WILL THE FUTURE RESEMBLE THE PAST?
Inductive Logic and Scientific Method
THE SEVENTEENTH century was an age of turmoil and blood, but it was also a time of rising trade, growing cities, insurgent middle classes—and tremendous scientific advance.
The period opened with the extraordinary assertions of the priest Giordano Bruno, who said stars were suns and the universe was infinite; he was burned at the stake by the Roman Inquisition in 1600.1 By 1609, Johannes Kepler in Germany had determined that the planets traveled around the sun in elliptical orbits. Kepler escaped the violence of his time, but his mother was imprisoned for thirteen months on a charge of witchcraft, and though Kepler finally secured her release, she survived the ordeal by only two months. In 1638, Galileo published a book explaining the laws that govern the motion of falling bodies; Galileo had the book printed in Holland but was unable to publish in Italy, being already confined to house arrest in Florence for the rest of his life by the Roman Inquisition for arguing that the earth moves.2 Still later, in 1687, Isaac Newton, flourishing in relative safety in England, showed that Kepler’s laws of planetary motion and Galileo’s laws of falling bodies were special cases of a more general set of principles for the whole physical universe, assuming that a universal force—gravity—emanated from all matter to attract all other matter.3
These insights made people think of the universe as rational and scientifically comprehensible, but they also made people think about reasoning, especially when contrasting the discoveries of seventeenth-century science with the earlier hysteria and frenzy of the wars of religion. The great discoveries of seventeenth-century physics define what we now call the Scientific Revolution, but they were also part of a larger revolt: of Europe’s commercial middle classes against the doctrines and restrictions of the Middle Ages. In logic, the result of this revolt was the rise of induction and the study of scientific method.
Those involved in trade in European societies had become far more numerous, and the effect of this change was to transform nearly every aspect of modern intellectual life. The newly expanding commercial classes generated a vast new audience for literature—literature based in vernacular languages rather than Latin—and the growth of this audience encouraged new political theories, new sciences (like those of Galileo and Newton), new literary forms (such as the novel), and a new spirit of reformist agitation (which eventually gave rise to the eighteenth-century Enlightenment).
The upshot was a general attack on the received learning of the past, and in logic the consequence was a tendency to discount deduction as the logic of authority and to elevate induction as the logic of fresh experience and novel experiment. In a changing world, probable inductions from new experience became the crucial method of argument, displacing the older method of necessary deductions from an ancient philosopher. These newly rising middle classes were far more disposed than other groups to challenge tradition and assert their individualism, and the logic of induction and scientific method served this independence.
In addition, the involvement of these same groups in an expanding world of commercial innovation forced them to be ever more tolerant of dissident opinions—religious, scientific, political, and logical—because, without this tolerance, their commerce was impossible to sustain. Persecutions and fanatical intolerance turned out to be bad for business. All these forces made early modern writers more interested in the logical role of physical experience in the forming of our beliefs, and the result, continuing into the present, was a detailed investigation of empirical science and experimental method.
THE CHALLENGE OF THE NEW LITERATURE
The origins of these developments lay in the growth of Renaissance trade, which undermined medieval authority and encouraged new kinds of literature. During the Middle Ages, the audience for most new writings had been priestly or aristocratic; medieval books and manuscripts had been the creations of cloistered churchmen working in Latin, or they were the inventions of bards and troubadours performing for aristocratic elites. From the Renaissance onward, however, new works of literature were increasingly traded for cash in the marketplace, and they increasingly appealed to people who fell outside the traditional medieval orders of churchmen, warlords, and illiterate peasants; they appealed to a mixed crowd of artists, artisans, lawyers, doctors, tutors, shopkeepers, and small capitalists. These were the people most impatient with traditional authority and most likely to see themselves as self-made and self-reliant. They prized their independence, and they were also the people most likely, for reasons of financial gain, to become literate. They were the rising middle classes of the towns and cities, and their appetite for new works gave rise to new sorts of writing in fiction, religion, politics, and science. (The term “middle class” is often used to mean those who stand between an industrial working class on the one hand and the wealthiest social strata on the other. But we use the term here in a different way, to mean those who stand between an ancient feudal peasantry and an ancient hereditary nobility.)4
Small groups of such people had always existed in the urban centers of medieval Europe, but never in such numbers. They first began to multiply in the cities of Italy during the thirteenth century in the wake of the Crusades (from 1096 to 1291), which, in seeking to recapture the Holy Land for Christendom, had stimulated Italy’s Mediterranean sea trade. By the 1500s, however, these same ranks had also started to prosper along Europe’s Atlantic coast, and now they became even more numerous.
This transformation didn’t happen overnight. Earlier, in the 1400s, the lucrative trade in spices had induced European mariners to develop new methods of navigation, and these explorers’ success in crossing the world’s oceans had led, in turn, to a much larger and more ruthless trade in overseas gold, silver, farm products, and slaves. As more trade shifted away from the Mediterranean and traveled along the Atlantic sea routes, Europe’s wealth and power gravitated toward its Atlantic rim, and Italy went into decline. The lure of large, new profits from across the oceans drew the Atlantic states of Portugal, Spain, the Netherlands, France, and England into a deadly struggle to shut one another out and to monopolize the sea lanes. Eventually, these states would construct immense overseas colonial empires and impose European rule on distant corners of the earth. At the same time, however, their expanding trade profoundly changed Europe’s internal social structure.
Within Europe itself, this new, growing sea trade generated much larger commercial communities, where livelihoods depended less on hereditary privilege and more on the circulation of money. These same middle-class groups had already supplied much of the talent behind Renaissance art and literature (many writers and most sculptors and painters of the Renaissance had come from the middle classes, though they still depended heavily on aristocratic patronage). By the seventeenth century, however, because these same middle classes had become so numerous, they also supplied something more: an expansive new audience. Crowded in a great port like London, they gave Shakespeare a hearing for his plays, and plying their trades in the commercial cities of France, the Netherlands, Spain, and lower Germany, they paid cash for the works of Rabelais, Montaigne, Cervantes, Galileo, and Descartes. They were gradually becoming the new patrons for new kinds of literature.
