Note (1/14/2004): I recently rediscovered these lecture notes from early in my teaching career, probably early 1980's. I have made only a few small changes to them. I do not claim any great originality for them. There is a good possibility that some of them were based on lectures of my own professors in the Graduate School at the University of Minnesota, especially Prof. Douglas Lewis, for whom I may have been a teaching assistant during the 1970's. These notes should not be directly quoted in scholarly work. Confirmation of the ideas contained in these notes may be sought in expert studies such as these: E. A. Burtt, The Metaphysical Foundations of Modern Science (Anchor, 1924); A. Koyre, From the Closed to the Open Universe; and Thomas Kuhn, The Copernican Revolution (Modern Library, 1957). --J. G.
Main points about the developments in the sciences1. Medieval Worldview and Ptolemaic Astronomy
2. Copernicus' Astronomy and His Motivation
3. Effects of Copernicus' Work
a. Astronomers are led to look for unnoticed phenomena
b. Changes in the conception of physical motions
4. Galileo's vs. Aristotelian physics,
The Medieval Worldview and Ptolemaic Astronomy
According to Ptolemy (2nd c. A.D.), the Earth is stationary. There are eight concentric spheres, of different radii. Each sphere has the center of the earth as its center. Each sphere rotates. The Sun, Moon, and what we call the planets are each attached, directly or indirectly, to one sphere. The spheres are in this order from the Earth: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn). Beyond the sphere of Saturn is the sphere of so-called fixed stars. All the (fixed) stars rotate together because they are attached to the same sphere.
For each planet, there is a deferrent, the main circle, and an epicycle, attached to the deferrent. Epicycles tended to be piled upon epicycles -- to fit the data,
The system was fairly accurate at the beginning. Changes were made over the centuries to refine it:
Two additional devices were eventually introduced: One was the eccentric, i.e., the distance off-center from the earth: One had to calculate distances from slightly off-center from the earth -- in different directions for the different planets. The other was the equant, a complexity explained in this article on the Ptolemaic System. See also Ptolemaic Astronomy.
The Ptolemaic theory came to be embedded in a general cosmology that can be traced by to Aristotle.
There were two kinds of stuff in the universe, terrestrial and celestial. Terrestrial matter was found on earth; it was heavy, it had weight, it could be moulded; it was imperfect and corruptible, subject to change; by nature it was at rest.
By contrast, celestial matter was found in the heavens, from the sphere of the moon and farther out from the center of the earth. It was light, weightless, not malleable. It was perfect and incorruptible, by nature in motion. It moves only in a circle, with constant velocity.
In this view, Earth is the sphere of corruption and evil. The heavens were the abode of goodness, closest to God (not in a physical sense, but in the degree of perfection). Moral and cosmological notions coincided.
There were two different sets of laws of motion, one for the heavens, one for the earth.
Ptolemaic astronomy was a kind of "confirmation" of the medieval worldview.
Copernicus' Astronomy and His Motivation
In his Revolutions of Heavenly Bodies (1545), Nicholaus Copernicus tries to impale the Ptolemaic astronomers on the horns of a dilemma. Either they employ only the device of concentric circles or they use in addition other devices such as the eccentric. If they employ only concentric circles, they are unable to get completely accurate predictions. If they use the additional devices, they are able to get accurate predictions but are able to do so only by procedures which produce a hybrid monster.
Copernicus wanted to construct a model that (i) did not violate the principle of circular constant motion and (ii) gave accurate predictions.
In the heliocentric model of Copernicus, the Sun is at the center. There are seven concentric spheres again, starting (near the Sun), with Mercury on the first, Venus on the second, then Earth, Mars, Jupiter, and Saturn. Once again, the sphere of fixed stars is the outermost sphere. There was also a sphere rotating around the Earth to which the Moon was attached.
The Copernican system required epicycles, though fewer than the Ptolemaic, and it did not require the odd devices such as the eccentric. It was more complicated to use than the Ptolemaic system because astronomers had to recalculate distances from the earth in terms of distances from the sun and the sun's distance from the earth. These complications made the Copernican system so complex for practical purposes that in the 20th century navigators still used the Ptolemaic model to do their calculations.
Copernicus' system attributes two motions to the earth: annual orbit and daily rotation. The heavens now become fixed. Under the Ptolemaic system, the distance from the heavens to the earth was thought to be finite, even small. Now it becomes possible to conceive that the heavens are infinitely distant. Copernicus himself did not draw this conclusion. Before long, however, somebody else did. In 1600 Giordano Bruno was burnt at the stake for arguing that the heavens were infinitely distant.
