SCIENTIFIC METHOD

SCIENTIFIC METHOD. Methods for investigating the natural world were transformed in the early modern era, leading to a variety of approaches that emerged from diverse philosophical orientations. To call these diverse methodologies "scientific" is a convenience but one that entails anachronistic usage. The Latin word scientia, meaning, broadly, 'knowledge', has none of the methodological implications of the modern term science. Early modern investigators called themselves philosophers, natural philosophers, physicians, and experimental or mathematical philosophers rather than scientists. Methodological issues often were the focus of lively discussions and bitter disputes. By the end of the era, approaches to investigating the natural world had undergone profound changes that historians traditionally have called the "scientific revolution."

ARISTOTELIANISM

The predominant methodology inherited by early modern learned culture was Aristotelian. The writings of Aristotle became the basis of the medieval university curriculum and remained so well into the seventeenth century. For Aristotle, knowledge (epistēmē in Greek, scientia in Latin) was universal and necessary. The goal of natural philosophy was to grasp the principles and natures of natural substances and to understand their causes. The method was a logical one based on syllogistic reasoning. If A equals B and B equals C, then A equals C. The four Aristotelian causes comprised the material cause (what a thing is made of), the formal cause (what kind of thing it is), the efficient cause (what made it), and the final cause (its purpose or goal), this last being most important. Demonstration was a process whereby a syllogistic proof of an effect was constructed through an analysis of its causes.

In the mid-sixteenth century at the University of Padua, traditional Aristotelian logic began to provide a renewed methodological basis for investigating the natural world. The most important figure in this development was Jacopo Zabarella (1533–1598). Remaining within an Aristotelian framework, the new logic asked how investigators got from sense perception to demonstrable truth. They discussed "demonstrative regress, a logical technique permitting the scholar to reason from an observed effect (fact) to its proximate cause and then to reason back (regress) from the cause to the effect where the reasoning began" (Grendler, p. 263). These methodological explorations influenced Galileo and other investigators until the mid-seventeenth century when Aristotelianism itself declined in influence.

HUMANISM AND NEOPLATONISM

Without replacing Aristotelianism, new approaches developed in the fifteenth and sixteenth centuries that emphasized particulars. Humanism was a broad intellectual movement that engaged in the reform of Latin and the rediscovery of ancient texts. Humanists criticized the logical approach of Scholasticism and often focused upon individuals in specific times and places, utilizing the dialogue and letter as literary forms that allowed the expression of individual points of view. They also studied and edited ancient texts, many of which became significant for the investigation of the natural world.

Renaissance Neoplatonism emerged as a result of this humanist textual work. A key figure is Marsilio Ficino (1433–1499), who during the second half of the fifteenth century translated and edited the writings of Plato, Neoplatonic philosophers such as Plotinus (205–270 c.e.), and the Hermetic corpus. The latter consisted of a group of writings actually dating from late antiquity that Ficino and his contemporaries believed were written before the time of Moses by one Hermes Trismegistus. They considered that the Hermetic corpus comprised a synopsis of ancient theology (prisca theologia). Ficino and his many successors in the sixteenth and seventeenth centuries believed in the reality of magic and in occult powers because they viewed the universe as a spiritual unity connected in all its various parts by sympathies and antipathies. The magus or magician could influence remote parts of the cosmos by manipulating these connections, and he or she did so to influence worldly matters, such as sickness and health. The operational aspects of Neoplatonic magical traditions may have influenced the development of experimentation, a methodology that entailed the active manipulation of the natural world.

Neoplatonic doctrines also influenced notions about experience and its role in investigating nature. One example entails the doctrine of signatures and illumination. In one version, that of the sixteenth-century physician Paracelsus (1493/94–1541), experience is framed by the biblical context of the Fall. Humans after their expulsion from paradise no longer had direct access to the Word of God or direct knowledge of the world of nature. Yet because God had put the light of nature (lumens naturalis) in them they could overcome their fallen state. The light of nature awakened in their minds, so they were able to see signs stamped on natural things. Directly experiencing such things, they could thereby see God's "signatures," which were external signs that pointed to the internal nature of things.

MEDICINE AND ALCHEMY

Within the discipline of medicine, interest in particulars and a validation of individual experience developed in a variety of ways. In the fourteenth century a branch of medicine known as practica emerged that concerned the particulars of disease and treatments. By the sixteenth century the writings of the ancient physician Galen (129–c. 199 c.e.) had become widely influential, particularly with respect to his empirical orientation and his practice of dissecting animals. Human dissection was taken up as part of the medical curriculum in the late medieval universities. Initially dissections were carried out in formal, public settings in which a high-status, learned doctor stood on a podium to read an authoritative text on anatomy, while a low-status person performed the handwork of dissection. In his famous De Humani Corporis Fabrica (On the fabric of the human body) published in 1543, Andreas Vesalius (1514–1564) advocated hands-on dissection by the high-status physician as well as careful observation and the visual depiction of body parts. Vesalius criticized but was also indebted to Galen. His famous treatise is part of a rich tradition of anatomical study that continued through the eighteenth century. This tradition notably includes the experimental work of William Harvey (1578–1657) in the 1620s on the circulation of the blood.

Alchemy represents a distinct discipline that developed in early modern Europe after the medieval transmission of key texts from the Islamic world. Alchemists often undertook hands-on, laboratory operations entailing separations, distillations, and the like. In the seventeenth century alchemy and related fields developed genuine experimental procedures. Jean Baptiste van Helmont (1579–1644) carried out numerous careful determinations of specific weights of substances he produced in his laboratory. George Starkey (1627–1665) undertook thousands of experiments to discover a single method of changing all sulfurs into medicines. The laboratory experiments of Robert Boyle (1627–1691) were influenced by this work. Scholars have investigated these seventeenth-century developments in detail and have traced their influence on eighteenth-century chemists, such as Antoine Lavoisier (1743–1794). This scholarship has brought into question the traditional sharp distinction between early modern alchemy and modern chemistry.

MECHANICAL ARTS

The mechanical arts entailed skilled craft work, including carpentry and weaving, but also arts that are now considered fine arts, such as painting and sculpture. The influence of artisanal craft values on early modern scientific methodology has been a longstanding topic of discussion in the history of science. The Viennese scholar and refugee Edgar Zilsel (1891–1944) argued that artisanal values that appreciated hands-on experience and craft work influenced the emergence of an experimental methodology in the seventeenth century. Subsequent scholarship has shown that the fifteenth- and sixteenth-century proliferation of writings on mechanical arts transformed the practical knowledge of the crafts into discursive subjects worthy of the attention of learned persons. Painters and other practitioners wrote books in which they articulated the value of practice and direct experience as crucial for obtaining knowledge of the natural world.

MATHEMATICS AND MECHANICS

Practical problems in the mechanical arts increasingly came to be analyzed in mathematical terms. The ancient mathematician Archimedes (c. 287–212 b.c.e.), who had applied geometric analysis to problems of statics (the science of weights), came to be highly influential. In the sixteenth century Niccolò Tartaglia (1499–1557) published the first Latin treatises of Archimedes and also wrote books in which he mathematically analyzed practical problems, such as the trajectory of cannonballs. Later in the same century authors, such as the nobleman and patron of Galileo, Guidobaldo del Monte (1545–1607), wrote treatises on machines and mechanics in the context of theory and mathematics.

This sixteenth-century tradition preceded the development of the new science of motion developed by Galileo Galilei (1564–1642). Galileo worked out the mathematical kinematics of motion. Disregarding air resistance, he concluded that all bodies fall in uniformly accelerated motion and that velocity increases in proportion to time elapsed. He went on to deduce the mathematical results of this conclusion, for instance, that the distance increases in proportion to the square of time. Following Galileo, Christiaan Huygens (1629–1695) worked out the mathematics of the pendulum and of circular motion. Near the end of the seventeenth century, in Philosophiae Naturalis Principia Mathematica (1687; Mathematical principles of natural philosophy), Isaac Newton (1642–1727) created a system of terrestrial and celestial dynamics in which he demonstrated mathematically a large array of propositions concerning natural phenomena. In these and many other examples in the seventeenth and eighteenth centuries, the aim of natural and experimental philosophers was to describe motion by means of mathematics. This project was possible because of simultaneous developments within mathematics itself, culminating in the invention of calculus by Newton and by Gottfried Wilhelm Leibniz (1646–1716) at the end of the seventeenth century.

INSTRUMENTATION AND EXPERIMENTATION

During the sixteenth and seventeenth centuries the use of instruments to measure and investigate the natural world came to be increasingly important. The Danish nobleman Tycho Brahe (1546–1601) is considered the greatest observational astronomer before the invention of the telescope. For twenty years, from his Uraniborg observatory, Brahe made systematic observations of the moon, the planets, and other phenomena, such as the comet of 1577. He used these observations not only to correct and improve available data but to investigate and develop theories about the nature of the heavens and the structure of the cosmos.

Observational astronomy changed with the invention of the telescope. With this new instrument Galileo made detailed observations of the moon and the stars of the Milky Way. He further discovered the four moons of Jupiter (the Medicean Stars). In The Sidereal Messenger (1610) he described these discoveries with both text and drawings. Galileo's conclusions were by no means instantly accepted. He had to persuade his contemporaries that his instrument produced valid data, not optical illusions. Like Brahe and others of his predecessors, Galileo produced new data, but he also used that data to make novel claims about the nature of the cosmos.