In some ways, these new urban crowds of early modern Europe mirrored the ancient crowds of the Greek popular assemblies. The difference was that the new, European audiences were rarely located in a single mass meeting like the Athenian Assembly; they typically consisted instead of independent readers, sometimes separated by hundreds of miles but still tied together by the printing press. All the same, their expansion also depended on another crucial innovation: the triumph of vernacular languages over Latin.
THE TRIUMPH OF THE VERNACULAR AND THE GROWING SPIRIT OF EQUALITY
The rise of these new middle-class audiences required that writers move away from the Latin of the past and develop a new literature in the everyday languages of Italian, French, Spanish, English, German, and so on. This, too, would deeply affect logic because it would bring about a revolution in intellectual life by changing the rules as to who could participate.
While the Renaissance was still young, the great humanists Thomas More and Desiderius Erasmus had composed their major works in Latin and had addressed them to an intellectual elite. By the seventeenth century, however, many writers worked routinely in vernacular languages, and they appealed to a broader, middle-class readership. Though Descartes published his Meditations in Latin in 1641 to defend his international reputation, his earlier and brasher Discourse on Method (1637) had been penned in French and had mocked the intellectual authorities of the age. Galileo had written his witty and sarcastic Dialogue Concerning the Two Chief World Systems (1632) in Italian, and Cervantes had delivered his satirical Don Quixote (1605) in Spanish. Eventually, political doctrines would appear in vernacular languages too. Machiavelli had already written The Prince in Italian in 1513 for the private reading of a Medici ruler, and Thomas Hobbes chose English for his Leviathan, published in 1651. By the time John Locke brought out his Two Treatises of Government, dated 1690, English was the natural choice.
This transition from Latin to the languages of ordinary people would eventually make possible the creation of novels (the novel being a “new” form of storytelling that used vernacular languages and that aimed at a mass, middle-class readership to cover the costs of printing). In logic, the tendency toward the vernacular would give rise to the Port Royal Logic of Antoine Arnauld and Pierre Nicole (a popular and influential handbook published in French in 1662 that mixed logic and the theory of knowledge and contained many passages much influenced by Descartes).5 But no matter what the genre, vernacular writing was the essential first step in fashioning a new readership.
The first person to foresee this new role for vernacular writing had been the Protestant leader Martin Luther. Back in the 1520s, Luther had translated the Bible into German. He was the first widely circulated author to realize that though the printing press had opened the possibility of a new, mass readership, the books it produced would need to appear in a language the mass of readers could understand. His translation of the Bible was quickly imitated by other translators working in other languages. The circulation of these translated Bibles then became the model for the publication of other vernacular books, and the Bibles also represented a unique experiment in human history—an experiment that seventeenth century thinkers often looked back on with dread.
The Protestant Reformation had turned out to be something entirely new in the history of the world: never before had tens of thousands of people been invited to read the same text (the Bible) and to interpret this text by the lights of their own common sense. (The works of earlier vernacular writers like Dante and Chaucer had circulated in much smaller quantities and in hand-copied form.) And the consequence of the experiment was also new. The result, as shocking as it was unexpected, was that thousands of these same readers then proceeded to murder one another over which interpretation was correct.
The wars of religion were the first dismal outcome of this new attempt at mass enlightenment, and the fear that such violence might somehow return haunted the public discussion of ideas long afterward. As a result, the seventeenth century, following in the grim wake of the sixteenth, represented the first time that large numbers of thoughtful intellectuals tried to work out how this new form of public edification, by way of mass literacy, might be managed—without setting off massacres.
One effect was to make many seventeenth-century writers profoundly afraid of irrational enthusiasm. They emphasized Reason (capitalized) in a way that later generations sometimes found difficult to understand. Later, especially in the nineteenth century, proponents of European colonialism would argue that European peoples were somehow more rational and reasonable than the peoples they had subjugated overseas, and similar arguments had long been used to justify turning non-Europeans into slaves. Nevertheless, seventeenth-century thinkers were surprisingly egalitarian. Seventeenth-century philosophers typically argued that reason was the common property of all humankind. (The first line of Descartes’s Discourse, for example, insists that no human attribute is so equally distributed as “good sense.” It was also orthodox for the period for Locke to assert that his “law of nature,” justifying his principles of government and property and evident to reason, was just as clear to the Indian nations of North America as it was to the people of England.)6
In place of a theory of inherited superiority, the seventeenth-century philosophers tended to stress the universality of reason, and this emphasis served the middle classes in one of the most profound struggles of the period: their sustained and pervasive campaign to win greater powers from Europe’s hereditary aristocracies. Middle-class readers were especially sympathetic toward any argument that undermined hereditary privilege, and many of these readers, in consequence, ended up embracing the theory that all classes (including themselves) could reason equally well. The effect of this tendency on logic was to stress the significance of everyday reasoning (which was often inductive, experiential, and middle class) and to play down the importance of the reasonings of priests and monarchists (which typically consisted of necessary deductions from the opinions of ancient authors). This theme of the equality of reason was especially evident in the rise of modern political theory.
THE RISE OF MODERN POLITICAL THEORY
Until modern times, monarchy and hereditary aristocracy were the unquestioned assumptions of all known political theories in all parts of the world, except where trade had so inflated the middle classes that they could partly escape the control of kings and nobles. The special effect of trade on politics had already been conspicuous in classical Greece, where small states and an acceleration of seafaring had given the commercial classes the upper hand. This same effect had also appeared, to a lesser extent, in republican Rome, which, in its early days, was no larger than a city-state and which had allowed Greek political theories to circulate among the urban plebeians. (Democratic tendencies in Roman politics, founded on Greek models, had persisted among the plebeians until the late Republic. Eventually, the state’s military conquests so enlarged Rome’s dominions that the commercial classes were submerged in a much larger population of peasants, slaves, and unemployed paupers, who lived on free grain from the state. The idea of rule by majority vote in a single mass meeting became increasingly impractical, and Rome finally fell back on government by a succession of military strongmen—the emperors.)