Copernicus' theory of the orbital motion of the earth placed the "corruptible" earth right in the middle of the heavens. (Recall that at this time the still dominant Aristotelian view held that they heavens were "incorruptible.") At the time this implication of the Copernican view was most unacceptable for the intellectual authorities.
The opponents of Copernicus' view objected that according to his theory the fixed stars must be closer to us at some times than at others. Hence we ought to notice a shift in the relative distances of stars from each other (as observed from changing location of the earth). This is called the "Problem of Parallax." Copernicus said that the reason one does not observe parallax is that the ratio of distance between the earth and sun to the distance between the sun and the fixed stars is almost infinitesimally small.
The anti-Copernicans argued that this would mean a huge gap between Saturn and the fixed stars, and what possible reason could God have had for leaving such a gap?
Copernicus was trying to solve a problem within the framework of medieval metaphysics. He wanted to show that you could get perfect accuracy and ascribe only perfect circular motion to the earth and celestial bodies. But ascribing motion to the earth violates the medieval physics, since it inserts the earth into the domain of the incorruptible. Hence there is an inconsistency in the project of Copernicus.
Other objections to this project were:
i) If you throw an object straight up and the earth is moving, then the object ought to come down in a different place. It doesn't.
ii) If the earth were moving through the heavens, there ought to be a great wind. We do not seem to experience this wind.
Most attempts at refuting Copernicus involve appeal to the senses. The Ptolemaic system is closer to sense-experience and observation, This is somewhat ironical, when you consider the traditional claim of modern science to be empirical science. In fact, modern science involves a greater degree of idealization than premodern natural philosophy. We tend not to notice this because modern science is more familiar to us.
Effects of Copernicus' Work
Astronomers Look for Unnoticed Phenomena
Familiar with Copernicus' work, Galileo Galilei decided to use it as a lever against medieval physics as a whole. Look at the Moon, he argued; you'll see mountains and seas there.
In 1607 Johannes Kepler claimed he saw the birth of a star. This was not supposed to be possible since coming to be and passing away, or as they are sometimes called, generation and corruption, supposed pertains to earthly matter alone. In 1611 Galileo claimed he'd observed moons of Jupiter. This suggested again that the Earth, which has a moon, is fundamentally the same sort of thing as the planets.
Galileo answers the medieval view that the mistake is in their assumption that there are two types of matter, not in the Copernican hypothesis of the earth's motion through the "celestial" realm. The basic division among bodies should not be between terrestial and celestial bodies, but between dark and self-illuminating bodies.
Copernicus' thesis that the earth moves among the heavenly bodies was the key move against the old system. Galileo's physics drew its consequences. Kepler's theory of elliptical orbits (proposed in 1609) refined the original Copernican version and made it conform more closely to observations.
The Catholic Church put Copernicus' work on the Index of Prohibited Books for understandable reasons. Medieval science dovetailed with religious and metaphysical conceptions. Faith was reinforced by "science," or "natural philosophy," as it was then called. Logically, the chief tenets of Christianity and the chief tenets of medieval science are independent, but in the Middle Ages and Renaissance there was a psychological connection between the two.
What the Catholic Church feared would happen did in fact happen. In the next 200 years belief in the literal truth of the tenets of Christianity drastically declined at least among intellectuals.
According to Francis Bacon, scripture prohibits prying into divine mysteries, not the investigation of natural phenomena. The latter will put down superstition, he says, and thus is an ally of, and should be supported by, religion. As a matter of historical fact, natural science tended to undermine established religions.
Kepler's observation of the birth of a star (1607) hit the intellectuals of the time as a shocker. Thomas Kuhn writes that during the hegemony of Ptolemaic astronomy in Europe, no new stars were reported, though European astronomers were generally careful observers. (During the same period, Chinese astronomers reported new stars.)
Galileo observed sunspots, i.e. blemishes, in what was supposed to be perfect, celestial matter. He also observed the movements of a comet, concluding that it was not moving between the Earth and the Moon, as medieval science had had it. The controversial point here is that the imperfect character of the comet -- its erratic path when compared with those of the planets and stars -- seemed to indicate that it was related to the imperfect matter of the Earth. Galileo's conclusion conflicted with this scheme.
We should not think the Ptolemaic astronomers were the only faction at this time to depend upon what we would regard as fanciful constructions to bolster their viewpoint. The tendency that leads to modern science has as part of its ancestry number mysticism, a tradition which goes back to the ancient Pythagoreans. Kepler believed in the harmony of the spheres, etc.
