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 Nicholas 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 ( 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 ( 1992). He later arrived at his harmonic rule (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 ( 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 (  1967). Galileo’s study of gravity faced the challenge that due to 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 (  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 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 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, Rule 1. No more causes of natural things should be admitted than are both true and sufficient to explain their phenomena. ( 1999, 794) Rule 2. Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same. (795),
endorse this inference. Newton argues that all bodies gravitate toward each planet with weights proportional to their masses. He adduces a number of phenomena which 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 and 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, Rule 3. 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. (795) supports 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 whatever. Newton’s fourth rule, Rule 4. In experimental philosophy propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses until yet other phenomena make such propositions either more exact or liable to exceptions. (796), 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 4, a mere hypothesis is an alternative that does not realize this ideal of empirical success sufficiently to count as a serious rival. Rule 4 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 (Will 1986, 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).