In the rest of the world, however, trade was so limited and states were so large that the commercial classes could never break free. Monarchy and hereditary privilege were the unchallenged assumptions of classical China, and they were likewise the unchallenged assumptions of ancient Egypt, ancient Indian civilization along the Ganges, and ancient Mesopotamia. Individual kings might be overthrown, and particular groups of nobles might revolt, but the theory and literature of these regions always assumed kingship. The only real question was whether a particular king happened to be good or bad—or whether he enjoyed (in the Chinese phrase) the mandate of Heaven. Many ancient peoples also lived as isolated villagers or nomads, of course, but these ancient pastoral communities had no political literature at all. (The political theory of the ancient Indus civilization, which flourished in the third millennium B.C. in what is now mostly Pakistan, is still unknown to us, its language being still undecipherable.)
As a result, as far as our knowledge of urban civilization is concerned, the political history of other regions of the world was largely dynastic. The merchant classes of these other societies were so outnumbered by armies under the control of hereditary elites that the very idea of alternative political systems was unthinkable. And this same predilection for monarchy and hereditary privilege also returned to the Mediterranean region once Roman power had collapsed with the onset of the Middle Ages. An Islamic medieval writer like al-Farabi, for example, or a Christian one like Thomas Aquinas, might consider the democracy of ancient Athens after reading about it in a book, but he would then dismiss the idea of such government for his own time as obviously misguided.7
All this began to change once the Mediterranean trade of Italy had revived after the Crusades and once a similar but larger change had occurred along the Atlantic coast of Europe. Radical political theories expanded in many new directions. Machiavelli, Thomas More, Hobbes, and Locke all differed dramatically in their ideas of what was politically desirable and politically possible, but they were alike in coming out of the middle classes and in rejecting the medieval notion that some castes were born to rule and others born to obey. They remained acutely conscious of hereditary elites, but they saw the power of these elites as founded on tradition, not inherited superiority.8
THE RIGHT OF DISSENT AND THE RELIANCE ON INDUCTION
As the composition of European society, especially in the cities, became more commercial, the freedom to publish and defend new doctrines grew wider. Many middle-class readers came to believe in the new political idea that ordinary people could reason just as well as aristocrats. As a result, new books challenged traditional dogmas in many fields—in science and logic, no less than in politics. The wars of religion had already given a stark demonstration of where fanatical intolerance could lead, but after those wars the general trend was toward increasing tolerance for other points of view. This tolerance was most conspicuous in exactly those places where the middle classes were most ascendant: commercial centers like seventeenth-century Amsterdam and seventeenth-century London.
During this period, the cities of Holland became famous as refuges for dissident intellectuals, among them Descartes, Locke, and Baruch Spinoza. Even Galileo, who was already confined to house arrest in Florence for the rest of his life, nevertheless sent his Dialogues Concerning Two New Sciences to Holland for publication by a Dutch printer.
London, though politically less stable than many Dutch cities of the time, was still increasingly hospitable to various forms of civil dissent. Even in 1644, in the midst of the English Civil War, John Milton could publish his famous “Areopagitica,” an essay that attacked book burning and defended freedom of expression. (“Who kills a man, kills a reasonable creature, God’s image; but he who destroys a good book kills reason itself.” And, “Give me the liberty to know, to utter, and to argue freely according to conscience, above all liberties.”)9 Somewhat later, in 1689, Locke published his first Letter Concerning Toleration, which argued against religious persecution (though it made strange exceptions in the cases of Catholics and atheists; Locke excepted atheists on the supposed grounds that they couldn’t be trusted to keep promises or oaths, as they had no fear of divine retribution, and he excepted Catholics on the theory that they served a foreign “prince,” the pope).
Seventeenth-century tolerance was, of course, much narrower than tolerance in many places today, and all sorts of draconian restrictions appeared (and continue to appear) in times of unrest, disorder, paranoia, and rebellion. But tolerance in the seventeenth century was still far greater than in the medieval past, and though it emerged first as a right of religious dissent, it soon evolved into additional rights of political and scientific dissent. Despite various setbacks, the doctrine of tolerance—religious, political, and scientific—continued to spread, and it culminated much later in the work of another middle-class author, John Stuart Mill, who published On Liberty in 1859. (Mill wrote, “The beliefs which we have most warrant for have no safeguard to rest on but a standing invitation to the whole world to prove them unfounded.”)10 On the whole, the toleration of dissent and the rise of the commercial middle classes went hand in hand, and for reasons that are not hard to see.
Commerce brought the middle classes into daily contact with new ideas and new people, often from foreign lands. Just as important, competition rewarded those who were curious. The money economy forced its participants to observe new situations that came about because of changing markets, and it made them collect new information so as to predict what would sell and what wouldn’t. These marketplace effects tended to make the middle classes chafe at restrictions on their freedom of enquiry, and they also encouraged the middle classes to become increasingly analytical and increasingly disputatious.
In a competitive environment, to succeed, they often had to think for themselves, and this thinking made it necessary to consider the pros and cons of competing opinions. Mill would later remark on this need to consider pros and cons, and he would contrast it with the sort of thinking that goes on in the deductive proof of a mathematical theorem:
The peculiarity of the evidence of mathematical truths is that all the argument is one side. . . . [But] even in natural philosophy [meaning science], there is always some other explanation possible of the same facts; some geocentric theory instead of heliocentric, some phlogiston instead of oxygen. . . . When we turn to subjects infinitely more complicated, to morals, religion, politics, social relations, and the business of life, three-fourths of the arguments for every disputed opinion consist in dispelling the appearances which favor some opinion different from it. . . . He who knows only his own side of the case knows little of that.
Mill stressed the importance of grasping opposing arguments, not simply one’s own. He added,
In the case of any person whose judgment is really deserving of confidence, how has it become so? Because he has kept his mind open to criticism of his opinions and conduct. Because it has been his practice to listen to all that could be said against him; to profit by as much of it as was just, and to expound to himself, and upon occasion to others, the fallacy of the fallacious. . . . No wise man ever acquired his wisdom in any mode but this.11
In making these remarks, Mill is actually commenting on what logicians call induction. Mill took mathematical theorems to be deductive, but the “business of life” he invoked is typically inductive. And the need to keep listening comes from the fact that inductive arguments never supply conclusive proof; at best, they offer a high probability (given the available evidence).