Instruments and devices became especially significant in the seventeenth and eighteenth centuries. Among these devises were "philosophical" machines especially devised to investigate the natural world. A prominent example of such a philosophical machine was the air pump, used by Boyle to investigate the nature of air. The pump was difficult to build and to use. Nevertheless, it was key to a whole series of experiments concerning air carried out in the mid-seventeenth century.

In seventeenth-century England the notion of the reliable witness to experiments emerged. Such a witness was an honorable person, preferably a gentleman (therefore immune from the self-interest of the artisan), who could attest to the accuracy of the stated results of a given experiment. Valid experimental results came to be tied to the social requirements of gentlemanly honor. By the eighteenth century, however, learned visitors interested in natural philosophy who came to London often visited the shops of instrument makers to purchase instruments but also to discuss philosophical and experimental issues. By this time the instrument maker's shop had become a space for philosophical discourse, while the status of certain kinds of craft practitioners had risen.

The use of instruments to investigate nature had important methodological implications because it challenged the notion of Aristotelian common experience. For Aristotelians common experience was valid because all reasonable people without question agreed that a particular claim was true. In contrast, truth derived from experimentation, and instrumentation depended on the manipulation of a device that was only available to particular individuals. Such individuals had to have access to the device itself and had to possess particular skills to use it. Aristotelian common experience and seventeenth-century experiment represented opposing methodologies. Further the use of instrumentation to investigate nature challenged the Aristotelian separation of the categories of technē (material production and reasoning about that production) and epistēmē (certain knowledge of unchanging truths).

BACONIAN EMPIRICISM AND NATURAL HISTORY

The English jurist and philosopher Francis Bacon (1561–1626) proposed a new methodology that aimed to bring about a continuous flow of new facts about the natural world. Bacon's most significant methodological work was Instauratio Magna (1620–1626; The great instauration), which included Novum Organum (1620; New instrument). Bacon rejected syllogistic logic, pointing out that the premises of the syllogism could be in error. His own method entailed gathering a large amount of data on a variety of subjects and applying that data to the development of axioms. His goal was to account for the many particular things in nature in all its diversity. Yet his method entailed more than the simple collection of sense experiences, for Bacon believed the senses could deceive. Rather, in the creation of axioms he took into account the "maker's knowledge," that is, the presuppositions necessary for the fabrication of a thing. To gather data, Bacon proposed a cooperative effort to write "histories of the trades," detailed accounts of the essential operations of productive arts, such as silk textiles, mining, printing, papermaking, and agriculture, as well as "natural histories" on topics such as snakes, birds, and metals.

In the sixteenth and seventeenth centuries, particularly in Italy, natural history was the focus of growing interest. The creation of natural history collections by naturalists, such as Ulisse Aldrovandi (1522–1605) and Athanasius Kircher (1601–1680), and the intense study of the specimens in those collections became an important aspect of the investigation of nature. Museums became "laboratories of nature" (Findlen, p. 154), where investigations entailing testing, dissection, and distillation occurred. In some instances the collection of specimens was accompanied by the creation of detailed drawings based on careful observations. Collecting specimens, examining them, and having them drawn or painted became important modalities for the study of nature. Federico Cesi (1585–1630) and other members of the Academy of the Lincei, a scientific society founded in 1603, were particularly active in this form of investigation of the flora and fauna of Italy.

DESCARTES AND THE MECHANICAL PHILOSOPHY

The methodological writings of René Descartes (1596–1650) laid the foundations for the "mechanical philosophy." Descartes's famous dictum "Cogito ergo sum" ('I think therefore I am') is the basis for his notion that mind is a thinking substance and is to be excluded from the physical world entirely. That world, composed of particles of matter, is characterized by extension. These particles move only by virtue of mechanical necessity. Their motions produce all the variety of natural phenomena. Descartes eliminated spiritual or mental qualities from the material world, leaving the thinking subject (the "I" of the cogito) as the discoverer of the clear and certain truths of nature. That natural world, characterized by extension, is ordered by mathematical relationships. For Descartes certain knowledge could be obtained by applying mathematical rules to the world of nature.

CONCLUSION

Investigations of the rich methodological cornucopia that characterizes the early modern period have been guided by several general principles. First, early modern thought is studied on its own terms, not according to the values of modern scientific methodology. Second, the wide-ranging connections of methodological thought to contemporaneous language and meaning on the one hand and to social and cultural conditions on the other are being explored in depth. Finally, studies have followed the sources, whatever that content might be. As a result, natural history has taken its place beside physics. The doctrine of signatures has been studied as thoroughly as the laws of planetary motion. Such contextual approaches have greatly expanded knowledge of early modern methodologies for investigating the natural world.

See also Alchemy ; Aldrovandi, Ulisse ; Astronomy ; Bacon, Francis ; Boyle, Robert ; Brahe, Tycho ; Descartes, René ; Galileo Galilei ; Harvey, William ; Helmont, Jean Baptiste van ; Hermeticism ; Huygens Family ; Kircher, Athanasius ; Leibniz, Gottfried Wilhelm ; Mathematics ; Natural History ; Nature ; Neoplatonism ; Newton, Isaac ; Paracelsus ; Scientific Revolution ; Vesalius, Andreas .

BIBLIOGRAPHY

Primary Sources

Aristotle. The Complete Works of Aristotle: The Revised Oxford Translation. Edited by Jonathan Barnes. 2 vols. Princeton, 1984.

Galilei, Galileo. Sidereus Nuncius; or, The Sidereal Messenger. Translated by Albert van Helden. Chicago, 1989. An English translation that reproduces all of Galileo's drawings. Contains an extensive and useful introduction and notes.

Newton, Isaac. The Principia: Mathematical Principles of Natural Philosophy. Translated by I. Bernard Cohen and Anne Whitman. Berkeley and Los Angeles, 1999. Translation of Principia, 3rd ed. (1726). The translation to use. Contains an extensive and useful guide by Cohen.

Secondary Sources

Applebaum, Wilbur, ed. Encyclopedia of the Scientific Revolution: From Copernicus to Newton. New York, 2000.

Bennett, James A. "Shopping for Instruments in Paris and London." In Merchants and Marvels: Commerce, Science, and Art in Early Modern Europe, edited by Pamela H. Smith and Paula Findlen, pp. 370–395. New York, 2002.

Bono, James J. The Word of God and the Languages of Man: Interpreting Nature in Early Modern Science and Medicine. Vol. 1, Ficino to Descartes. Madison, Wis., 1995.

Dear, Peter. Discipline and Experience: The Mathematical Way in the Scientific Revolution. Chicago, 1995.

Des Chene, Dennis. Spirits and Clocks: Machine and Organism in Descartes. Ithaca, 2001.

Findlen, Paula. Possessing Nature: Museums, Collecting, and Scientific Culture in Early Modern Italy. Berkeley and Los Angeles, 1994.

Freedberg, David. The Eye of the Lynx: Galileo, His Friends, and the Beginnings of Modern Natural History. Chicago, 2002.

Grant, Edward. The Foundations of Modern Science in the Middle Ages: Their Religious, Institutional, and Intellectual Contexts. Cambridge, U.K., 1996.

Grendler, Paul F. The Universities of the Italian Renaissance. Baltimore, 2002.

Lindberg, David C., and Robert S. Westman, eds. Reappraisals of the Scientific Revolution. Cambridge, U.K., 1990.

Long, Pamela O. Openness, Secrecy, Authorship: Technical Arts and the Culture of Knowledge from Antiquity to the Renaissance. Baltimore, 2001.

Newman, William R., and Lawrence M. Principe. Alchemy Tried in the Fire: Starkey, Boyle, and the Fate of Helmontian Chymistry. Chicago, 2002.

Pérez-Ramos, Antonio. Francis Bacon's Idea of Science and the Maker's Knowledge Tradition. Oxford, 1988.

Shapin, Steven, and Simon Schaffer. Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life. Princeton, 1985.

Siraisi, Nancy G. Medieval and Early Renaissance Medicine: An Introduction to Knowledge and Practice. Chicago, 1990.

Wallace, William A. Galileo's Logic of Discovery and Proof: The Background, Content, and Use of His Appropriated Treatises on Aristotle's Posterior Analytics. Dordrecht, 1992.

Pamela O. Long

SCIENTIFIC METHOD

What follows is a description of various views on inductive inference and methods for inferring general theories as they have developed from the scientific revolution to modern times. Later, the development of methods for discovering causal relationships will be discussed.

modern methodology

A strong influence on contemporary methodology is interdisciplinary research. In the twentieth century, the question of how we can use observations to attain empirical knowledge became the subject of research in a number of disciplines, such as statistics, econometrics, and computer science. Modern philosophy of method continues to contribute to and draw on developments in related disciplines.

Another strong influence on contemporary methodology arises from studies of the history of science, which captured the attention of philosophers because of the groundbreaking work of Thomas Kuhn (1922–1996) on the Structure of Scientific Revolutions. Kuhn argued that scientific textbook accounts of the history of science as a wholly progressive series of discoveries are false for scientific revolutions. His work has suggested that changes of method across revolutions undercut attempts to apply common standards to evaluate prerevolution and postrevolution theories.

Kuhn also criticized the methodological ideas of Karl Popper (1902–1994). Popper had asked the question of what distinguishes ("demarcates") scientific hypotheses from nonscientific hypotheses. He emphasized that science proceeds by testing hypotheses against empirical data, and thus located the characteristic of scientific hypotheses in their empirical testability. Popper's basic view of testing a hypothesis against data was to derive predictions from the hypothesis and see if they matched the data (conjectures and refutations). If the data does not match the predictions, they falsify the hypothesis.

