What Science Knows: And How It Knows It

By James Franklin

To scientists, the tsunami of relativism, scepticism, and postmodernism that washed through the humanities in the twentieth century was all water off a duck’s back. Science remained committed to objectivity and continued to deliver remarkable discoveries and improvements in technology.

In What Science Knows, the Australian philosopher and mathematician James Franklin explains in captivating and straightforward prose how science works its magic. He begins with an account of the nature of evidence, where science imitates but extends commonsense and legal reasoning in basing conclusions solidly on inductive reasoning from facts.

After a brief survey of the furniture of the world as science sees itincluding causes, laws, dispositions and force fields as well as material thingsFranklin describes colorful examples of discoveries in the natural, mathematical, and social sciences and the reasons for believing them. He examines the limits of science, giving special attention both to mysteries that may be solved by science, such as the origin of life, and those that may in principle be beyond the reach of science, such as the meaning of ethics.

What Science Knows will appeal to anyone who wants a sound, readable, and well-paced introduction to the intellectual edifice that is science. On the other hand it will not please the enemies of science, whose willful misunderstandings of scientific method and the relation of evidence to conclusions Franklin mercilessly exposes.

• Language: English
• Publisher: Encounter Books
• Release date: Nov 1, 2009
• ISBN: 9781594034398

James Franklin

James Franklin is the Episcopal Campus and Young Adult Missioner to Wake Forest University, Salem College, UNC School of the Arts, and Winston Salem State. After the military, seminary, and a brief stint in parish ministry, he answered the call to be a campus minister, where he helps create beloved community. James can usually be found in campus coffee shops meeting with students.

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PREFACE

Any time is a good time to contemplate the advances of science. But the ideal occasion is a visit to the dentist. Not only is the distraction welcome, but the intrusion of drill or laser into the mouth—so close to where he feels one’s real self is located—prompts reflection on how much worse things could be. Or how much worse they actually were, before science worked its magic.

Take the case of Charles Whitworth (1752–1825). The state of Earl Whitworth’s teeth as of 1825 is known exactly because he was buried in a triple-shelled lead coffin, excavated in the 1990s. He had been British ambassador to Napoleon and Lord Lieutenant of Ireland and could afford the highest standard of dental care his age could provide. That care, unfortunately, included the provision of tooth powders and tinctures of the sort advertised to eradicate the scurvy and tartar from the gums; make the teeth, however yellow, beautifully white.… The reason teeth came up beautifully white was that the products contained abrasive materials made of shells, corals, and ground pebbles, along with tartaric acid—and Whitworth’s teeth show the effects. On the front of the right upper incisors, where a right-handed man would naturally brush hardest, the enamel is completely missing. Having exposed dentine is a very painful condition, especially when trying to eat or drink anything cold or hot.¹

A normal citizen of any functioning country today is the beneficiary of dental knowledge that Whitworth would have given his eye teeth for, what was left of them. We accept these benefits, and if we choose to, we can understand the science behind how they work.

Victims of land mines and napalm, it is true, are entitled to their vote that science sometimes has serious ill effects, and it is possible that a biology laboratory will yet come up with a microorganism that eats us all. It is the nature of science that it delivers power without responsibility. It delivers power because it delivers knowledge.

But scientific knowledge has many enemies. They resent not just the uses of science, but its aims, methods, and discoveries. The Internet and World Wide Web (provided by science, of course) are flooded with complaints and suspicion about science. Scientific theories, it is variously alleged, are socially constructed, determined by vested interests, underdetermined by data, dependent on the observer, logically impossible to confirm, always falsified in the long run, Western, godless, linear, patriarchal, reductive, and so on—all with the implication that scientific theories are not to be believed.

Science has its defenders too, many of them excellent at such individual tasks as refuting postmodernist attacks and defending particular aspects of science and the philosophy of science. What these defenders have not done is provide a simple and straightforward introduction to why science is rational.

This book attempts that task. With a mixture of considerations about the logic of science and illustrations from real science, it explains from the ground up how science has established conclusions that are worthy of belief—absolutely certain conclusions in the case of the mathematical sciences, very highly probable ones in empirical science.

At the core of the defense of scientific rationality lies the objectivity of logical relations. This applies both to the deductive relations of mathematics and the probabilistic or non-deductive relations of empirical science. The reason we can prove—and hence believe with certainty—that the square of any even number is even is that deductive relations exist between truths about numbers and those about their squares. The reason we can rely on what the dentist tells us about our fate over the next hour—though with less than 100 percent certainty—is that there are logical relations between evidence and hypothesis. The evidence lies in the clinical trials that the dentist’s materials, equipment, and procedures have undergone; the results of those trials bear on our case for logical reasons.