The possibility of alternative explanations was a daily occurrence in middle-class life, and the successful entrepreneur was usually the one who, in spite of all, could still make a series of probable predictions inductively, on the basis of personal observation and experience. The successful investor had to predict the market, and the middle-class artisan needed to anticipate what he could sell. As a result, the middle classes eventually came to oppose many restrictions on their ability to investigate and analyze, except when plainly necessary to keep the peace. (Admittedly, Mill makes these points some two centuries after the formative period we now mean to discuss, but his comments concern the nature of induction itself—and he is right.)
In addition, all other considerations aside, religious and ideological persecutions turned out to be bad for business. The trouble with persecutions, as far as investment was concerned, was that they increased the chances that your commercial partners would be arrested arbitrarily and made to disappear. In the modern world, we sometimes think of the right of dissent as a fundamentally “Western” notion, as if it were merely an arbitrary cultural preference like language or dress, but this is a mistake. Instead, the idea of the right of dissent, if not already latent in all people who wish to know, is an especially commercial idea because it tends to expand with economic competition and with the growth of the middle classes who engage in it. Business competition forces people of differing opinions to interact, and it rewards those who can still trade, invest, and make deals in a dissonant environment. In the seventeenth century, the right of dissent first emerged in Europe’s Atlantic states because these were the places where ocean-going commerce first accelerated. Nevertheless, as economic competition has continued to swell the ranks of the middle classes in developing countries, so the right of dissent has also expanded there.12
INDUCTION AS THE NEW RATIONALITY
Though the seventeenth century prized rationality, the rationality in question wasn’t the rationality of logically necessary deductions from a received set of timeless truths. It had nothing to do with the deductions of priests or monarchists, who might seek to establish the divine right of kings or the doctrine of papal supremacy. Instead, in a world of increasing commercial innovation, the most prized of all rationality consisted in drawing probable inferences from new data—data that concerned evolving and changing circumstances. It was the rationality of a different social group, the middle classes, and this meant it was the rationality of induction.
Induction, by definition, aims at proving a conclusion as a matter of probability or likeliness, not logical necessity. And most inductive arguments rely on premises that describe things we have already observed so as to draw conclusions about things that are still unobserved.13 The premises describe things we already know, but the conclusion makes an assertion about something new. The seventeenth century was very much devoted to the new.
Take a simple case: We all know that the sun will rise tomorrow, but how do we know it? Do we know daylight will reappear every twenty-four hours because it has always done so in the past? The answer might not be as simple as it seems. Our knowledge of the sun’s continuing behavior is surely based on an inference, but what is the form of the inference?
If the sun has risen every day we can remember, does it follow as a logical necessity that the sun will rise tomorrow? Even conceding past experience, isn’t there still some sense in which it is possible that the sun will simply fail to rise and that the laws of nature will change radically? Possible, perhaps, but not likely.
More precisely, given past experience, we can say the sun will probably rise and that all the laws discovered by Galileo, Kepler, and Newton will probably continue to operate, but not that the sun must rise and that the laws must continue to operate—at least not in the same way that, if all humans beings are mortal and Socrates is a human being, Socrates must be mortal. The sun’s behavior (or rather, the earth’s rotation) is perhaps physically inevitable but not logically inevitable. No conclusion about a new case can follow as a logical necessity from a mere assertion about an old one. In our inference about Socrates, the relation between premises and conclusion is one of necessity, but when it comes to tomorrow’s sunrise, we seem to be dealing with something different: a very high probability. Moreover, this same probability attaches to any empirical law in any physical science because all such laws apply as much to new situations as to old ones; the laws are assumed to have operated yesterday, but they are also expected to operate tomorrow.
From Aristotle to the present, the traditional way of marking this distinction is to say that our inference about Socrates is a case of deduction and that our example of the sunrise is induction. Deduction, if valid, establishes a conclusive tie between premises and conclusion, but induction establishes a merely probable tie. And it appears that no argument that goes exclusively from past experience to a future prediction can be deductively valid. After all, it is one thing to talk about the past, quite another to talk about the future. Our premises concern the past, but the future is something new.
The ancients had long distinguished between deduction and induction, but what they didn’t do was investigate induction, and this is where seventeenth-century thinkers struck out on a new path. Deduction had already become equated with authority, and so the attack on authority became an attack on the utility of deduction itself and a plea for the elevation of induction as a rational alternative. This was the plea to which middle-class audiences were most receptive. All the same, deduction had become associated with authority only by degrees, and the cause of this association had been Aristotle’s immense influence on scholars of the Middle Ages across a thousand years. If we now add a few words about the origins of this influence, it may help to throw light on why seventeenth-century thinkers finally reacted against deduction so vehemently.
ARISTOTLE’S INFLUENCE ON THE MEDIEVALS
Aristotle’s ideas had dominated medieval thought because so many of his ideas had been insightful, and this was especially so in logic. After the days of Aristotle and Chrysippus, logic as a discipline tended to stagnate. To be sure, the logicians who followed were often shrewd. Aristotle’s student Theophrastus perfected the theory of categorical syllogisms and added a theory of hypothetical syllogisms; in India, an independent tradition mixing rhetoric and logic developed in service to the metaphysical schools. Nevertheless, the driving force behind logical innovation had almost always been public debate, and when the debate languished, so did logic. Logic went into decline in the absence of public assemblies.
The decline was gradual. While Aristotle and Chrysippus still lived, the Athenian Assembly still met, and though already stripped of military power by Athens’s overlords, the Assembly still debated a wide range of local issues. Likewise, in the early days of Roman rule, many Romans studied Greek techniques for their application to Roman politics. (Athenian logic and rhetoric were particularly useful in the class conflict between Rome’s patricians and plebeians—the hereditary aristocrats and the common people. The patricians controlled the Senate, where policy often depended on private counsels and secret negotiation, but the plebeians met in a vast assembly in the Roman forum, and many Romans wanted to expand the powers of this assembly by modeling it on the assembly at Athens. Even Romans who resisted this tendency still saw the need to address large crowds in the Athenian manner, and consequently the most famous of these orators, Cicero, translated much Greek logic and rhetoric into Latin. Nevertheless, Roman public assemblies were always more restricted in their prerogatives than the Greek ones, and when Rome’s emperors finally came to power, logic and rhetoric retreated into a bookish world of quiet scholarship.)14
With the onset of the Middle Ages, public debate virtually died out; politics fell into the hands of warlords, and logic, when studied at all, was studied only as part of a general analysis of Greek philosophy. Among the original masters of this medieval endeavor were Arab scholars who first served as physicians to powerful caliphs and whose initial aim was to advance medicine. Various schools developed, especially under the influence of al-Farabi, Abu ibn Sina (Avicenna), and Ibn Rushd (Averroës), but the chief emphasis was on broader questions of ethics, metaphysics, and theology. Early Arab logic, it turns out, was inaugurated by Syrian Christians, but it was quickly appreciated by scholars working in the tradition of the Koran. Arab scholars took special interest in Aristotle’s treatment of inferences about possibility and necessity—the field now called modal logic15—and they explored many related questions of epistemology (meaning the theory of knowledge).16 All the same, Arab logicians of the Middle Ages usually saw themselves as reconstructing and perfecting Greek logic rather than building something fundamentally new, and when medieval Christians in Western Europe began to imitate this Arab example, they adopted a similar outlook. In consequence, medieval logic, like Roman logic, was essentially an elaboration and refinement of Greek ideas. Only with the coming of the early modern period did the influence of extensive public debate reassert itself, and until that time, Aristotle’s authority loomed large.