This led Popper to postulate that scientific hypotheses must be falsifiable. Popper's falsifiability criterion has been very influential, arguably more outside of the philosophy of science than inside. Kuhn objected to the falsifiability concept because, according to him, history shows that scientists do not subject major scientific theories (or paradigms) to falsification. Instead, scientists view a mismatch between theory and data as an anomaly, a puzzle to be resolved by further research. Many philosophers of science took Kuhn's moral to be that logic-based analyses of scientific method cannot capture the dynamics of major scientific change. Scientific revolutions would instead be determined by complex sociopolitical processes within the scientific community, played out within the specific historical context. Modern methodologists aim to avoid both the extremes of a context-free universal scientific logic on the one hand, and an entirely context-specific study of particular historical episodes on the other.

Method in the Scientific Revolution

Two topics of inquiry held center stage during the scientific revolution: the traditional problems of astronomy, and the study of gravity as experienced by bodies in free fall near the surface of the earth. Johannes Kepler (1571–1630) proposed that the predictive empirical equivalence between geocentric and heliocentric world systems that holds in principle could be offset by appeal to physical causes (Jardine 1984). He endorsed the appeal by Nicolas Copernicus (1473–1543) to the advantage offered his system from agreeing measurements of parameters of the earth's orbit from several retrograde motion phenomena of the other planets (1596/1981). In his classic marshaling of fit to the impressive body of naked eye instrument observation data by Tycho Brahe (1546–1601), Kepler appealed to this advantage as well as qualitative intuitions about plausible causal stories and intuitions about cosmic harmony to arrive at his ellipse and area rules (1609/1992). He later arrived at his harmonic rule (1619/1997). His Rudolphine Tables of 1627 were soon known to be far more accurate than any previously available astronomical tables (Wilson 1989).

Galileo Galilei (1564–1642) described his discovery of Jupiter's moons and exciting new information about our moon in the celebrated report of his telescope observations (1610/1989). His later observations of phases of Venus provided direct observational evidence against Ptolemy's system, though not against Tycho's geoheliocentric system. This was included in his argument for a Copernican heliocentric system in his famously controversial Dialogue (1632/1967).

Galileo's study of gravity faced the challenge that because of complicating factors such as air resistance one could not expect the kind of precise agreement with measurement that was available in astronomy. In his celebrated Two New Sciences (1638/1914), Galileo proposed uniformly accelerated fall as an exact account of idealized motion that would obtain in the absence of any resistant medium, even though the idealization is impossible to actually implement. He argues that the perturbing effects of resistance are too complex to be captured by any theory, but that the considerations he offers, including inclined plane experiments that minimize the effects of resistance, support his idealized uniformly accelerated motion as the principal mechanism of such terrestrial motion phenomena as free fall and projectile motion.

An important part of what distinguishes what we now characterize as the natural sciences is the method exemplified in the successful application of universal gravity to the solar system. Isaac Newton (1642–1727) characterizes his laws of motion as accepted by mathematicians and confirmed by experiments of many kinds. He appeals to propositions inferred from them as resources to make motion phenomena measure centripetal forces. These give systematic dependencies that make the areal law for an orbit measure the centripetal direction of the force maintaining a body in that orbit, that make the harmonic law for a system of orbits about a common center, and that make the absence of orbital precession (not accounted for by perturbations) for any such orbit, measure the inverse square power for the centripetal force. His inferences to inverse-square forces toward Jupiter, Saturn, and the sun from orbits about them are inferences to inverse-square centripetal acceleration fields backed up by such measurements.

Newton's moon-test shows that the length of a seconds pendulum at the surface of the earth and the centripetal acceleration of the moon's orbit count as agreeing measurements of a single earth-centered inverse-square acceleration field. On this basis Newton identified the force maintaining the moon in orbit with terrestrial gravity. His first two rules endorse this inference. Rule number one states "no more causes of natural things should be admitted than are both true and sufficient to explain their phenomena" (Newton 1726/1999, p. 794). Rule number two adds that, therefore, "the causes assigned to natural effects of the same kind must be, so far as possible, the same" (Newton 1726/1999, p. 795).

Newton argues that all bodies gravitate toward each planet with weights proportional to their masses. He adduces a number of phenomena that give agreeing measurements of the equality of the ratios of weight to mass for bodies at equal distances from planets. These include terrestrial pendulum experiments and the moon-test for gravitation toward the earth, as well as the harmonic laws for orbits about them for gravitation toward Saturn, Jupiter, and the sun. They also include the agreement between the accelerations of Jupiter and its satellites toward the sun, as well as between those of Saturn and its satellites and those of the earth and its moon toward the sun.

His third rule endorses the inference that these all count as phenomena giving agreeing measurements of the equality of the ratios of weight to mass for all bodies at any equal distances from any planet whatsoever. Rule number three states that "those qualities of bodies that cannot be intended and remitted (i.e., qualities that cannot be increased and diminished) and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally" (Newton 1726/1999, p. 795).

Newton's fourth rule added that "In experimental philosophy propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypothesis until yet other phenomena make such propositioins either more exact or liable to exceptions" (Newton 1726/1999, p. 796). This rule was added to justify treating universal gravity as an established scientific fact, notwithstanding complaints that it was unintelligible in the absence of a causal explanation of how it results from mechanical action by contact.

Newton's inferences from phenomena exemplify an ideal of empirical success as convergent accurate measurement of a theory's parameters by the phenomena to be explained. In rule four, a mere hypothesis is an alternative that does not realize this ideal of empirical success sufficiently to count as a serious rival.

Rule four endorses provisional acceptance. Deviations count as higher order phenomena carrying information to be exploited. This method of successive corrections guided by theory mediated measurement led to increasingly precise specifications of solar system phenomena backed up by increasingly precise measurements of the masses of the interacting solar system bodies.

This notion of empirical success as accurate convergent theory mediated measurement of parameters by empirical phenomena clearly favors the theory of general relativity of Albert Einstein (1879–1955) over Newton's theory (Harper 1997). Moreover, the development and application of testing frameworks for general relativity are clear examples of successful scientific practice that continues to be guided by Newton's methodology (Harper 1997, Will 1986 and 1993). More recent data such as that provided by radar ranging to planets and lunar laser ranging provide increasingly precise post Newtonian corrections that have continued to increase the advantage over Newton's theory that Newton's methodology would assign to general relativity (Will 1993).

Hypothetico-Deductivism

In the preface to his Treatise on Light, Christian Huygens (1629–1695) provided a nice characterization of the hypothetico-deductive (H-D) alternative to Newton's method:

There will be seen in it demonstrations of those kinds which do not produce as great a certitude as those of Geometry, and which even differ very much therefrom, since whereas the Geometers prove their Propositions by fixed and incontestable Principles, here the Principles are verified by the conclusions to be drawn from them; the nature of these things not allowing of this being done otherwise. It is always possible to attain thereby to a degree of probability which very often is scarcely less than complete proof. To wit, when those things which have been demonstrated by the Principles that have been assumed correspond perfectly to the phenomena which experiment has brought under observation; especially when there are a great number of them, and further, principally, when one can imagine and foresee new phenomena which ought to follow from the hypotheses which one employs, and when one finds that therein the fact corresponds to our prevision.
(huygens 1690/1962, p. vi and vii)

Thus H-D method construes empirical success as success in prediction. The limitation of empirical success to prediction alone has suggested to some philosophers of science that distinguishing between theories that agree on predictions would have to be based on nonempirical criteria.

Predicted Fit to Future Data

Given plausible assumptions about errors in data, a model that fits a given body of data too closely is likely to be tracking random errors in the data in addition to the lawlike phenomenon under investigation. Statisticians refer to this as "overfitting the data." They have designed many criteria to reveal cases where a simpler model has better expected fit-to-future data generated by repetitions of an experiment than a more complex model that better fits the data so far. Among philosophers of science, Malcolm Forster and Elliott Sober have appealed to the Akaike Information Criterion to challenge the assumption that fit-to-past data exhausts the criteria for scientific inference. This criterion is not sufficient to recover Newton's method (Myrvold and Harper 2002). The extent to which other such proposals can recover Newton's method is an open question.

Bayesian Methods

Central to the Bayesian methods is epistemic probability, a rational agent's degree of belief. A number of arguments have been put forward to defend the probability axioms as coherence conditions for rational degrees of belief, in analogy to the way logical consistency can be taken as a coherence condition for rational acceptance. Dutch book arguments have shown that degrees of belief violating the probability axioms would assign positive expectations to each bet in a system of bets and conditional bets that would result in sure loss if they were all made together. A number of other arguments for this synchronic condition on rational degrees of belief have been advanced (particularly by Frank Plumpton Ramsey, Leonard J. Savage, Abner Shimony, Bas van Fraassesn, Richard T. Cox, Irving John Good, and J. Aczel).

David Lewis (1941–2001) provided a diachronic Dutch book argument (published in Teller 1976) to defend the Bayesian conditionalization learning model, according to which assigning new degrees of belief given by P′ (B) = P(B&A)/P(A) is the appropriate response to a learning experience in which the total relevant empirical input is to accept A as new evidence. In 1984 van Fraassen (1941–) extended this diachronic Dutch book argument to defend a condition he called reflection. His proposal to treat the reflection condition as a constraint on degrees of belief that could be counted as rational has led to much controversy.

