up most of what they know from the culture. On the stage of whole cultures as well as in the minds of individuals, the feedback loop between worldview and evidence is played out.

But while we have been enthusing over the way science advances by discovering contradictions and reformulating theories, our epistemological ship has sprung a leak. For it turns out that the scientific method we’ve been extolling invites disastrous misapplication. In the next chapter, we'll see why, without some way of disciplining what theories may be treated as legitimate candidates for Bayesian confirmation, the feedback Ioop between worldview and evidence can be manipulated to prove anything, and what can be done about it.