The medievals had revered Aristotle because they found so much of his work enlightening. Aristotle had not only elaborated a theory of deduction; he had also offered a great many general principles, philosophical and scientific, and from these principles a great many consequences could be deduced. Aristotle himself was by no means wedded to deducing things; he was a careful, empirical observer whose reasonings mixed both deduction and induction. Aristotle in the hands of the medievals, however, was something else.
If you assumed, as many medievals did assume, that Aristotle was usually right, then you usually found yourself either recommending his doctrines or deducing further consequences from them. As a result, most of your inferences were deductive. Moreover, many medievals did indeed assume that Aristotle was usually right. (One sees this assumption, for example, in the tendency of a thinker like Thomas Aquinas to call Aristotle simply “the Philosopher.”)17 Reflecting on the intellectual accomplishments of their own time, especially in the Christian West, a place of grinding poverty and recurring chaos, many medieval readers found Aristotle’s insights truly astonishing, and medieval readers typically had a similar attitude toward all ancient writers. The novelist and Oxford scholar C. S. Lewis describes this reverential attitude of medieval intellectuals toward ancient literature:
They are indeed very credulous of books. They find it hard to believe that anything an old auctour has said is simply untrue. And they inherit a very heterogeneous collection of books: Judaic, Pagan, Platonic, Aristotelian, Stoical, Primitive Christian, Patristic. Or (by a different classification) chronicles, epic poems, sermons, visions, philosophical treatises, satires. Obviously their auctours will contradict one another. They will seem to do so even more often if you ignore the distinction of kinds and take your science impartially from the poets and philosophers; and this the medievals very often did in fact though they would have been well able to point out, in theory, that poets feigned. If, under these conditions, one has also a great reluctance flatly to disbelieve anything in a book, then here there is obviously both an urgent need and a glorious opportunity for sorting out and tidying up. All the apparent contradictions must be harmonised.18
The medievals interpreted, systematized, and harmonized, but they also implicitly believed, and this attitude carried over into European universities, even down to the seventeenth century when university education was still dominated by medievalism. In addition, however, we must also remember the social role of medieval scholars.
The first thing to recall when we now look back at medieval scholars, especially from Europe, is that most of them were churchmen. This meant that, whenever they considered a new idea, they first had to ask (if only for their own safety) whether this new idea was consistent with the church’s articles of faith. They had to determine whether the idea was consistent with authority, and most questions of consistency are answered deductively. That is, to determine whether A and B are logically consistent, we usually deduce consequences from A or B until we reach a contradiction.
For example, in determining whether the belief that the universe is less than ten thousand years old is consistent with the assertions of modern astronomers, we must ask ourselves what each of these beliefs or assertions logically implies and then look to see if the result is a contradiction. (If what modern astronomers say is true, then light has been traveling from distant stars for millions of years; yet, if so, the universe can’t be only ten thousand years old.) This is how we show that A and B are incompatible. But, in that case, deduction is the principal method, and the only inductive form that typically appears is argument by analogy. (An analogy compares one case to another, similar one; thus, to determine how a general principle like A or B might apply to a particular case, we might also look at how it applies to other, similar cases.) In consequence, medieval argument was typically deductive or analogical—a pattern of thought that we still see today in legal argument.19
None of this implies, of course, that medieval people didn’t reason inductively in practice; quite the reverse: daily life requires countless inductive inferences, and this has been true in all historical periods. (No one masters the art of cooking, for example, without a good deal of inductive experiment.) Nevertheless, what the medievals didn’t do was extensively study induction, and this was because the arguments on which their crucial controversies depended were usually deductive, being questions of consistency with the great authorities of the past. The result, then, was a general tendency toward deduction in the medieval tradition, and it was just this tendency against which the new authors of the seventeenth century conducted their stubborn campaign.20
Remarking sarcastically in 1690 on the habit of thinking that all reasoning must be deductive, Locke writes, “God has not been so sparing to men to make them barely two-legged creatures, and left it to Aristotle to make them rational.”21 Locke thinks much of rationality has nothing to do with Aristotelian deduction. Beyond this, however, religious warfare had reinforced the dangers of irrational enthusiasm, and this, too, encouraged the study of induction and scientific method. With the notable exception of Mill (and perhaps also the American pragmatist C. S. Peirce; Mill and Peirce both came of age in the nineteenth century), nearly all the great names of induction and the philosophy of science wrote in the wake of the wars of religion, and they often had religious controversy fresh in their minds—such writers as Locke, Francis Bacon, Galileo, and David Hume. To be sure, scholarly studies of induction and scientific method have continued from the nineteenth century to the present, but it was writers of the seventeenth and eighteenth centuries who first turned the analysis of induction into an ideological cause.22 In effect, all these writers asked how we know what we know, and they thought much of our reasoning was inductive. As a result, their recurring complaint was that medieval authors had paid scant attention to induction, and their fervent effort was to explore it.
(So far as the philosophy of science is concerned, we can also distinguish a further period of intense interest much later in history, just after the First World War and culminating in the “Vienna Circle” of 1920s Austria, but this, too, was in many ways a reaction to fanaticism—the chauvinistic fanaticism that preceded the horrors of 1914 to 1918. In English and American universities, this interest, further provoked by the rise of Nazism in Germany, became the heart of so-called analytic philosophy, which has always stressed logic and scientific method.)