One central Bayesian theme has been to investigate conditions under which evidence leads to convergence of opinion. Bruno de Finetti (1906–1985) specified conditions that would lead Bayesian agents, who update by repeated conditionlization on the outcomes of the same observations, to converge toward agreement in their degrees of belief, however otherwise divergent their prior degrees of belief may have been (1937/1980). Brian Skyrms (1990) has given what is probably the most general possible version of de Finetti's condition for convergence.

In 2003 Wayne Myrvold (1963–) argued that, for Bayesians, the degree to which a hypothesis unifies phenomena contributes to the degree to which these phenomena support the hypothesis. This suggests that Bayesians can recover important aspects of Newton's method. It may well be that investigating the representation of Newton's method of provisional acceptance in a Bayesian model will result in enriching the Bayesian framework to make it offer more resources for illuminating scientific method.

Causation, Correlation, Experimentation

In his famous methods (1843), John Stuart Mill (1806–1873) combined ideas about causal inference previously proposed by John Duns Scotus (1265/66–1308), William Ockham (1280–1349) and Francis Bacon (1561–1626). The work of twentieth century statisticians such as Jerzy Neyman (1894–1981), Karl Pearson (1857–1936), and Ronald A. Fisher (1890–1962) addressed two major shortcomings of Mill's method.

First, Mill assumed that we would observe deterministic causal relationships: Given the cause, the effect must follow every time. However, in a complex situation we typically do not have a complete specification of all operative causes, so we expect to observe trends rather than necessary relationships. For example, although smoking causes lung cancer, it does not do so in every person, because people's physiology varies. Rather, what we observe is a strong association between smoking and lung cancer: Among smokers, the incidence of lung cancer is much higher than among nonsmokers. To define precisely the intuitive notion of "strong association," statisticians developed the concept of correlation, which defines degrees of association (DeGroot 1975).

A second deficiency in Mill's methods is that they fail in the presence of common causes (confounders in statistical terminology). For example, suppose we observe that children who play violent video games are more prone to aggressive behavior than children who do not. Mill's logic would lead us to infer that playing violent video games causes aggressive behavior. But another possibility is that the correlation is because of personality traits: that children with an aggressive nature are drawn to violent video games and tend toward aggressive behavior; a preference for violent video games does not cause the behavior, but is merely a symptom of preexisting aggressive tendencies. If this alternative explanation is true, then Mill's methods lead us to the wrong conclusion. The policy implications are significant: If there is a direct causal relationship between video games and aggressive behavior, we expect to reduce aggressive behavior by restricting the availability of video games. But if personality is the underlying common cause of both, restricting access to video games should not decrease aggressive behavior.

A great advance for the problem of unobserved common causes was Fisher's revolutionary idea of the randomized experiment. Suppose that we have the ability to randomly assign half of a group of children to playing violent video games (the treatment group) and the other half to playing something else (the control group). For example, we might flip a coin for each participating child to make the assignment. Then we expect that personality traits, such as a tendency to aggression, would be randomly distributed in each half so that the children playing the video games would, on average, have no more aggressive personalities than the children playing something else. Under those circumstances, if we still find that significantly more of the video game players engage in aggressive behavior than the children playing something else, we can infer a direct causal relationship.

The idea of using randomization to rule out unobserved common causes has been applied in countless practical problems of causal inference, from clinical studies of the effectiveness of medical treatments to experiments for agricultural methods. It has been a most effective tool for addressing the problem of unobserved common causes that besets many of the traditional philosophical proposals for causal inference.

The power of randomization is available only when we have the ability to experimentally create the conditions we wish to investigate. In many settings of interest, we cannot perform experiments but can only passively gather data (these are called "observational studies" in statistics). A prominent physical science based on passive observation is astronomy. Many examples occur in the social sciences and economics. For instance, an economist cannot randomly assign inflation rates to various countries to study how inflation affects employment. A recent set of examples comes from computer science: While many companies gather vast amounts of data about their customers and the transactions they engage in, they rarely have the ability to assign customers randomly to various conditions (e.g., household income).

Philosophers continued to refine their understanding of the relationship between correlation and causation in nonexperimental settings. The work of Hans Reichenbach (1891–1953), published in 1956, was seminal. Reichenbach expounded the common cause principle: roughly, for every correlation between two events A and B, there is some causal explanation that posits either that one is a cause of the other (e.g., A causes B) or that A and B share a common cause. Reichenbach argued that the assumption that significant associations or correlations have causal explanations is deeply ingrained in our scientific and everyday reasoning. Another important concept of Reichenbach was the notion of screening off. The purpose of this concept is to capture the distinction between immediate and intermediate causes in terms of correlations.

For example, suppose that tar content in lungs is the direct cause of cancer, while smoking directly causes tar to accumulate in the lungs, and thereby indirectly causes lung cancer. Then we would observe a correlation between smoking and lung cancer; but knowing the tar content of the lung would make smoking irrelevant to lung cancer. By contrast, even if we knew whether a subject smokes, the tar content of one's lungs would still be relevant to, or correlated with, the subject getting lung cancer. In Reichenbach's terms, information about tar content screens off information about smoking from conclusions about lung cancer. Because tar content screens off smoking from lung cancer, but not vice versa, Reichenbach suggested that such evidence rules out smoking as a direct cause of lung cancer, and allows us to infer that the effects of smoking are mediated through tar in the lungs.

The philosophers of science—Peter Spirtes, Clark Glymour, and Richard Scheines—developed Reichenbach's ideas about the relationships between correlation and causation using the framework of causal graphs or diagrams (Spirtes 1993). A causal graph is an intuitive representation of causal relationships, in which direct causes are connected with their effects by arrows pointing from cause to effect.

Using the language of causal graphs, Spirtes, Glymour, and Scheines gave a precise formulation of Reichenbach's precept that direct causes screen off indirect ones, known as the Markov condition (I-map in computer science terminology). The common cause principle—that there is no correlation without causation—can be formulated as another principle about diagrams, termed faithfulness (perfect I-map in computer science terminology). Given these principles relating causation and correlation, it is possible to characterize when valid inferences about causal relationships can be drawn from passive observation of associations. The theory is powerful and precise enough to develop computer programs that perform these inferences automatically (the TETRAD system, for instance). With such a program, we can analyze the kind of large datasets that we find in practice, realizing the vision of Bacon and Mill of applying causal inference methods to extensive observation histories.

In computer science, causal diagrams (often called Bayes Nets) have been firmly established as a scheme to capture and reason about associations and causal relationships, giving rise to thriving commercial developments with many practical applications (Pearl 1988, 2000). Econometrics, the study of statistical methods for economic problems, has a rich tradition of developing methods for nonexperimental causal inference going back to the early twentieth century (path diagrams and structural equation models). It turns out that many of these ideas and techniques can be seen as instances of causal diagram methods (Pearl 2000). While the theory of causal inference from passive observation is not yet as firmly established as the methodology based on randomization, at the beginning of the twenty-first century we see a common framework emerging shared and sustained by philosophy, computer science, and economics.

See also Bayes, Bayes' Theorem, Bayesian Approach to Philosophy of Science; Philosophy of Statistical Mechanics; Scientific Revolutions.

Bibliography

Aczel, J. Lectures on Functional Equations and Their Applications. New York: Academic Press, 1966.

Cox, R. The Algebra of Probable Inference. Baltimore, MD: John Hopkins Press, 1961.

de Finetti, B. "Foresight: Its Logical Laws, Its Subjective Sources" (1937). Translated by H. E. Kyburg and H. Smokler. In Studies in Subjective Probability. Huntington, NY: Kreiger, 1980.

DeGroot, Morris H. Probability and Statistics. Reading, MA: Addison-Wesley, 1975.

Earman, J. Bayes or Bust?: A Critical Examination of Bayesian Confirmation Theory. Cambridge, MA: MIT press, 1992.

Forster, M., and E. Sober. "How to Tell When Simpler, More Unified, or Less Ad Hoc Theories Will Provide More Accurate Predictions." In British Journal for The Philosophy of Science 45 (1994): 1–35.

Galilei, G. The Sidereal Messenger (1610). Translated by A. Van Helden. Chicago: University of Chicago Press, 1989.

Galilei, G. Dialogue concerning the Two Chief World Systems (1632). Translated by Stillman Drake. Los Angeles: University of California Press, 1967.

Galilei, G. Two New Sciences. Translated by H. Crew and A. De Salvio. New York: Dover, 1914.

Good, I. J. Probability and The Weighing of Evidence. London: Griffin, 1950.

Harper, W. L. "Isaac Newton on Empirical Success and Scientific Method." In The Cosmos of Science: Essays of Exploration, edited by J. Earman and J. D. Norton. Pittsburgh, PA: University of Pittsburgh Press, 1997.

Harper, W. L., and C. A. Hooker, eds. Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Vol. 1. Dordrecht; Boston: D. Reidel, 1976

Huygens, C. Treatise On Light (1690). Translated by S. P. Thompson. New York: Dover, 1962.

Jardine, N. The Birth of History and Philosophy of Science: Kepler's "A Defense of Tycho against Ursis. Cambridge, MA: Cambridge University Press, 1984.

Jeffreys, H. Scientific Inference. 3rd ed. Cambridge, MA: Cambridge University Press, 1973.

