Chapter 10
A Model of Critical Thinking?
Learning from Galileo
From prehistoric times until the beginning of the sixteenth century, almost all scientists and philosophers believed that the Earth stands still at the center of the universe and all heavenly bodies revolve around it. By the end of the seventeenth century, most scientists and philosophers had come to believe that the Earth is the third planet circling the Sun once a year and spinning around its own axis once a day. The transition was a slow, difficult, and controversial process. We may fix its beginning with the publication in 1543 of Nicolaus Copernicus’s book On the Revolutions of the Heavenly Spheres, and its completion with the publication in 1687 of Isaac Newton’s Mathematical Principles of Natural Philosophy.
The discovery that the Earth moves and is not situated at the center of the universe involved not only key astronomical and cosmological facts, but was interwoven with the discovery of the most basic laws of nature and principles of physics: the law of inertia, the relation between force and acceleration, the law of action and reaction, and the principle of universal gravitation. It was also connected with the clarification and improved understanding of key principles of scientific method. It represents, therefore, without a doubt the most significant breakthrough in the whole history of science. Accordingly, the series of developments that started with Copernicus in 1543 and ended with Newton in 1687 is sometimes labeled the Scientific Revolution.
More generally, it would perhaps be no exaggeration to say that this transition represents the most important intellectual transformation in human history.1 One reason for this involves the world-wide repercussions of the Scientific Revolution itself: science seems to be the only cultural force that has managed to penetrate and dominate human societies and cultures in all parts of the Earth. Another reason involves the broad interdisciplinary impact of the transition from a geocentric to a geokinetic world view, which had profound effects not only on the many branches of science, but also on philosophy, theology, religion, art, literature, technology, industry, and commerce; indeed, it changed mankind’s self-image in general. We may thus also call this transition the Copernican Revolution, if we want a label that leaves open its broad ramifications outside science; this label also gives due credit to the one thinker whose contribution initiated the process.
As we have seen, Galileo made essential and crucial contributions to the Copernican Revolution. His trial and the original Galileo affair hinged precisely on the key scientific claims of the Copernican world view and the corresponding methodological issues. So it is only natural to try to derive from these events general lessons about scientific method, critical thinking, and human rationality. One would thereby be using Galileo as a kind of model. Indeed, scientists like Isaac Newton, Albert Einstein, and Stephen Hawking have tried to derive such methodological inspiration from the Galilean model; and the same has been done by philosophers like David Hume, Immanuel Kant, and José Ortega y Gasset.2
Fallibility and Reasonableness
One of the things that makes the Copernican Revolution so relevant to human rationality stems from the fact that it involves some beliefs which today are known with certainty to be false and incorrect, and others which are now established with equal conclusiveness as being absolutely true and correct. No sane person today would question the fact that the Earth moves. If human knowledge encompasses any item of information, then the Earth’s motion is surely one such. Conversely, if we know anything to be false, it is the idea that the Earth stands still at the center of the universe.
These epistemological facts have two sets of implications that point in opposite directions. On the one hand, there are positive lessons to be drawn. One is that knowledge is possible because it is actual, and it is actual because we know at least one thing, namely that the Earth moves and is not standing still at the center of the universe. Another positive lesson is that progress is possible because the Copernican Revolution is an instance of it; and this is so because the result was to replace ignorance by knowledge in regard to the question of the location and the behavior of the Earth in the universe.
However, there are also lessons that might be called negative, and these are the ones that point more explicitly in the direction of human rationality. To see this, we must focus on the fact that for thousands of years, until relatively recently in human history, almost everybody was wrong about a very fundamental matter; and this included scientists and philosophers, the supposed experts. So it is possible for everyone to be wrong, or at least for everyone to be wrong for some time, and even for a long time; for that was certainly the case in regard to the motion of the Earth up until the time of the Copernican Revolution.
This lesson can give encouragement to would-be critics, no matter how radical; it is possible they may be the only persons to see the truth about the topic in question. Be that as it may, the point is that it is always possible that almost everyone is wrong about almost anything. But this is just one side of the lesson relevant to human rationality, the one that concerns the element of what may be called criticism or fallibility. There is another element, which we may call reasoning or reasonableness.
If we do not neglect the element of reasonableness, then we are led to ask the following about the Copernican Revolution. Although subsequently found to be factually wrong in the content of their belief, were pre-Copernicans reasonable or unreasonable in holding their incorrect belief? In other words, was their reasoning sound or unsound?