Even so, these historical points still leave open the more basic question of what exactly induction is and whether or not it really is different from deduction, as many seventeenth-century writers assumed. Like previous logicians and most logicians today, seventeenth-century philosophers took deduction and induction to be different. (Locke, for example, divided all arguments into “demonstrative,” meaning deductive, and “probable,” meaning inductive.)23 All the same, the acute observations of Hume, a Scottish philosopher writing in the eighteenth century, led a number of later thinkers to wonder whether the two methods of induction and deduction were truly different after all.
The answer isn’t so simple (though we do indeed find ourselves more inclined to side with the seventeenth-century philosophers and less convinced by the later thinkers). In trying to understand induction and scientific method, several later writers, including Mill and the twentieth-century philosopher Bertrand Russell, came to the view that all inductive arguments actually assume an additional, unstated premise—what they called a “principle of induction” or a “principle of the uniformity of nature”—the addition of which causes inductive arguments to become deductive. They also supposed that, without this further premise, no inductive argument would be rational in the first place. All such inferences, they said, assume that the old cases we have observed have something in common with the new cases about which we make predictions. Thus these writers found themselves asking, What makes induction reasonable from the start?
THE RATIONAL FOUNDATIONS OF INDUCTION
In trying to answer this question, much depends on how we construe an inductive argument’s form. Schematically, we might represent an argument from past experience to a future prediction like this:
The sun rose Monday.
The sun rose again Tuesday.
The sun rose again Wednesday.
The sun rose again Thursday . . .
Therefore, the sun will probably rise tomorrow.
Given enough examples of past experience, this sort of argument certainly seems rational, but where is the assumption that the old cases we have observed have something in common with the new cases about which we make predictions?
Why not suppose that all inductive arguments really contain a further premise that expresses this assumption and that the premise is supplied silently but automatically by the mind? Why not suppose that inductive arguments actually look like this:
The sun rose Monday.
The sun rose again Tuesday.
The sun rose again Wednesday.
The sun rose again Thursday . . .
[And the more often any event has been observed without exception in the past, the greater the probability that, in similar circumstances, it will occur in the future.]
Therefore, the sun will probably rise tomorrow.
The premise in brackets might be conceived as the one supplied silently but automatically by the mind, and it connects the sunrises of the past with the probability of a sunrise tomorrow.
Given the premise in brackets, it might now seem that inductive arguments are rational in the first place for the very reason that they are deductively valid—so long as the missing premise is added. (Of course, the conclusion in our example still doesn’t tell us that a sunrise is logically necessary; it characterizes the sunrise as merely “probable.” But this characterization might itself be the thing that is logically necessary. The characterization itself might follow deductively from the premises—given the additional, silent assumption and some further statements to the effect that Monday, Tuesday, Wednesday, and so on, are each events in the past and that tomorrow is a similar circumstance that is still in the future.) On this view, then, inductive arguments are really just a species of deductive ones—deductions in disguise—and the distinguishing feature of this species is that all such arguments assume an additional, tacit principle that allows a leap from statements about the past to a probable statement about the future.
This tacit principle is the one that later writers conceived as the principle of induction or the principle of the uniformity of nature, and the principle can also be phrased so as to allow any inductive inference that goes from cases we have already observed to cases we haven’t. (The idea that some such principle must be at work in inductive reasoning emerged with Hume; Hume asserted that all our conclusions about the future “proceed upon the supposition that the future will be conformable to the past.” Mill, Russell, and others then offered different versions of the principle, but they agreed that the principle must be a tacit premise in all our inductive reasonings, thereby making inductive arguments actually deductive.)24 Nevertheless, in all these musings, what we are actually trying to clarify is how our minds make sense of experience.
To see better how we make sense of experience, try a little thought experiment:
Suppose you met a man who believed that the future would never resemble the past, not in the slightest. From this moment forward (according to this man) every new instant will be entirely different from the last. Now the strangeness of this belief aside, how would you go about proving to this person that he was mistaken? How would you convince him that the past is a reasonable guide to the future? How would you do this, that is, without already taking for granted something he denies? What evidence would you invoke—past experience?
If you say that the past is prologue to the future, he denies it. If you say that, in the past, the past has always been prologue to the future and therefore it must be so in the future, he accuses you of missing the point; you are still supposing that what comes before is somehow relevant to what comes after. This is exactly what he denies. If you say that the past has to be relied on anyway, because it supplies all the evidence we have, he accuses you of failing in your burden of proof. From his point of view, you are still preaching to the converted and assuming that relying on the past will somehow put us in a better position than not relying on it. You are still assuming that the future will be similar to it. And this, again, is what he disputes.
Hume stresses the difficulty of such attempts at persuasion in his Enquiry Concerning Human Understanding, published in 1748: “If there be any suspicion that the course of nature may change and that the past may be no rule to the future, all experience becomes useless and can give rise to no inference or conclusion.”25 Yet, if you yourself do indeed differ from the strange man we have just imagined (and you’d better differ, since your very survival depends on reasoning from experience), then what exactly is the difference? Is there some particular proposition that you accept and he doesn’t? Alternatively, is your idea of what constitutes reason and logic different from his? If so, how is it different?
These are exactly the questions the principle of induction purports to answer. It purports to tell us what it is that you accept and he doesn’t. The principle seems to do this very well but for one difficulty: the principle is glaringly false. In fact, no rational person could ever really rely on the principle as we have just conceived it.
Consider: is it really true that the more “any” event is repeated in the past, the greater the probability that it will be repeated in the future? For example, if one were now to take, say, a tennis ball and bounce it repeatedly against a wall, would it follow that each time one made the ball rebound from the wall the probability of a further rebound would increase? The principle in brackets, taken literally, says yes, and according to the principle, this effect of increasing probability would continue even if one had already decided, in advance, not to repeat the bouncing of the ball more than ten times. The same error occurs whenever a person who travels abroad for the first time assumes that everyone in the world must speak his own language simply because everyone he has met in the past spoke his own language. It also occurs when a succession of cloudless days induces a person to think that the next day must be cloudless too.
