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
|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”. 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 moontest 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”.
This rule was added to justify treating universal gravity as an established scientific fact, not withstanding 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).