In fact, the reasoning of the pre-Copernicans in believing that the Earth stands still at the center of the universe was essentially correct. We have already seen the many arguments for the geostatic view and against Copernicanism. So the Copernican Revolution does not demonstrate that it is possible for everyone to be unreasonable. On the contrary, it suggests that at the level of reasoning, humankind is essentially reasonable. Another lesson of the Copernican Revolution is, then, that it is possible for almost everybody to hold a false belief, but not for almost everyone to be unreasonable.
At this point some people would begin to despair about how the transition to a geokinetic view was ever possible, and they may think that the transition was itself unreasonable or irrational. This conclusion does not follow, for at least three reasons. First, the reasonableness of the arguments against the Earth’s motion does not mean that they were perfectly right or totally correct; it was quite proper to look for their weak points. Second, the situation was not static, but evolved when new discoveries were made. And third, although the criticism of opposite arguments that are reasonable is difficult, it can be done in a fair-minded way. We’ll consider each of these points below.
Reasoning and the New Physics
As we have seen, Galileo was at first primarily interested in physics and mechanics, and was working on a research program designed to understand in general how bodies move. He was critical of the ancient physics of Aristotle and was developing a new theory of motion more in line with the work of another ancient Greek—Archimedes. Galileo was aware of Copernicus’s new argument, but felt its insufficiency and the greater power of the many anti-Copernican and pro-geostatic arguments. He was initially attracted to the Copernican theory because its key geokinetic hypothesis was more in accordance with the new physics he was developing. In fact, his new physics provided him with an effective criticism of the mechanical objections to the Earth’s motion, and with some physical evidence in its favor. The connection can be seen most clearly and most simply for the case of the vertical fall objection.
Recall that the vertical fall objection argued that the Earth cannot rotate because on a rotating Earth freely falling bodies would have no reason to keep up with the Earth’s motion, and hence during free fall they would be left behind; this in turn means that they would be falling in a slanted direction and not vertically; but it is obvious that they do fall vertically. Here the last step in reasoning can be reconstructed as an instance of denying the consequent. This is the argument-form consisting of two premises and one conclusion, such that one premise (called the major premise) is a conditional (“if–then”) proposition, the other premise (called the minor premise) denies the consequent (“then”) clause, and the conclusion denies the antecedent (“if”) clause:
Galileo begins his critique by asking us to focus our attention on the meaning of the proposition that bodies fall vertically. What does it mean? What is meant by vertical fall? Does it mean fall from the terrestrial point where the body is released to the point on the Earth’s surface directly below, such as the motion from the top to the base of a tower? Or does vertical fall mean fall along the straight line in absolute space going from the point of release to the center of the Earth? In other words, does vertical fall mean fall perpendicular to the Earth’s surface as viewed by a terrestrial observer (standing on the Earth’s surface), or as viewed by an extraterrestrial observer (looking at the whole globe from a fixed point at a distance)? Let us call the first apparent or relative vertical fall, and the second actual or absolute vertical fall. These are indeed different.
To understand this difference, consider Figure 21. The semicircles on the left side represent portions of the Earth’s equator, and the structures labeled AB and A´B´ represent towers on the Earth’s surface. The parts of the figure on the right side are simply highly magnified representations of the situations on the left, so that the Earth’s surface appears flat because the distance involved (BB´) is very small. Figure 21a represents a motionless Earth, whereas Figures 21b and 21c represent the Earth undergoing axial rotation from west to east (or clockwise), as suggested by the arrows. Figures 21b and 21c show two different positions of the tower: the unprimed position (AB) represents the tower’s position at the beginning of the experiment of dropping a rock from the top of a tower and letting it fall freely; the primed position (A´B´) represents the tower’s position at the end of the experiment when the fallen rock has reached the ground. The solid lines represent apparent vertical fall, and the dotted lines actual vertical fall. The lines (whether solid or dotted) between towers are drawn both as straight slanted lines and as parabolic slanted lines; here the main point to note is that they are both slanted, and although the parabolic representation is more accurate, this refinement plays no role in this discussion. In Figure 21a representing a motionless Earth, apparent and actual vertical fall coincide. In Figure 21b, in which the Earth is rotating, apparent vertical fall is experienced on Earth, but actually slanted fall takes place. In Figure 21c, also representing a rotating Earth, actual vertical fall is taking place, but apparently slanted fall is experienced on Earth.