Plainly, our judgments about what is probable and what isn’t are far more complicated than the little schema we suggested earlier would indicate, and it seems clear that the principle we have added in brackets is literally untrue. More generally, though repetition increases the probability of some events, it certainly doesn’t increase the probability of all events. Determining which repetitions will persist and which won’t depends on the totality of the relevant evidence before us, and this depends, in turn, on a great deal of background knowledge that we bring to any such question.
All the same, we might try tinkering with the principle by adding a qualifying phrase: “everything else being equal.” Everything else being equal, past repetitions increase the probability of future repetitions, or so we might suppose. Now we might say the principle is correct. Still, this can’t be how a rational mind works.
THE APPARENT IRREDUCIBILITY OF INDUCTION
Here’s why: The trouble is that our new, revised argument isn’t deductively valid in the first place unless we also make a similar adjustment to its conclusion. The principle in brackets, the tacit one, now holds only on the condition, “everything else being equal.” Yet, in that case, our conclusion will also hold only on condition (“everything else being equal”). So our new conclusion will have to read, “Everything else being equal, the sun will probably rise tomorrow.” Yet this surely is not what reasonable people conclude about sunrises. On the contrary, on normal occasions, we don’t merely suppose the sun will probably rise everything else being equal; we suppose it will probably rise even though we know many other things won’t be equal. (The earth tomorrow will be substantially different from the earth today, yet we still infer that a sunrise will occur.) The tacit premise is now true, but the conclusion of the argument is far too weak.
In all these speculations about how our minds actually work, we seem to be involved, perhaps, in a fundamental mistake: we have begun to expect things from our analysis of induction that, perhaps, we shouldn’t expect at all. Specifically, we have tried to treat the two methods of deduction and induction as basically alike in that induction is simply a disguised form of deduction. The only difference is that induction assumes a further, tacit premise, a premise that turns an inductive argument into a deductive one. Yet we ought to know from the start that, if described correctly, the two methods of induction and deduction should give different results.
We ought to know that repetitions only sometimes show an inductive conclusion to be probable. Not everything repeated in the past is likely to be repeated in the future. (This is what we see in the case of the tennis ball.) On the other hand, we should also know that, when it comes to valid deduction, the premises always guarantee the conclusion. Once the premises are established, the conclusion is proved true invariably; this is part of proving the conclusion necessarily. (More exactly, logical necessity is a matter of form; arguments are deductively valid only because they embody certain patterns or schemas. But the whole point of talking about forms, patterns, or schemas is to describe all cases of a certain type; the very idea of logical necessity carries with it some sense of universality, even if the universality in question can’t always be defined with precision.) And the key point is that “sometimes” is different from “always.” A conclusion that is only sometimes reasonable can never be always reasonable. Consequently, any attempt to reduce the one sort of argument to the other—to reduce induction to deduction—would seem to be mistaken; every such attempt will replace an inference that is only sometimes reasonable with an inference that is always so. And in that event, we will have lost sight of what being reasonable truly is.
(More generally, no assumption about regularities in nature can reduce inductive arguments to deductively valid ones, it would seem, because the most any such assumption can tell us, if stated properly, is that some regularities will be repeated. But “some” is indefinite, whereas the particular laws of nature are specific. And the specific never follows deductively from the indefinite.)
It seems, then, that the later writers, Mill and Russell, were mistaken, even though Hume’s initial insight was right. Hume’s initial insight (to recall it once more) was that our future predictions proceed upon the supposition that the future will resemble the past. If the supposition were false, induction wouldn’t be reasonable in the first place. And indeed, in Hume’s defense, what his supposition seems to do is explain why we engage in inductive reasoning from the start. We reason inductively because we believe there are underlying patterns in the world of which our experience is a sample. Our inductive inferences involve probabilities just as reasoning from a sample does. The more often we find a pattern repeated in a random sample, the most probable we think that the pattern is also characteristic of the whole. Just so, the more we find something repeated in our experience, the more we think it likely that, everything else being equal, it will be repeated in the future.26
On the other hand, Mill and Russell took Hume’s idea a step further, and this, we suspect, is where Mill and Russell went wrong. They insisted that Hume’s supposition had to be a premise. We suspect this further step to be erroneous. A supposition is an assumption, but not all assumptions are premises; instead, some are corollaries. A supposition isn’t always something that supports a conclusion; it is sometimes a thing supported by a conclusion.
For example, in arguing that the sun will rise tomorrow because it has always done so in the past, we not only assume that the future will resemble the past; we also assume there won’t be a cosmic collision that alters the earth’s rotation or a cataclysm at the sun’s core that extinguishes its brilliance. (If these further propositions were false, then our conclusion about tomorrow’s sunrise couldn’t be true in the first place.) But these “assumptions” aren’t premises. Instead, they follow from our conclusion as further consequences; they are things our conclusion entails.
What Hume has done, in other words, is to identify the further consequence of all inductive inferences—that the unobserved will indeed have something in common with the observed. He has singled out a universal corollary of induction. He has identified what all inductive conclusions entail, and so they all “suppose” it. Nevertheless, this doesn’t make the assumption he invokes a premise. (By analogy, the later theorems of Euclid are consequences of the axioms, and they are usually proved by way of the earlier theorems; accordingly, if the later theorems were false, then something in the earlier theorems—or something in the axioms—would also have to be false. As a result, the body of earlier theorems “assumes” that the later theorems could be true. But this doesn’t make any later theorem a premise for an earlier one. In the order of argument, Hume’s supposition is a consequence of induction, not a premise of it, and what distinguishes the strange man of our imagination is that he chooses to preclude this consequence in advance. The strange man is like a student of geometry who insists from the start that he knows all Euclid’s later theorems to be necessarily false and who therefore concludes that all arguments from the axioms must be rationally unpersuasive.)
It all sounds rather tricky and complicated, but we seem to come back once more to something fairly straightforward: reasonableness, when applied to arguments, comes in two varieties—inductive and deductive—and neither seems to be reducible to the other. Apparently, they are apples and oranges. Neither is a disguised form of the other.27 But then what, if anything, must empirical science assume?