We begin, then, by explaining how an objective view of the relation of evidence to conclusion solves the classical problem of induction, which asks how we can know (with high probability) that all ravens are black when we have observed only finitely many black ravens and it is logically possible that the next raven we observe should be white. If that problem cannot be solved, there is not much hope for defending the rationality of the more esoteric reaches of science.

Basic though it is, the rationality of induction is sufficient for defending science against the broad-brush irrationalist attacks on it—by twentieth-century philosophy of science and, later, sociologists of science and postmodernists. An excursus on their objections reveals their logical mistakes and gross misunderstandings about the logic of evidence and conclusion.

We then survey some typical examples of knowledge in the natural, cognitive, and social sciences, to give some sense of the variety of methods used in real science. There is more than usual attention paid to the mathematical sciences, not only because they long ago found what is the gold standard of knowledge, mathematical proof, but also because the computer revolution has extended the reach of mathematical methods through most of science.

After a brief glance at how science as actually realized in people and institutions supports the discovery of scientific truths (or occasionally does not), we conclude with a view of the limits of science. Some of those limits are imposed by the problems of observing the very big, very small and very old, and understanding the very complex. In particular, the controversies about evolution and global warming arise from the inherent difficulty of understanding the complex systems involved. But beyond that there are more principled limitations to science, namely the essentially non-scientific character of some of the topics on which we most desire and need knowledge: consciousness and ethics.

Science has taught us not only what to think but how to think. Let us learn how it did it.

CHAPTER 1

Evidence

Some science is about hidden worlds, either smaller than the microscopic or more distant than our galaxy. Some involves such esoteric concepts as curved space-time or infinite dimensional Hilbert spaces. But the true lover of science will revel first in the many low-level empirical generalizations that summarize and give shape to our long perceptual experience: All ravens are black Last night’s stars form much the same patterns as tonight’s Banana peels are normally slippery Virgins don’t have children It’s in spring that the wheat comes up Lithium is effective against bipolar disorder Tossed coins come up heads about half the time.

All Ravens Are Black: How Do They Know That?

An enormous amount of careful human observation has gone into recognizing and establishing these fundamental facts of science, which provide the foundations on which the edifice of more theoretical science rests. If we are to understand the rationality of science, we need to grasp first how we know those straightforward kinds of truths.

Logically speaking, there are three potential problems with establishing such simple generalizations:

▪ Do we have our classifications and concepts straight, so that we know definitely what potential new instances are or are not ravens and black?

▪ Have we established how we know by perception a single instance, This raven is black?

▪ How do we manage to make the leap of inductive inference from all the (finite number of) observed ravens have been black to all ravens (including unobserved and future ones) are black? Are we justified in doing so, and, if so, with what degree of confidence?

Those are all good questions. The first two, dealing with the scientific and logical underpinnings of our commonsense knowledge, will be considered in later chapters. The last one, the problem of induction, has rightly been regarded as the classic problem that must be solved first in order to understand why science is rational.

To be in a position to solve it, one must first understand why seeing a black raven is evidence for the proposition that all ravens are black. We need to start at the beginning with the notion of evidence for beliefs.

EVIDENCE PRAISED

Don’t you believe in flying saucers, they ask me? Don’t you believe in telepathy?—in ancient astronauts?—in the Bermuda Triangle?—in life after death?

No, I reply. No, no, no, no, and again no.

One person recently, goaded into desperation by the litany of unrelieved negation, burst out, Don’t you believe in anything?

Yes, I said. I believe in evidence. I believe in observation, measurement, and reasoning, confirmed by independent observers. I’ll believe anything, no matter how wild and ridiculous, if there is evidence for it. The wilder and more ridiculous something is, however, the firmer and more solid the evidence will have to be.

Isaac Asimov, The Roving Mind (Amherst: Prometheus Books, 1997), 43.

It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence.

William K. Clifford, The Ethics of Belief in Lectures and Essays, ed. Leslie Stephen and Sir Frederick Pollock (London: Macmillan and Co., 1879).

The Objective Bayesian View of Evidence

Objective Bayesianism, or logical probabilism, holds that the relation of uncertain evidence to conclusion is one of pure logic.¹ That the Big Bang theory is well-supported by present evidence, that a defendant’s guilt has been proved beyond reasonable doubt, that there is good reason to believe well-confirmed conjectures in pure mathematics such as the Riemann hypothesis, are objective matters of the same nature as the deducibility of the Pythagorean theorem from Euclid’s axioms.

Objective Bayesianism contrasts with deductivism (the thesis that all logic is deductive). Objective Bayesians argue for the existence of a non-deductive logic—a logical probability, or partial implication, between a body of evidence and a hypothesis that it supports or confirms but does not deductively imply.

The probability spoken of here is distinct from the probability involved in stochastic processes like throwing dice or tossing coins. More will be said on the kinds of probability in chapter 10.