Figure 21. Apparent vs. actual vertical fall on motionless vs. rotating Earth
With these pictures in mind, we are now in a position to better follow Galileo’s reasoning. To explain the difference between actual and apparent vertical fall, Galileo points out that although apparent and actual vertical fall would coincide on a motionless Earth (Figure 21a), they would not coincide on a rotating Earth (Figures 21b and 21c).
Assume the Earth were in rotation and a rock is dropped from the top of a tower (A). If the rock appeared to fall vertically to a terrestrial observer (Figure 21b), then it would be seen to land at the foot of the tower (B´). But, on a rotating Earth, the foot of the tower would have undergone some rotational motion during the time of fall, and so as viewed by an extraterrestrial observer the actual path (AB´) of the rock would be slanted toward the east. So on a rotating Earth, apparent vertical fall would not produce actual vertical fall, but rather actually slanted fall.
Similarly, given the same assumption of terrestrial rotation, if the rock were to move with actual vertical fall (AB in Figure 21c), then it would land to the west of the base of the tower because the base of the tower would have moved eastward to point B´. Therefore, to a terrestrial observer the path of the falling rock would appear slanted westward, because when the rock reached point B the terrestrial observer would have moved to A´, and so the apparent path would be A´B, which is not vertical. So, on a rotating Earth, actual vertical fall would not produce apparent vertical fall, but rather apparently slanted fall. This contrasts with a motionless Earth, for which if the path were from the top to the base of the tower as seen by the terrestrial observer, then it would also be straight and perpendicular to the Earth’s surface for the extraterrestrial observer, and vice versa (Figure 21a).
Having made such a distinction, Galileo applies it to the argument above. Suppose that, when the argument claims that the Earth cannot rotate because bodies fall vertically, the vertical fall in question is actual vertical fall. Then we would be entitled to ask how you know that bodies do actually fall vertically, for observation on the Earth only reveals apparent vertical fall. While it is undeniable that to us bodies are seen to fall from the top to the base of a tower, we have no experience about how their paths look from an extraterrestrial viewpoint. How could one answer that question? How could one justify that falling bodies move with actual vertical fall?
It seems that one could only try an empirical justification, by basing actual vertical fall on apparent vertical fall. But to do this would presuppose that apparent vertical fall implies actual vertical fall, and in turn this implication amounts to assuming that the Earth is motionless, since this is the only condition under which the implication holds. Unfortunately, the motionlessness of the Earth is the very conclusion the argument is trying to prove. In short, interpreted in terms of actual vertical fall, the objection from vertical fall begs the question because the premise that bodies fall vertically is either assumed gratuitously or supported circularly (by reasons that presuppose the conclusion).
But perhaps the objection from vertical fall intends apparent vertical fall. Then, the minor premise of the above-mentioned argument would be both true and uncontroversial. In this case, Galileo questions the major premise, the conditional proposition that if the Earth were in rotation then bodies would not undergo apparent vertical fall. What are the grounds for asserting this conditional claim?
At that time, the justification of this claim was based on some basic principles of Aristotelian physics. One was the principle that a body can have only one natural motion; another was the principle that the natural state of heavy material bodies is rest; a third was that motion requires a force to sustain it. To understand the connection, we have to understand the first answer the Aristotelians would give in this discussion.
On a rotating Earth, if bodies appeared to fall vertically, then in reality they would follow a path slanting eastward (Figure 21b), the resultant of downward and horizontal components. Now, according to Aristotelian physics such a mixture or combination is impossible because the horizontal component of motion would be motion under the influence of no external force, and so it would have to be natural; but such a second natural motion could not coexist with the first, downward motion.
The issue then becomes whether it is possible for a free-falling body to have a horizontal component of motion. This is where some of the principles of the new Galilean physics come in; they are the principle of the conservation of motion and the principle of the superposition or composition of motions. Conservation of motion is an approximation to such laws of modern physics as the law of inertia, the law of conservation of linear momentum, and the law of conservation of angular momentum. The Galilean formulation relevant here is that if a body is moving horizontally, then it will conserve its motion as long as it is left undisturbed. And the principle of superposition asserts that it is physically possible for a body to have more than one tendency to move; and in these cases the actual motion will be the resultant, as defined by the diagonal of the corresponding parallelogram.