Changes in the conception of physical motions
According to the Aristotelian physics of the Middle Ages, terrestial objects were by nature at rest; celestial objects were by nature in motion. Terrestial bodies experienced two kinds of motion: (i) natural, e.g. falling (caused by the body's own heaviness), and (ii) unnatural, e.g. being thrown (there is an external cause, the thrower). For Aristotle, all motion is change, and an agent or efficient cause is required to cause the change.
A suspended object, when dropped, moves of its own accord (desire or conatus) towards the center of the cosmos.
In the fourteenth century there was a debate about Aristotle's theory of motion, Unnatural motion requires an external agent to come into contact with the object. How is it that the object nevertheless continues in motion after the contact is broken off? Aristotle's answer was that air continues to push the object.
A vacuum is created behind the object; because nature abhores a vacuum, air rushes in and propels the object forward. Modern physics explains the same phenomenon by the quite different notion of the inertia of bodies.
According to the Aristotelians, the heavier the body, the greater the conatus to get to the center of the comsos, and the faster the fall. Analyzing the course of a projectile, they said that the first, or forward, component of the projectile's motion was unnatural, the downward component was natural.
Galileo (1564-1642) threw out the notion of natural motion towards some specific place. According to him, and to modern physics since, all bodies fall with equal acceleration regardless of weight.
For Galileo, forward velocity is constant; downward motion or velocity increases with constant acceleration. After the initial push of the projectile, it required no agent to continue moving. Forward velocity is inertial. The result is that forward motion on Earth, like celestial motion, required no external agents. Once again, the new physics broke down the once-separate domains of heavenly and terrestial physics.
Galileo still believed that inertial motion was circular, Descartes corrected Galileo, holding (as modern physics does) that inertial motion is inherently rectilinear. But why then were planetary motions elliptical? Several decades later Newton will propose the idea of gravitational force to explain this phenomenon.
For Galileo the path of a projectile is parabolic--it begins to fall at the beginning of the flight. The Aristotelians ruled out fall of the projectile at the beginning of the flight. It was theoretically possible to test this difference. But the tests were imprecise and inconclusive. The Aristotelians fell back on a priori arguments.
Early Modern Physics vs. Aristotelian Physics
Galileo developed a general approach to physics to counter the physics of the Aristotelians, The key notion is "Nature is in her essence mathematical."
The Aristotelians refuted Galileo by appealing to their own metphysics. In 1625 Galileo wrote "The Assayer," in which he attacked his Aristotelian opponents rather ruthlessly. Galileo attacks the Aristotelian reliance on authority. One must learn to comprehend not textual authorities but the book of nature. One must learn its language, which is mathematics; i.e. one must understand that the universe is essentially mathematical before one can go about to investigate it.In Sarsi [his Aristotelian opponent] I seem to discern the firm belief that in philosophizing one must support oneself upon the opinion of some celebrated author, as if our minds ought to remain completely sterile and barren unless wedded to the reasoning of some other person. Possibly he thinks that philosophy is a book of fiction . . . productions in which the least important thing is whether what is written there is true. Well, ... that is not how matters stand. Philosophy is written in this grand book of the universe, which stands continually open to our gaze. But the book cannot be understood unless one learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth.
-- "The Assayer," in R. H. Popkin, ed., The Philosophy of the 16th and 17th Centuries (New York: The Free Press, 1966), 65.
All advocates of the new science tended to hold that the perceptions of the senses, taken by themselves, were inadequate, The senses must be corrected (a) by the use of instruments like telescopes and microscopes and (b) by the use of conceptual aids-a proper conception of the sort of thing one is investigating, which perceptions are relevant, which are irrelevant.
Francis Bacon, more empiricist than Galileo and Descartes, thought the senses, properly corrected, could give rise to knowledge, As we shall see, Descartes distrusted the senses, although even he held that, properly interpreted, they could add to the less general (i.e., nonfoundational) parts of scientific knowledge.
Galileo and Descartes held that sensory elements--colors, sounds, tastes, smells--are the consequence of actions of geometrical physical elements on other geometrical physical elements. Colors, sounds, tastes, smells, etc. are mere states of consciousness somehow arising when the shapes and sizes of external things collide with the shapes and sizes of the sense-organs.
Cf. Galileo p. 10 in Ariew and Watkins, eds., Modern Philosophy. He distinguishes between those properties which can be dealt with mathematically and geometrically, regarding them as real, and those qualities which are produced in the consciousness by impact of elements of the real world upon each other. (The real, quantifiable properties are later called "primary qualities," those produced only in consciousness are later called "secondary qualities.")
Descartes too held the primary-secondary quality distinction. He also thought that the senses are not strictly speaking a means of acquiring knowledge at all. The thinker must withdraw his attention from the objects of sensation, according to Descartes.