Let us lay out the main arguments for the existence of non-deductive logic. Some of them are:

▪ The heated arguments among jurors, scientists, and others about whether particular bodies of evidence do render particular conclusions highly credible is a reason to believe that high credibility on evidence is a genuine relation, unless some better account of it can be given.

▪ The inference scheme variously called the proportional syllogism or statistical syllogism or direct inference² certainly looks like the standard argument of deductive logic called the syllogism. The syllogism is the classic argument form of which an example is:

All men are mortal.

Socrates is a man.

So, Socrates is mortal.

The premises entail that the conclusion is true: it is impossible for the premises (All men are mortal, and Socrates is a man) to be true and the conclusion (Socrates is mortal) to be false. The statistical syllogism is an argument such as:

99.9 percent of men are mortal.

Socrates is a man.

So, Socrates is mortal.

In this instance, it is possible, but not likely, for the premises to be true and the conclusion false. What is so special about 100 percent, as opposed to 99.9 percent, that could make the first argument part of logic but the second not? A stipulation that the word logic should only apply to cases where it is impossible for the premises to be true and the conclusion false would simply evade the issue, which is whether propositions can support one another in ways that fall short of strict entailment. Evasions based on what would happen if extra premises (for example, Socrates is divinely favored) were added to one or both of these inferences are no better, since the question, like any concerning inference, deals with the relation of the givenpremises to the conclusion, not the relation of some other set of premises to the conclusion.

▪ The simplest principle of logical probability, called by Polya the fundamental inductive pattern³ (and the main content of the celebrated Bayes’ theorem that gives Bayesianism its name), is:

q is a (non-trivial) consequence of hypothesis p.

q is found to be true.

So, p is more likely to be true than before.

It is hard to begin reasoning about the world without a commitment to that principle. Imagine a tribe that did not believe in it, and thought instead that agreement between theory and observation was a reason for disbelieving the theory. Its members guess there are bison in the river field and go there to hunt them. They find none. So they conclude they will probably find bison there tomorrow and the next day and they go there day after day with high hopes. You will need to imagine that tribe because you will not be meeting them. They are extinct.

▪ The evaluation of conjectures in pure mathematics uses the usual non-deductive inference schemes such as the confirmation of theories by their consequences. There are inductive arguments used in experimental mathematics, such as conjectures that arise from observations of the digits of π. (More in chapter 10.) Because mathematics is true in all possible worlds, the rationality of these inferences must be matters of logic.

▪ The concept of inference to the best explanation (more later in this chapter) is widely regarded as necessary to make the most basic inferences about the existence of the external world, the existence of laws of nature, of atoms, and so on. Such inferences are obviously non-deductive, and if they depended on any contingent facts, such as the existence of laws of nature, they could not perform the tasks assigned to them.

SOME FORMULAS (OPTIONAL)

There is no need for jurors evaluating evidence in a trial to know formulas of logical probability. Suggestions that jurors should be instructed in Bayes’s theorem have not progressed far, understandably. But there is a formalism that has proved very serviceable in studying logical probability. It says:

The probability of hypothesis h on evidence e is represented by a number P(h | e) between 0 and 1 (inclusive), which satisfies two axioms:

P(not-h | e) = 1 – P(h | e)

P(h | h’ & e) × P(h’ | e) = P(h’ | h & e) × P(h | e)

From these axioms various theorems can be derived, such as:

▪ If e is a consequence of h (but not of background evidence b), then

P(h | e & b) > P(h | b)

(Polya’s fundamental inductive principle that theories are confirmed by their non-trivial consequences)

▪ If e is a consequence of h (but not of b) and P(e | b) is low, then

P(h | e & b) is much greater than P(h | b)

(that is, verification of a surprising consequence renders a hypothesis much more credible)

Those are substantial reasons for accepting logical probability. They are too substantial to be dismissed with generalized complaints, for example about the difficulty of discovering the exact numerical relation between given bodies of evidence and conclusions. Objective Bayesianism does not claim that it is typically easy to discover the relation of a body of evidence to a conclusion, only that it is there to be discovered.

The theory does not in itself take a position on whether some of the evidence on which science is based is or is not certain. Simple observational facts like I see a black bird in front of me, and easy mathematical truths like 2 + 2 = 4 have a claim to be more certain and unshakeable than complicated theories that use them as evidence. Nevertheless, it may be that a sufficiently well-confirmed theory could make us doubt apparently contradictory observations or the results of calculations. The solidity of observational and mathematical truths is something to be considered later.