These principles can now be applied to answer the objection from apparent vertical fall. If the Earth rotated, then it is possible that bodies would undergo apparent vertical fall, because on a rotating Earth, a body before being released would be carried eastward by the Earth’s rotation; and after being released this horizontal component of motion would be conserved. The body would also start moving downward; but this motion would not be a disturbance to the other one. Instead they would combine, by the principle of superposition, to produce the actually slanted path which would carry the body directly below the point of release, for example to the base of the tower, since the Earth’s surface has also moved eastwards.
One last piece of reasoning was needed to complete Galileo’s criticism. In that context, he could not simply assert the conservation of motion without justification. But he had one ready, which reflected the way he himself had arrived at the principle. The argument is in part an empirical one. Observation reveals that bodies accelerate as they move downwards, and slow down when they move upwards. Therefore, Galileo reasoned, if a body were moving along a path that was neither downwards nor upwards, its motion should be neutral, so to speak; its speed should remain constant in the absence of disturbances. But horizontal motion is an instance of motion which is neither upwards nor downwards. Therefore, bodies moving in a horizontal direction will conserve their speed of motion if left undisturbed.
So Galileo showed that the vertical fall objection is based on some untenable assumptions and is therefore groundless if vertical fall in its premises means apparent vertical fall, while the objection begs the question if the premises refer to actual vertical fall.
It should be noted, however, that none of this, by itself, supports the Earth’s motion, let alone proves it; here we have simply the criticism or refutation of an argument, not a counter-argument justifying the opposite conclusion. There were many other mechanical objections to the Earth’s motion, involving such things as the ship’s mast experiment, east–west gunshots, north–south gunshots, etc.; these had to be similarly criticized, separately and piecemeal. Galileo did precisely that in the Dialogue.
And as we saw, eventually Galileo did formulate several positive arguments for the Earth’s motion, some contributed by himself and some adapted from Copernicus: the simplicity argument for diurnal terrestrial rotation; the argument from the law of the periods of revolutions; the simplicity argument from the heliocentrism of planetary revolutions; the coherence argument from the explanation of planetary retrogressions; the argument from the annual motion of sunspots; and the argument based on the explanation of the tides. These positive arguments, together with the criticism of the objections, confirmed Copernicanism in the sense of rendering the Earth’s motion more likely to be true than the Earth’s rest. However, such a confirmation relied crucially on observational evidence with the telescope. And this leads us to a distinct and crucial methodological element of rationality.
Judgment and Telescopic Observation
Galileo’s attitude toward the geokinetic idea before his telescopic discoveries is, in my opinion, a beautiful illustration of judgment. We are no longer dealing primarily with questions of reasoning, for it wasn’t merely a matter of reasoning one’s way out of the various astronomical objections. Nor was it a matter of criticism, for there was no question of his willingness and ability to challenge authority, as shown by the fact that he was engaged in a program of physical research which was undermining the foundations of Aristotelian physics. Rather, we are dealing with questions of proportion and balance.
In his early career, Galileo did indeed appreciate the novelty of Copernicus’s argument, and he had begun to conceive ways of refuting the physical objections, and ways of providing mechanical evidence in favor of the Earth’s motion. All that this meant was that physics and the criterion of explanatory coherence favored the geokinetic idea. But direct observation was still fully on the side of the geostatic view, and Galileo could not bring himself to any one-sided disregard of sense experience. That situation changed only with the telescope.
The telescope made possible the observation of phenomena that enabled answering the objection from the deception of the senses (together with the general observational argument for the geostatic view), the objection from the Earth–heaven dichotomy, and most of the specific astronomical objections. In regard to the latter, the planet Mars could now be seen to vary in apparent brightness and size as required by the hypothesis of the Earth’s annual revolution. Similarly, the planet Venus exhibited the required phases.
The Earth–heaven dichotomy was undermined and the way paved for a unified view of heaven and Earth. The Moon’s surface could be seen to be full of mountains and valleys like the Earth, and they could be seen to be nonluminous and to cast shadows from sunlight, very much as happens on the Earth. The Sun appeared to have on its surface dark spots that underwent changes similar to those of clouds on Earth. The planet Jupiter had four moons analogous to the one circling the Earth. And the phases of Venus also indicated that it was not composed out of a luminous aether, but out of some opaque nonluminous substance like the Earth.