Kepler, J. The Harmony of The World (1619). Translated by E. J. Aiton, A. M. Duncan, and J. V. Field. Philadelphia: American Philosophical Society, 1997.

Kepler, J. New Astronomy (1609). Translated by W. H. Donahue. New York: Cambridge University Press, 1992.

Kepler, J. The Secret of the Universe (1596). Translated by A.M. Duncan. New York: Abaris Books, 1981.

Kuhn, T. S. The Structure of Scientific Revolutions. Chicago: University of Chicago Press, 1962.

Kyburg, H. E. Science & Reason. New York: Oxford University Press, 1990.

Myrvold, W. C. "A Bayesian Account of The Virtue of Unification." Philosophy of Science 70 (2003): 399–423.

Myrvold, W. C., and W. Harper. "Model Selection, Simplicity, and Scientific Inference." Philosophy of Science 69 (2002): 135–149.

Newton, I. Mathematical Principles of Natural Philosophy. 3rd ed. (1726). Translated by I. B. Cohen and A. Whitman. Los Angeles: University of California Press, 1999.

Pearl, J. Causality. San Mateo, CA: Morgan Kaufmann, 2000.

Pearl, J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, CA: Morgan Kaufmann, 1988.

Popper, K. R. Conjectures and Refutations: The Growth of Scientific Knowledge (1962). New York: Harper & Row, 1963.

Popper, K. R. The Logic of Scientific Discovery (1959). New York: Harper & Row, 1965.

Ramsey, F. P. "Truth and Probability." In The Foundations of Mathematics and Other Logical Essays. London: Kegan Paul, 1931.

Reichenbach, H. The Direction of Time. Berkeley, CA: University of Los Angeles Press, 1956.

Reichenbach, H. The Theory of Probability. London: Cambridge University Press, 1949.

Savage, L. J. Foundations of Statistics. New York: Wiley, 1954.

Shimony, A. Search for a Naturalistic World View: Scientific Method and Epistemology. Vol. 1. Cambridge, U.K.: Cambridge University Press, 1993.

Skyrms, B. The Dynamics of Rational Deliberation. Cambridge, MA: Harvard, 1990.

Spirtes, P., C. Glymour, and R. Scheines. Causation, Prediction, and Search. New York: Springer Verlag, 1993.

Teller, O. "Conditionalization, Observation, and Change of Preference." In Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, edited by W. L. Harper and C. A. Hooker. Dordrecht; Boston: D. Reidel 1 (1976): 205–257

van Fraassen, B. "Belief and The Will." Journal of Philosophy 81 (1984): 235–256.

van Fraassen, B. "Calibration: A Frequency Justification for Personal Probability." In Physics, Philosophy, and Psychoanalysis: Essays in Honor of Adolf Grünbaum, edited by R. S. Cohen and L. Laudan. Dordrecht: Reidel, 1983.

Will, C. M. Theory and Experiment in Gravitational Physics. 2nd ed. Cambridge, U.K.: Cambridge University Press, 1993.

Will, C. M. Was Einstein Right? Putting General Relativity to the Test. New York: Basic Books, 1986.

Wilson, C. "Predictive Astronomy in The Century after Kepler." In The General History of Astronomy: Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part A: Tycho Brahe to Newton. Vol. 2, edited by R. Taton and C. Wilson. Cambridge, U.K.: Cambridge University Press, 1989.

Willam Harper (2005)

Oliver Schulte (2005)

Scientific Method

BIBLIOGRAPHY

Research is scientific if and only if it follows a procedure known as scientific method. A received view of this method has evolved in the seventeenth century as a synthesis of ideas of Bacon, Boyle, and Newton. Roughly, scientific method consists of indiscriminate observations of regularities, gathering information on repeatable phenomena, and using it as a sound basis for theorizing. Scientific method is, then, a talisman for success. Accordingly, researchers strive to show that their work conforms to scientific method—to the point of distortion. Yet, famously, all guarantees of success in research are worthless. Plato declared that the validity of ideas depends on their pedigree. Tradition offers only two views on the source of ideas: It is intuition—intellectualism, apriorism (Plato)— or it is observation—empiricism, inductivism (Aristotle). Question: Where should thinking or observing begin? No answer. Reliance on both thought and experience as sources of knowledge is impossible, as they may mismatch; yet their judicious use as procedures is possible: Apriorism admits experience as hints; inductivism admits hypotheses as temporary scaffolding.

The promise of success that scientific method grants depends on the unlearning of prejudices. Sir Francis Bacon, the father of the modern scientific method and a precursor of the Enlightenment, was the first to realize that preconceived opinions distort observation, as they invariably confirm themselves; reliable observations come from unbiased minds. So he recommended relinquishing all preconceptions. This is radicalism; it bespeaks utter rationality. The classical rationalists of the Age of Reason viewed humans as utterly rational, with reason as free of local (individual) differences. Their theories ignored these differences; their economic theory concerned only free trade; their political theory deemed the state as taking care of the contracts, including those between ruler and subject; religion they viewed as private, independent of any established church. Social researchers thus viewed individual conduct as purely rational and as yielding to individually endorsed motives exclusively. Thus, their views on scientific method embody a view of humanity as rational and the individual as preceding society.

The received view of scientific method remained excessively rationalist, radical, ahistorical, individualist, and liberal. To date it dominates the natural sciences, economics, and behaviorist and Freudian psychology. After the failure of the French Revolution, the dominant view within social studies had history as its paradigm, and its agenda largely aimed at shunning radicalism by presenting political theory historically, deprecating democracy and science. As views on scientific method differed, so views differed as to whether social studies start with individuals and reach the study of the social whole or vice versa. This was then a backlash against radicalism. Its prime initiator was Georg Friedrich Wilhelm Hegel, who traced the roots of French revolutionary terror to the Enlightenment’s dismissal of social authority as resting on prejudice. Scientific method is inapplicable to society, he declared, since societies have historical roots; there is no social prediction even though nations are subject to historical laws. Schelling, Hegel, and others, developed new methods, variants of which some twentieth-century thinkers embraced, especially Henri Bergson and Edmund Husserl. Following Hegel’s claim that the methods of the natural and social sciences diverge, Wilhelm Dilthey suggested that whereas the natural sciences employ deductive explanations, the social sciences employ empathy. (Karl Popper endorsed this distinction, incidentally: His theory of explanation—situational logic—encompasses both models, and allows for reference to both individuals and institutions.) Hegel’s methodology is still popular among those who ignore scientific method. Conspicuous among his twentieth-century followers are Gabriel Marcel, Paul Ricouer, Martin Heidegger, Hans-Georg Gadamer, Jean-Paul Sartre, and Jacque Derrida. They all adopted variants of Husserl’s method. Heidegger preferred poetic truth to scientific truth. Gadamer endorsed Hegel’s objection to the Enlightenment movement’s sweeping dismissal of prejudice. He recommended the study of texts, not of facts, hoping that certitude is achievable there, with wider conclusions. Derrida objected: There is no one certain way to read a text. Gadamer was adamant, expressing preference for Aristotle’s text on physics over modern ones. Sartre first accepted scientific method and endorsed behaviorism. As he was later impressed with psychoanalysis, he gave up both. (Incidentally, Popper considered both violations of the rules of scientific method, as he rejected the received view.)

Hegel also influenced adherents to science, including Henri de St. Simon, Auguste Comte, John Stuart Mill, and Karl Marx. They sought the scientific historical laws that permit predictions. Marx stressed that scientific method sanctify his predictions, rendering them incontestable. (Not all his followers share his respect for science.) Does the use of scientific method validate Comte’s theory of the three stages of history or Marx’s view of history as propelled by the class struggle? Is dissent a challenge to their scientific credentials? Or did prejudice distort their use of scientific method? These are difficult questions.

William Whewell, a significant nineteenth-century transitional figure, dismissed the fear of prejudice. He contested Bacon’s proposal to empty our minds of preconceived opinions, declaring all ideas preconceived. He trusted rigorous tests to eliminate error. Bacon promised that empty minds will follow scientific method and produce true theories; Whewell denied that: We need hypotheses; occasionally, researchers hit upon true ones and verify them empirically, he said. His view won popularity among physicists while social thinkers followed Mill.

Marx challenged the individualist, ahistorical economics with his historical prediction: As markets must be increasingly unstable, capitalism will give way to socialism—probably through civil war. At the end of the nineteenth century, Émile Durkheim and Max Weber, known as the fathers of modern sociology, circumvented him and shifted the debate away from history back to the other question that Hegel had raised: Which is primary, the individual or the social whole? Their writings on society and on scientific method ignore historical laws.

Durkheim’s starting point was the claim that some “social facts” are observable (such as conformity to laws). This is hard to comprehend, but clearly, he wanted to broaden classical individualist methodology to make it recognize collective entities. He steered between Hegel’s view of social forces and Marx’s view of economic forces. He considered national cultures to be the glue that maintains collectives; in particular, religion is society’s representation or celebration of itself.

Durkheim valued individual contributions to culture, as he admired science. Does his view of culture allow for this? He left this question open. Hence, as a response to Hegel, his theory is incomplete. His attention lay elsewhere: He insisted that a culture coheres with its society. He invented functionalism, the view that social wholes are coherent. A clear counterexample to this is crime: It is dysfunctional. He suggested that crime has a function: to remind society of the law. This does not block the counterexample: The need for violent reminders bespeaks incoherence. Once functionalism incorporates dysfunctional aspects, it becomes trivial and abandons coherence. Durkheim was inspired by Claude Bernard’s observation that cold-blooded animals are more adapted to the environment but less energetic than warm-blooded ones. He applied this to the division of labor: High specialization enables a striking worker to bring society to a halt and forces it to cohere (organic solidarity). This is too vague to be open to criticism.