THE ASSUMPTIONS OF EMPIRICAL SCIENCE
Despite the difference between induction and deduction, the discoveries of Galileo, Kepler, and Newton still involved the same mental leap described by Hume: the leap from past to future. This is because the whole point of their work was to expound general laws that applied as much to the future as to the past. The evidence for their laws consisted in past observations, and the purpose of the laws was to describe mechanisms that, if real, would cause the phenomena they had already seen. Yet the laws also applied to the future because they resulted in testable predictions. In publishing their results, they were inviting other people to think for themselves and to arrive at similar observations, and they were also making it possible for future scientists to test their laws by devising further experiments that would challenge the laws in novel ways. In that case, however, the connection between past and future was essential. Only if the past really is a guide to the future will a scientific theory have testable consequences in the first place, and this is so whether the subject is physics, chemistry, astronomy, or biology. The effect of such theories is always to connect things observed to things still unobserved. Hume insisted that this same leap—from the observed to the unobserved—is also involved in any conclusions we draw about cause and effect.
In seeking to discover the cause of a particular event, we normally assume that no such event can be uncaused. We suppose all events have causes, and we suppose that causes are related to their effects by general principles. In addition, we suppose that effects never precede their causes (unless we are somehow talking fancifully about time travel). These are the assumptions that make physical science possible, and we normally suppose them to apply as much to the future as to the past. Even so, we can still ask the same question posed by that strange, hypothetical man we conjured up a moment ago: how do we know these things? How do we know that tomorrow won’t be radically different, even in terms of cause and effect?
How these causal assumptions are known to be true at all is a deep and famous problem of metaphysics. Can their truth be proved by physical observation, or does the intelligibility of physical observation already assume their truth? If we didn’t, in fact, presuppose that events have causes that conform to these rules, how would we go about proving it?
(The German philosopher Immanuel Kant, writing in the eighteenth century, replied that such assumptions are, in fact, supplied automatically by the mind and that, without them, no intelligible experience of physical objects would be possible. Thus, according to Kant, no one can prove that events have such causes. Instead, we simply assume it.28 Hume, by contrast, took a different approach. Hume argued that, despite appearances, causation is nothing more than the constant conjunction of two events—A and B. To say A causes B is only to say that B always follows A.29 Of course, we usually suppose that cause and effect is more than a merely perpetual coincidence, but, according to Hume, this is a mistake. In essence, then, Hume’s theory seeks to reduce cause and effect to the observable alone, in the tradition of British empiricism, whereas Kant’s theory insists on additional assumptions supplied by the mind, in the tradition of Continental rationalism. Mill, as it turns out, took yet another view. He regarded the principle of the uniformity of nature as an empirical proposition that is freshly confirmed every time a scientist discovers a new physical law.)30
The crucial point for the logician is more basic; to the logician, the crucial point is that the strange man in question—the one who challenges all connection between past and future—might reason deductively as well as anyone else. He might see the validity of modus ponens perfectly, and he might analyze categorical syllogisms with all the ease of Aristotle. What he doesn’t do, however, is draw inferences from the observed to the unobserved. He differs when he tries to reason inductively, meaning when he tries to draw conclusions about anything new. (It would seem to follow, then, that deduction and induction must be different things.)
Another way to describe the strange man is to say that he refuses to see his experience as a representative sample of a larger reality. The result is that he refuses to regard predictions about the future as in any way probable. We, however, differ from this strange man, meaning we do see our experience as representative (at least if we are sane). We believe the observed and unobserved have something in common, a common nature, and our science seeks to discover this nature by looking at only part of reality—the part that experience discloses to us.
Of course, in making these last points, we don’t mean that anyone normally thinks about parts of reality or the whole of it when reasoning about sunrises. We don’t mean that anyone normally thinks of reasoning from experience as a form of reasoning from a sample. On the contrary, as Hume suggested, whenever we reason from past to future, we probably operate on a kind of instinct. (Hume thought deeply about these matters, and his word for the instinct was “custom”).31 Instead, what we mean is that the instinct, perhaps a product of our evolutionary struggle for survival, does have a rational justification, and the justification is the same that underlies sampling. If a sample is selected randomly and contains successive repetitions, the probability that the repetitions are themselves only random accidents is less the longer the repetition is. A purely random event is far less likely to happen ten times in a row than twice in a row. Thus, the more we see something repeated, the more probable, everything else being equal, that the repetition exhibits something nonrandom—like a causal law or a principle of nature.32 (Moreover, without some such justification—some principle in virtue of which the instinct actually is rational—the instinct probably wouldn’t exist in the first place, at least not on Darwinian grounds, because otherwise it would have given no advantage to our ancestors in their struggle for survival. The utility of the instinct depends precisely on the fact that it does indeed result in probable inferences. Those who say induction is rational only because it is instinctive have the matter, in our view, backward. Induction isn’t rational because it is instinctive; induction is instinctive because it is rational.)
All the same, the justification of inductive reasoning we have just sketched is limited in a fundamental way: we must still suppose (not as a premise but as a corollary) that whatever nonrandom feature probably accounts for repetitions in the past will also give rise to repetitions in the future. We must still suppose a common nature that connects the observed to the unobserved. But of course there is nothing in deductive logic to tell us that this assumption is correct. There is nothing to tell us that the seen must be anything like the unseen. (Asking why it is rational to assume that the seen should have anything in common with the unseen is like asking why it is ever rational to rely on modus ponens; at some point, there can be no further answer.) This is just where that strange “irrational” man we conjured up earlier suddenly veers down a different path. For him, tomorrow is a different day.
The seventeenth century was a watershed in the history of logic because it gave induction and scientific method the attention they deserved. And the insight of the century’s most forward-looking philosophers was to see in this approach the basis of a new rationality.
The wars of religion had made them wary of enthusiasms, and the growth of trade had broadened their world. As the money economy expanded, they, and the middle-class audiences who surrounded them, came to rely less on deductions from ancient authorities and more on fresh inferences from novel experiment. Experience became their touchstone, and as new sciences and new literary forms emerged, so the new logic of induction emerged, too.
What set the middles classes of the seventeenth century apart—classes that were often brash, assertive, and insurgent—was their willingness to follow this path and to rely above all on their own experience, their own intellect, and their own ability to reason from the observed to the unobserved. Over time, the effect of this transformation would be to give the world a startling new sample of larger things to come.