Finally, the general observational argument for the geostatic view could now be criticized. One could say that, besides the direct experience of the unaided senses, the indirect observations made with the telescope should be taken into account. Since almost all indirect observation favored the Earth’s motion, at the very least it was no longer true to say that observation unequivocally favored the geostatic system, and perhaps it was possible to say that it favored the Copernican system.
These discoveries may be said to have tipped the overall balance of evidence and argument in favor of the geokinetic and against the geostatic idea. Consequently, Galileo became increasingly outspoken about the issue, and in general an irreversible historical trend was produced which was to result in the eventual triumph of the geokinetic theory. However, the process was slow and gradual. The telescopic discoveries did not immediately decide the issue.
One reason was that at least one important astronomical objection could still not be answered—the argument from annual stellar parallax. Even the telescope did not reveal any yearly change in the apparent position of fixed stars. Galileo was correct in arguing that stellar distances are so immense that the parallax is very minute, and therefore more powerful instruments were needed to detect it.
Another reason why the telescope was not immediately decisive was that for some time there were proper concerns about the legitimacy, reliability, and practical operation of the instrument. Some questioned its legitimacy in principle, on the grounds that there was no place in scientific inquiry for instruments which make us see things that cannot be seen without them. Obviously, this objection could not be dismissed, as we can appreciate today if we compare the situation at that time with the more modern issue of whether psychedelic drugs put users in contact with a deeper level of reality, or merely make them see things that are not there. Others questioned the reliability of the telescope by pointing out that Galileo had not provided a scientific explanation of how and why the telescope worked. Moreover, all empirical checks involved terrestrial observation, and there was not even one instance of a test showing that it was truthful in the observation of phenomena in the heavens. Finally, the practical operation of the instrument required that one learn how to avoid aberrant and deviant observations stemming from impurities of the lenses, improper lens shape, and other features of poor design.3
A third reason why the telescopic discoveries were not decisive and did not provide a conclusive proof of the Earth’s motion was the existence of biblical and other theological arguments against it. For example, as we have seen, one anti-Copernican passage in the Bible was taken to be Joshua 10:12–13, where God performs the miracle of stopping the Sun in its course in order to prevent it from setting at a place called Gibeon, and thus to give that region some extra daylight, needed by the Israelites to win a battle they were fighting. Understandably, it took some time for Galileo to come to terms with the scriptural objection by arguing that the Bible is not a scientific authority. Others, including the Church herself, of course, required an even longer time. Moreover, even though Galileo may have won all the arguments on this issue, he personally lost all the actual battles.
Finally, there was an epistemological issue connected with the objection from the deception of the senses which also required time for a full assimilation. The difficulty was that, although deception may be too strong a word, the Earth’s motion was then and remains today a phenomenon which is not observable either with telescopes or by astronauts from outer space. Do such unobservable processes have any role in science, and if so what is their role? Can they be taken seriously as descriptions of physical reality, or can they only be regarded as useful fictions, useful, that is, for the calculation, computation, and prediction of other phenomena that are indeed observable? To admit unobservable entities in the scientific description of the world was a giant step for mankind, to be undertaken with great caution and circumspection.
Galileo’s skepticism about Copernicanism before the telescope, and his caution about its observational status afterwards, attest to the importance of observation and judiciousness in the Copernican Revolution. He could not bring himself to take Copernicanism seriously, disregarding the pre-telescopic observational counter-evidence and exaggerating the role of the theoretical arguments in favor, until the telescope made possible a new kind of observation which could be judged to favor Copernicanism.
Fair-mindedness, Not Sophistry
Recall that in the winter of 1615–16 Galileo went to Rome to try to defend himself and Copernicanism, while the Inquisition was conducting an investigation started by some formal complaints against his views. From an intellectual and methodological point of view, his discussions there exhibited a memorable technique: before criticizing the anti-Copernican arguments, he made sure that their meaning was understood and their strength appreciated. Many scholars have misinterpreted this technique as the sophistical art of confusing and ridiculing opponents by first defending one thesis and then its opposite, and thus winning an argument even when logic and evidence are against you. I argued that such a technique is a sign that one is not demonizing one’s opponents, but treating them as reasonable people; and it is a very effective manner of arguing, both to convince other people and to arrive at the truth.