Weber rejected “one-sided materialism”—in allusion to Marx—and ascribed social values to ideas. His studies identify typical value-systems of typical members of various classes and societies. Unlike classical individuals who represent humanity in general, Weber’s typical individuals represent subcollectives. His theory of scientific method thus steers between classical individualism and collectivism. To emphasize his reluctance to say whether societies are real, he called it “individualism of method.”

Georg Simmel (a contemporary of Durkheim and Weber, but influential only after World War II) suggested that individual and society are equally primary, so that conflict is never totally avoidable. Karl Popper suggested considered action as strictly individual but within social contexts—situational logic—thus achieving a view that is in the traditional individualist mode, without being radical. This opens the road for new kinds of explanation—especially for actions aiming at institutional reform.

Popper’s suggestion rests on his groundbreaking description of scientific theory as (not proven but) testable, namely, refutable. For success, this is necessary but insufficient: There is no guarantee. Scientific truth is then not the truth, but the best available approximation to it. This closes the debate comparing the rules for natural and social studies. For explanations in the social sciences to be refutable, they should center on individual actions. Science is now increasingly seen as the search for answers to interesting questions that are open to criticism.

Another development is of the systemist outlook: Both individual and society are systems of sorts (Mario Bunge). How is action at all possible? This question is outside the domain of social studies; these take actions as given and center on their unintended consequences (Hayek)—especially actions intended to improve society. Systemism is incomplete without a theory of scientific method. Some variant of Popper’s theory is an obvious candidate. This, however, is a matter for future discussions of scientific method adequate for social studies. The starting point of any such study has to be an examination of the history and sociology of the social sciences, especially of the question, what do we owe to the diverse school of thought of the past and to their august members?

SEE ALSO Positivism

BIBLIOGRAPHY

Agassi, Joseph. 1977. Towards a Rational Philosophical Anthropology. Dordrecht, Netherlands: Kluwer.

Agassi, Joseph, and Ian C. Jarvie, eds. 1987. Rationality: The Critical View. Dordrecht, Netherlands: Kluwer.

Aron, Raymond. 1967. Durkheim, Pareto, Weber. Vol. 2 of Main Currents in Sociological Thought. Trans. Richard Howard and Helen Weaver. Garden City, NY: Doubleday.

Bacon, Sir Francis. 1620. The Collected Works of Francis Bacon, Volume I Part I, Philosophical Works. London: Routledge, [1879] 1996.

Bendix, Reinhardt. 1970. Embattled Reason: Essays on Social Knowledge. New Brunswick, NJ: Transaction Books.

Bochenski, Joseph M. 1957. Contemporary European Philosophy. Trans. Donald Nicholl and Karl Aschenbrenner. Berkeley: University of California Press.

Boyle, Robert. 1661. “Proëmial Essay” to Certain Physiological Essays. In The Works of Robert Boyle. Vol. 2, eds. Michael Hunter and Edward B. Davis. London: Pickering & Chatto, 1999–2000.

Bunge, Mario. 1996. Finding Philosophy in Social Science. New Haven, CT: Yale University Press.

Durkheim, Émile. 1893. Émile Durkheim on the Division of Labor in Society. Trans. Louis Coser. New York: Macmillan, 1933.

Durkheim, Émile. 1895. The Rules of Sociological Method. Trans. Sarah A. Solovay and John H. Mueller. Chicago: University of Chicago Press, 1938.

Durkheim, Émile. 1912. The Elementary Forms of the Religious Life. Trans. Joseph Ward Swain. London: George Allen & Unwin, 1915.

Durkheim, Émile. 1928. Socialism and Saint-Simon, ed. Alvin W. Gouldner; trans. Charlotte Sattler. Yellow Springs, OH: Antioch Press, 1958.

Durkheim, Émile, and Marcel Mauss. 1903. Primitive Classification. Trans. Rodney Needham. Chicago: University of Chicago Press, 1963.

Hayek, Friedrich von. 1952. The Counter-Revolution of Science: Studies on the Abuse of Reason. New York: Free Press.

Hegel, Georg Friedrich Wilhelm. 1837. Philosophy of History, ed. Eduard Gans; trans. John Sibree. New York: Dover, 1956.

Marx, Karl. 1849. Wage-Labor and Capital, ed. Friedrich Engels; trans. J. L. Joynes. Chicago: C. H. Kerr, 1891.

Marx, Karl. 1859. A Contribution to the Critique of Political Economy. Trans. N. I. Stone. Chicago: C. H. Kerr, 1904.

Marx, Karl. 1865. Wages, Price, and Profit. Moscow: Foreign Languages Publishing House, 1951.

Marx, Karl, and Friedrich Engels. 1848. The Communist Manifesto. Trans. Samuel Moore. New York and London: Verso, 1998.

Mill, John Stuart. 1843. A System of Logic, ed. J. M. Robson. London: Routledge & Kegan Paul, 1974.

Newton, Isaac. 1730. “Query 31.” In his Opticks, 4th ed. (London 1730) New York: Dover, 1952.

Pickering, William S. F., ed. 1975. Durkheim on Religion: A Selection of Readings with Bibliographies. London: Routledge.

Popper, Karl. 1935. The Logic of Scientific Discovery. London: Hutchinson, 1959.

Popper, Karl. 1942–1943. The Poverty of Historicism. London: Routledge, 1957.

Popper, Karl. 1945. The High Tide of Prophesy: Hegel, Marx, and the Aftermath. Vol. 2 of The Open Society and Its Enemies. London: Routledge.

Simmel, Georg. 1950. The Sociology of Georg Simmel, ed. and trans. Kurt H. Wolff. Columbus: Ohio State University Press.

Weber, Max. 1903–1917. The Methodology of the Social Sciences, eds. and trans. Edward A. Shils and Henry A. Finch. New York: Free Press, 1949.

Weber, Max. 1904–1905. The Protestant Ethic and the Spirit of Capitalism. Trans. Talcott Parsons. New York: Scribner, 1930.

Whewell, William. 1847. Philosophy of the Inductive Sciences. 2nd ed. 2 vols. New York: Johnson Reprint, 1967.

Joseph Agassi

Scientific Method

Scientific models

Historical evolution of the scientific method

Scientific thought seeks to make sense of nature. One test of the adequacy of a scientific explanation is its ability to make accurate predictions about future events and observations. Just as the engineer who designs a bridge ensures that it will withstand the forces of nature and use, so the scientist considers the ability of any new scientific model to hold up under scientific scrutiny as new data become available.

Until the seventeenth century, scientific prediction simply amounted to observing the changing events of the world, noting any regularities, and making predictions based upon those regularities. The Irish philosopher and bishop George Berkeley (1685–1753) was the first to rethink this notion of predictability.

Berkeley noted that each person experiences directly only the signals of his or her five senses. An individual can infer that a natural world exists as the source of his sensations, but he or she can never know the natural world directly; one can only know it through one’s senses. In everyday life, people tend to forget that their knowledge of the external world comes to them through their five senses.

The physicists of the nineteenth century described the atom as though they could see it directly. Their descriptions changed as new data arrived, and these physicists had to remind themselves that they were only working with a mental picture built with fragmentary information, not with a direct vision of atomic reality.

Scientific models

In 1913, Niels Bohr used the term model for his published description of the hydrogen atom. This term is now used to characterize theories developed long before Bohr’s time. Essentially, a model implies some structure of ideas and images that is intended to correspond to some physical reality. A partial correspondence is often enough to provide a very useful model, but the intent of creating the model is to make predictions as well as to describe existing data, and all scientific models are ultimately judged by their ability to make correct predictions. The events predicted may be observations, not just experiments: for example, the theory of evolution makes many predictions about what kinds of fossils will be found (transitional forms). When such fossils are found, as they frequently are, an “event” has been correctly predicted by the theory.

There are many types of models. A conceptual model refers to a mental picture of a model that is introspectively present when one thinks about it. A geometrical model refers to diagrams or drawings that are used to describe a model. A mathematical model refers to equations or other relationships that provide quantitative predictions.

It is an interesting fact that if a mathematical model predicts the future accurately, there may be no need for interpretation or visualization of the process described by the mathematical equations. Many mathematical models have more than one interpretation. But the interpretations and visualization of the mathematical model should facilitate the creation of new models.

New models are not constructed from observations of facts and previous models; they are postulated. That is to say that the statements that describe a model are assumed and predictions are made from them. The predictions are checked against the measurements or observations of actual events in nature. If the predictions prove accurate, the model is said to be validated. If the predictions fail, the model is discarded or adjusted until it can make accurate predictions.

The formulation of the scientific model is subject to no limitations in technique; the scientist is at liberty to use any method he can come up with, conscious or unconscious, to develop a model. Validation of the model, however, follows a single, recurrent pattern. Note that this pattern does not constitute a method for making new discoveries in science; rather it provides a way of validating new models after they have been postulated. This method is called the scientific method and is an idealized account—not a fully realistic one—of how science works. In fact, a description of the scientific method is itself a model.

The scientific method (1) postulates a model consistent with existing experimental observations; (2) checks the predictions of this model against further observations or measurements; (3) adjusts or discards the model to agree with new observations or measurements.