Why Induction Is Logically Justified

Some people have a psychology that makes them describe as half-empty a glass that others think of as half-full. In the same way, some philosophers of science never manage to move beyond the shocking discovery that induction is fallible to ask seriously why it mostly works. True, no matter how many black ravens have been observed (without exception), it is always logically possible that the next one will be white. A universal generalization like All ravens are black is not logically implied by any finite number of observations. The same is true of any sample-to-population inference such as opinion polling: it is possible that the sample is not representative of the population. That is very old news. It does not need constant reiteration. The question is, can we rely on inductive arguments with true premises to have true conclusions most of the time? If I have observed many black ravens and no ravens of any other color, does that give me high confidence, or indeed any reason at all to believe, that the next one will be black?

BLACK SWANS

All swans are white used to be a standard example of a well-known empirical generalization as much as all ravens are black. On January 5, 1697 a small party from Willem de Vlamingh’s exploratory expedition for the Dutch East India Company landed on the coast of New Holland (near present-day Perth, Western Australia). Over the next few days they explored the mouth of a substantial river and were surprised to find swimming in it a number of birds very similar to European swans, every single one of them black. They captured a few which unfortunately died before reaching Europe, but the news necessitated a change in one of the examples which had sufficed for logicians since time immemorial. Most embarrassing.

What conclusions should we draw from this contretemps? Surely

▪ Induction is fallible: no amount of observational data can make an empirical generalization certain (unless we have surveyed all the cases).

▪ A generalization beyond the spatial or temporal range of the data (extrapolation) is less certain than one within the range of the data (interpolation).

▪ These sorts of events do not happen often.

Black Swan, watercolor by Richard Browne for Lieut. Thomas Skottowe’s manuscript Select Specimens from Nature (1813). Reprinted with permission from Mitchell Library, State Library of New South Wales.

The leading argument as to why induction is justified (as a matter of logical probability) is one put forward by Donald Williams and later refined by David Stove. They explained how to reduce inductive inference—any inference from sample to population—to the proportional syllogism, using this argument:

▪ The vast majority of large samples resemble the population (in composition).

▪ This is a large sample.

▪ So, this sample resembles the population. (Equivalently, the population resembles the sample.)

This is the same kind of argument as the one considered above:

▪ 99.9 percent of men are mortal.

▪ Socrates is a man.

▪ So, Socrates is mortal.

The premises give good, though not conclusive, reason fo believing the conclusion, as a matter of logic.

The vast majority of large samples resemble the population is a necessary mathematical truth, so this argument, if there is anything in it, gives an explanation of why inductive inference is generally reliable. There is no need for any cement of the universe such as causality or natural law to glue the unobserved to the observed, or for contingent principles about the uniformity of nature.⁴

The mathematical nature of the premise the vast majority of large samples resemble the population possibly needs some clarification and illustration. Vast, large, and resemble are of course imprecise words. But in whatever (reasonable) way we choose to make them precise, we arrive at a fact that can be shown to be true simply by counting.

Suppose, for example, we take a population of 100 balls, black or white in an unknown proportion, and consider samples of size 50. Let us say a sample resembles the population if its white/black proportion is within 4 percent of the population proportion. Thus if the actual proportion of whites is 60 percent (i.e., 60 white balls and 40 black), then a sample of size 50, which should have 30 whites, is said to resemble the population if it has 28, 29, 30, 31, or 32 whites. (A proportion of 28/50, for example, is 56 percent, which is just within 4 percent of the true 60 percent). Now—remembering that the actual population proportion of whites is unknown—what can we say about the proportion of size 50 samples that resemble the population?

The answer is that it is at least 68 percent. It does differ depending on the population composition—if the 100 balls are all white, then all the samples are all-white and so match the population exactly. But in the worst case—when half are white and half are black—68 percent of the size 50 samples resemble the population (according to our criterion: having composition within 4 percent of the population.)

Perhaps 68 percent is not quite a vast majority. But we did have a quite restrictive definition of resembles, we were taking the worst case, and 50 is not a very large sample. As soon as we relax our requirements, the majority resembling the population increases.

HUME’S SKEPTICISM ABOUT INDUCTION

The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction, than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind.

It may, therefore, be a subject worthy of curiosity, to enquire what is the nature of that evidence, which assures us of any real existence and matter of fact, beyond the present testimony of our senses, or the records of our memory.…

All reasonings may be divided into two kinds, namely demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence. That there are no demonstrative arguments in the case, seems evident; since it implies no contradiction, that the course of nature may change, and that an object, seemingly like those which we have experienced, may be attended with different or contrary effects. May I not clearly and distinctly conceive, that a body, falling from the clouds, and which, in all other respects, resembles snow, has yet the taste of salt or feeling of fire? Is there any more intelligible proposition than to affirm, that all the trees will flourish in DECEMBER and JANUARY, and decay in MAY and JUNE? Now whatever is intelligible, and can be distinctly conceived, implies no contradiction, and can never be proved false by any