The third step leads back to the second, so, in principle, the process continues without end. (Such a process is said to be recursive.) No assumptions are made about the reality of the model. The model that ultimately prevails may be the simplest, most convenient, or most satisfying model; but it will certainly be the one that best explains those problems that scientists have come to regard as most acute.

Paradigms are models that overarch or include a whole way of looking at a scientific field. Sometimes, a new paradigm is sufficiently unprecedented and convincing to attract a group of adherents away from an older paradigm. A new paradigm must explain what is already known better than the paradigm it seeks to replace, while making testable predictions about future observations. A paradigm is thus a theory or explanatory structure from which a coherent tradition of scientific research springs. Examples of such traditions include Ptolemaic astronomy, Copernican astronomy, Aristotelian dynamics, Newtonian dynamics, relativity, evolution, and more.

Paradigms acquire status because they are more successful than their competitors in solving a few problems that scientists have come to regard as acute. Normal science consists of extending the knowledge of those facts that are key to understanding the paradigm, and in further articulating the paradigm itself.

Scientific thought should in principle be cumulative; that is, a new model should be capable of explaining everything the old model did. In some sense the old model may appear to be a special case of the new model. This is particularly clear in the case of Newtonian physics, whose equations are recovered as special cases or approximations of the equations of the next paradigm, quantum mechanics and relativity.

The descriptive phase of normal science involves the acquisition of experimental data. Much of science involves classification of these facts. Classification systems constitute abstract models, and it is often the case that examples are found that do not precisely fit in classification schemes. Whether these anomalies warrant reconstruction of the classification system depends on the consensus of the scientists involved.

Predictions that do not include numbers are called qualitative predictions. Only qualitative predictions can be made from qualitative observations. Predictions that include numbers are called quantitative predictions. Quantitative predictions are often expressed in terms of probabilities, and may contain estimates of the accuracy of the prediction.

Historical evolution of the scientific method

The Greeks constructed a model in which the stars were lights fastened to the inside of a large, hollow sphere (the sky), and the sphere rotated about the Earth as a center. This model predicts that all of the stars will remain fixed in position relative to each other. But certain bright stars were found to wander about the sky. These stars were called planets (from the Greek word for wanderer). The model had to be modified to account for motion of the planets. In Ptolemy’s (AD 90–168) model of the solar system, each planet moves in a small circular orbit, and the center of the small circle moves in a large circle around Earth as center.

Copernicus (1473–1543) assumed the Sun was near the center of a system of circular orbits in which Earth and planets moved with fair regularity. Like many new scientific ideas, Copernicus” idea was initially greeted as nonsense, but over time it eventually took hold. One of the factors that led astronomers to accept Copernicus” model was that Ptolemaic astronomy could not explain a number of astronomical discoveries.

In the case of Copernicus, the problems of calendar design and astrology evoked questions among contemporary scientists. In fact, Copernicus’s theory did not lead directly to any improvement in the calendar. Copernicus’s theory suggested that the planets should be like Earth, that Venus should show phases, and that the universe should be vastly larger than previously supposed. Sixty years after Copernicus’s death, when the telescope suddenly displayed mountains on the moon, the phases of Venus, and an immense number of previously unsuspected stars, the new theory received a great many converts, particularly from non-astronomers.

The change from the Ptolemaic model to Copernicus’s model is a particularly famous case of a paradigm change. As the Ptolemaic system evolved between 200 BC and AD 200, it eventually became highly successful in predicting changing positions of the stars and planets. No other ancient system had performed as well. In fact Ptolemaic astronomy is still used today as an engineering approximation. Ptolemy’s predictions for the planets were as good as Copernicus’s. But with respect to planetary position and precession of the equinoxes, the predictions made with Ptolemy’s model were not quite consistent with the best available observations. Given a particular inconsistency, astronomers for many centuries were satisfied to make minor adjustments in the Ptolemaic model to account for it. But eventually, it became

KEY TERMS

Inference —The action of drawing a conclusion from data or premises. Compare with deduction, an inference from the general to the particular.

Normal science —Scientific activity involving the extension of knowledge of facts key to understanding a paradigm, and in further articulating the paradigm itself. Most scientific activity falls under the category of normal science.

Paradigm —A model that is sufficiently unprecedented to attract an enduring group of adherents away from competing scientific models. A paradigm must be sufficiently open-ended to leave many problems for its adherents to solve. The paradigm is thus a theory from which springs a coherent tradition of scientific research. Examples of such traditions include Ptolemaic astronomy, Copernican astronomy, Aristotelian dynamics, Newtonian dynamics, etc.

Postulate —Something assumed as a basis of reasoning.

Qualitative prediction —A prediction that does not include numbers. Only qualitative predictions can be made from qualitative observations.

Quantitative prediction —A prediction that includes numbers. Quantitative predictions are often expressed in terms of probabilities, and may contain estimates of the accuracy of the prediction.

apparent that the web of complexity resulting from the minor adjustments was increasing more rapidly than the accuracy, and a discrepancy corrected in one place was likely to show up in another place.

Tycho Brahe (1546–1601) made a lifelong study of the planets. In the course of doing so he acquired the data needed to demonstrate certain shortcomings in Copernicus’s model. But it was left to Johannes Kepler (1571-1630), using Brahe’s data after the latter’s death, to come up with a set of laws consistent with the data. It is worth noting that the quantitative superiority of Kepler’s astronomical tables to those computed from the Ptolemaic theory was a major factor in the conversion of many astronomers to Copernicanism.

In fact, simple quantitative telescopic observations indicate that the planets do not quite obey Kepler’s laws, and Isaac Newton (1642–1727) proposed a theory that shows why they should not. To redefine Kepler’s laws, Newton had to neglect all gravitational attraction except that between individual planets and the sun. Since planets also attract each other, only approximate agreement between Kepler’s laws and telescopic observation could be expected.

Newton thus generalized Kepler’s laws in the sense that they could now describe the motion of any object moving in any sort of path. It is now known that objects moving almost as fast as the speed of light require a modification of Newton’s laws, but such objects were unknown in Newton’s day.

Newton’s first law asserts that a body at rest remains at rest unless acted upon by an external force. His second law states quantitatively what happens when a force is applied to an object. The third law states that if a body A exerts a force F on body B, then body B exerts on body A, a force that is equal in magnitude but opposite in direction to force F. Newton’s fourth law is his law of gravitational attraction.

Newton’s success in predicting quantitative astronomical observations was probably the single most important factor leading to acceptance of his theory over more reasonable but uniformly qualitative competitors.

It is often pointed out that Newton’s model includes Kepler’s laws as a special case. This permits scientists to say they understand Kepler’s model as a special case of Newton’s model. But when one considers the case of Newton’s laws and relativistic theory, the special case argument does not hold up. Newton’s laws can only be derived from Albert Einstein’s (1876-1955) relativistic theory if the laws are reinterpreted in a way that would have only been possible after Einstein’s work.

The variables and parameters that in Einstein’s theory represent spatial position, time, mass, etc. appear in Newton’s theory, and there still represent space, time, and mass. But the physical natures of the Einsteinian concepts differ from those of the Newtonian model. In Newtonian theory, mass is conserved; in Einstein’s theory, mass is convertible with energy. The two ideas converge only at low velocities, but even then they are not exactly the same.

Scientific theories are often felt to be better than their predecessors because they are better instruments for solving puzzles and problems, but also for their superior abilities to represent what nature is really like. In this sense, it is often felt that successive theories come ever closer to representing truth, or what is “really there.” Thomas Kuhn, the historian of science whose writings include the seminal book The Structure of Scientific Revolution (1962), found this idea implausible. He pointed out that although Newton’s mechanics improve on Ptolemy’s mechanics and Einstein’s mechanics improve on Newton’s as instruments for puzzle-solving, there does not appear to be any coherent direction of development. In some important respects, Kuhn has argued, Einstein’s general theory of relativity is closer to early Greek ideas than to Newton’s.

See also Geocentric theory; Heliocentric theory; Laws of motion; Relativity, general; Relativity, special.

Randall Frost

Scientific method

Scientific thought aims to make correct predictions about events in nature. Although the predictive nature of scientific thought may not at first always be apparent, a little reflection usually reveals the predictive nature of any scientific activity. Just as the engineer who designs a bridge ensures that it will withstand the forces of nature, so the scientist considers the ability of any new scientific model to hold up under scientific scrutiny as new scientific data become available.

It is often said that the scientist attempts to understand nature. But ultimately, understanding something means being able to predict its behavior . Scientists therefore usually agree that events are not understandable unless they are predictable. Although the word science describes many activities, the notion of prediction or predictability is always implied when the word science is used.

Until the seventeenth century, scientific prediction simply amounted to observing the changing events of the world, noting any irregularities, and making predictions based upon those regularities. The Irish philosopher and bishop George Berkeley (1685-1753) was the first to rethink this notion of predictability.

Berkeley noted that each person experiences directly only the signals of his or her five senses. An individual can infer that a natural world exists as the source of his sensations, but he or she can never know the natural world directly. One can only know it through one's senses. In everyday life people tend to forget that their knowledge of the external world comes to them through their five senses.

The physicists of the nineteenth century described the atom as though they could see it directly. Their descriptions changed constantly as new data arrived, and these physicists had to remind themselves that they were only working with a mental picture built with fragmentary information.

Scientific models

In 1913, Niels Bohr used the term model for his published description of the hydrogen atom. This term is now used to characterize theories developed long before Bohr's time. Essentially, a model implies some correspondence between the model itself and its object. A single correspondence is often enough to provide a very useful model, but it should never be forgotten that the intent of creating the model is to make predictions.

There are many types of models. A conceptual model refers to a mental picture of a model that is introspectively present when one thinks about it. A geometrical model refers to diagrams or drawings that are used to describe a model. A mathematical model refers to equations or other relationships that provide quantitative predictions.

It is an interesting fact that if a mathematical model predicts the future accurately, there may be no need for interpretation or visualization of the process described by the mathematical equations. Many mathematical models have more than one interpretation. But the interpretations and visualization of the mathematical model should facilitate the creation of new models.

New models are not constructed from observations of facts and previous models; they are postulated. That is to say that the statements that describe a model are assumed and predictions are made from them. The predictions are checked against the measurements or observations of actual events in nature. If the predictions prove accurate, the model is said to be validated. If the predictions fail, the model is discarded or adjusted until it can make accurate predictions.

The formulation of the scientific model is subject to no limitations in technique; the scientist is at liberty to use any method he can come up with, conscious or unconscious, to develop a model. Validation of the model, however, follows a single, recurrent pattern. Note that this pattern does not constitute a method for making new discoveries in science; rather it provides a way of validating new models after they have been postulated. This method is called the scientific method.

The scientific method: 1) postulates a model consistent with existing experimental observations; 2) checks the predictions of this model against further observations or measurements; 3) adjusts or discards the model to agree with new observations or measurements.

The third step leads back to the second, so, in principle, the process continues without end. (Such a process is said to be recursive.) No assumptions are made about the reality of the model. The model that ultimately prevails may be the simplest, most convenient, or most satisfying model; but it will certainly be the one that best explains those problems that scientists have come to regard as most acute.

Paradigms are models that are sufficiently unprecedented to attract an enduring group of adherents away from competing scientific models. A paradigm must be sufficiently open-ended to leave many problems for its adherents to solve. The paradigm is thus a theory from which springs a coherent tradition of scientific research. Examples of such traditions include Ptolemaic astronomy , Copernican astronomy, Aristotelian dynamics, Newtonian dynamics, etc.

To be accepted as a paradigm, a model must be better than its competitors, but it need not and cannot explain all the facts with which it is confronted. Paradigms acquire status because they are more successful than their competitors in solving a few problems that scientists have come to regard as acute. Normal science consists of extending the knowledge of those facts that are key to understanding the paradigm, and in further articulating the paradigm itself.

Scientific thought should in principle be cumulative; a new model should be capable of explaining everything the old model did. In some sense the old model may appear to be a special case of the new model. In fact, whether this is so seems to be open to debate.

The descriptive phase of normal science involves the acquisition of experimental data. Much of science involves classification of these facts. Classification systems constitute abstract models, and it is often the case that examples are found that do not precisely fit in classification schemes. Whether these anomalies warrant reconstruction of the classification system depends on the consensus of the scientists involved.

Predictions that do not include numbers are called qualitative predictions. Only qualitative predictions can be made from qualitative observations. Predictions that include numbers are called quantitative predictions. Quantitative predictions are often expressed in terms of probabilities, and may contain estimates of the accuracy of the prediction.

Historical evolution of the scientific method

The Greeks constructed a model in which the stars were lights fastened to the inside of a large, hollow sphere (the sky), and the sphere rotated about the Earth as a center. This model predicts that all of the stars will remain fixed in position relative to each other. But certain bright stars were found to wander about the sky. These stars were called planets (from the Greek word for wanderer). The model had to be modified to account for motion of the planets. In Ptolemy's (a.d. 90-168) model of the solar system , each planet moves in a small circular orbit , and the center of the small circle moves in a large circle around the Earth as center.

Copernicus (1473-1543) assumed the Sun was near the center of a system of circular orbits in which the Earth and planets moved with fair regularity. Like many new scientific ideas, Copernicus' idea was initially greeted as nonsense, but over time it eventually took hold. One of the factors that led astronomers to accept Copernicus' model was that Ptolemaic astronomy could not explain a number of astronomical discoveries.

In the case of Copernicus, the problems of calendar design and astrology evoked questions among contemporary scientists. In fact, Copernicus's theory did not lead directly to any improvement in the calendar. Copernicus's theory suggested that the planets should be like the earth, that Venus should show phases, and that the universe should be vastly larger than previously supposed. Sixty years after Copernicus's death, when the telescope suddenly displayed mountains on the moon , the phases of Venus, and an immense number of previously unsuspected stars, the new theory received a great many converts, particularly from non-astronomers.

The change from the Ptolemaic model to Copernicus's model is a particularly famous case of a paradigm change. As the Ptolemaic system evolved between 200 b.c. and 200 a.d., it eventually became highly successful in predicting changing positions of the stars and planets. No other ancient system had performed as well. In fact the Ptolemaic astronomy is still used today as an engineering approximation . Ptolemy's predictions for the planets were as good as Copernicus's. But with respect to planetary position and precession of the equinoxes , the predictions made with Ptolemy's model were not quite consistent with the best available observations. Given a particular inconsistency, astronomers for many centuries were satisfied to make minor adjustments in the Ptolemaic model to account for it. But eventually, it became apparent that the web of complexity resulting from the minor adjustments was increasing more rapidly than the accuracy, and a discrepancy corrected in one place was likely to show up in another place.

Tycho Brahe (1546-1601) made a lifelong study of the planets. In the course of doing so he acquired the data needed to demonstrate certain shortcomings in Copernicus's model. But it was left to Johannes Kepler (1571-1630), using Brahe's data after the latter's death, to come up with a set of laws consistent with the data. It is worth noting that the quantitative superiority of Kepler's astronomical tables to those computed from the Ptolemaic theory was a major factor in the conversion of many astronomers to Copernicanism.

In fact, simple quantitative telescopic observations indicate that the planets do not quite obey Kepler's laws , and Isaac Newton (1642-1727) proposed a theory that shows why they should not. To redefine Kepler's laws, Newton had to neglect all gravitational attraction except that between individual planets and the sun. Since planets also attract each other, only approximate agreement between Kepler's laws and telescopic observation could be expected.

Newton thus generalized Kepler's laws in the sense that they could now describe the motion of any object moving in any sort of path. It is now known that objects moving almost as fast as the speed of light require a modification of Newton's laws, but such objects were unknown in Newton's day.

Newton's first law asserts that a body at rest remains at rest unless acted upon by an external force . His second law states quantitatively what happens when a force is applied to an object. The third law states that if a body A exerts a force F on body B, then body B exerts on body A, a force that is equal in magnitude but opposite in direction to force F. Newton's fourth law is his law of gravitational attraction.

Newton's success in predicting quantitative astronomical observations was probably the single most important factor leading to acceptance of his theory over more reasonable but uniformly qualitative competitors.

It is often pointed out that Newton's model includes Kepler's laws as a special case. This permits scientists to say they understand Kepler's model as a special case of Newton's model. But when one considers the case of Newton's laws and relativistic theory, the special case argument does not hold up. Newton's laws can only be derived from Albert Einstein's (1876-1955) relativistic theory if the laws are reinterpreted in a way that would have only been possible after Einstein's work.

The variables and parameters that in Einstein's theory represent spatial position, time, mass , etc. appear in Newton's theory, and there still represent space , time, and mass. But the physical natures of the Einsteinian concepts differ from those of the Newtonian model. In Newtonian theory, mass is conserved; in Einstein's theory, mass is convertible with energy . The two ideas converge only at low velocities, but even then they are not exactly the same.

Scientific theories are often felt to be better than their predecessors because they are better instruments for solving puzzles and problems, but also for their superior abilities to represent what nature is really like. In this sense, it is often felt that successive theories come ever closer to representing truth, or what is "really there." Thomas Kuhn, the historian of science whose writings include the seminal book The Structure of Scientific Revolution (1962), found this idea implausible. He pointed out that although Newton's mechanics improve on Ptolemy's mechanics, and Einstein's mechanics improve on Newton's as instruments for puzzle-solving, there does not appear to be any coherent direction of development. In some important respects, Kuhn has argued, Einstein's general theory of relativity is closer to early Greek ideas than relativistic or ancient Greek ideas are to Newton's.

See also Geocentric theory; Heliocentric theory; Laws of motion; Relativity, general; Relativity, special.

Randall Frost

KEY TERMS

Inference

—The action of drawing a conclusion from data or premises. Compare with deduction, an inference from the general to the particular.

Normal science

—Scientific activity involving the extension of knowledge of facts key to understanding a paradigm, and in further articulating the paradigm itself. Most scientific activity falls under the category of normal science.

Paradigm

—A model that is sufficiently unprecedented to attract an enduring group of adherents away from competing scientific models. A paradigm must be sufficiently open-ended to leave many problems for its adherents to solve.The paradigm is thus a theory from which springs a coherent tradition of scientific research. Examples of such traditions include Ptolemaic astronomy, Copernican astronomy, Aristotelian dynamics, Newtonian dynamics, etc.

Postulate

—Something assumed as a basis of reasoning.

Qualitative prediction

—A prediction that does not include numbers. Only qualitative predictions can be made from qualitative observations.

Quantitative prediction

—A prediction that includes numbers. Quantitative predictions are often expressed in terms of probabilities, and may contain estimates of the accuracy of the prediction.