This technique involves skills and qualities of mind that may be labeled open-mindedness and fair-mindedness. Generally speaking, Galileo’s Dialogue is full of such open-minded and fair-minded argumentation. The best example is probably his discussion of the argument from the extruding power of whirling.
To recap, this objection argued that the Earth cannot rotate because if it did, bodies on its surface would have to move along curved paths following the Earth’s circumference; and if they moved in this manner, then they would experience an extruding power away from the Earth’s center, and so they would fly off toward the sky; but, obviously, this phenomenon is not observed. This argument was one of the mechanical objections to the Earth’s motion, whose full answer required the discovery and understanding of the laws of circular motion and centrifugal force, toward which Galileo made some preliminary contributions.
To better explain Galileo’s critique of this extrusion argument, we can refer to one of his own diagrams. In Figure 22, CEH represents a portion of the Earth’s surface; A, the Earth’s center; AC, a terrestrial radius; CD, a tangent. The hypothetical terrestrial rotation is taken to be in a counterclockwise direction (here, right to left). Galileo’s refutation of the argument consists of three objections.
Figure 22. Extruding power of whirling on a rotating Earth
First, if a body were to be extruded from a rotating Earth, the extrusion would occur along the tangent (line CD) to the point of last contact with the terrestrial surface; the reason for this stems from the principle of conservation of motion (what we now call inertia). But, because of gravity, on a rotating Earth the body would still have a tendency to move downward along the secant (DA) from the point of its position to the center of the Earth. So we need to do a comparison between these two tendencies; we can’t consider just the centrifugal extrusion, as the anti-Copernican argument seems to be doing. The comparison shows that, in fact, the downward tendency happens to be greater than the extruding one.
In the second criticism, Galileo tries to show that the downward tendency not only happens to exceed the tangential one, but that it necessarily does so for mathematical reasons; that is, he argues that extrusion would be mathematically impossible on a rotating Earth. He tries to prove this mathematical impossibility on the basis of the geometry of the situation in the neighborhood of the point of contact between a circle and a tangent, and the behavior of the external segments (called exsecants, such as DE) of the secants (such as AD) drawn from the center of the circle to the tangent. The key point in this mathematical demonstration is that, as one gets closer and closer to the point of tangency (C), the exsecants (such as DE) get smaller and smaller at a much faster rate than the tangential segments (such as DC), and so the distances of fall required to prevent extrusion become infinitely smaller than the distances required to achieve extrusion.
Galileo’s third objection concerns the point that in circular motion, the extruding tendency increases with the linear speed but decreases with the radius. Now, on a rotating Earth, the linear speed at the equator would be about 1,000 miles per hour, which sounds high in absolute terms; but such a speed is actually very small compared with the Earth’s circumference, which is about 24,000 miles, or even with the Earth’s radius, which is about 4,000 miles. In other words, the Earth’s rotation is really very slow, in the sense that the Earth rotates just once in 24 hours. Thus, on a rotating Earth the extruding tendency would really be very small. This can be illustrated in the figure by imagining that that the Earth’s radius were much smaller than it is (AB instead of AC), and that the linear speed were the same (BG = CE, both traversed in the same time); then the extruding tendency would be a function of the exsecant DE for the larger radius, and a function of exsecant FG for the smaller radius; and DE is smaller than FG. The anti-Copernican argument ignores this aspect of the situation, and so it assumes that on a rotating Earth extrusion would be more likely to happen than is the case.
This critique of the extrusion argument is an attempt to show that the argument is quantitatively invalid, based on an analysis of the mathematical physics of terrestrial extrusion. When so reconstructed, Galileo’s refutation is essentially correct, but not completely. This is especially true for his second criticism, which tries to prove the mathematical impossibility of extrusion on a rotating Earth; this proof contains parts that are mathematically valid but are misapplied to the physical situation, and parts that would be physically applicable but are mathematically incorrect.4
However, the more important point in the present context is that before refuting the extrusion argument, Galileo amplifies and strengthens it in several ways. One is that he gives some examples and evidence to establish the reality of the extruding power of whirling, which is a crucial premise of the argument. For example, he mentions the experiment of tying a small pail of water at the end of a string, making a small hole in the bottom of the pail, whirling the pail in a vertical circle by the motion of one’s hand, and observing water rushing out of the hole always in a direction away from one’s hand. Galileo makes his intention clear in the Dialogue. Referring to the extrusion argument, he says that “I want to strengthen and tighten it further by showing even more sensibly how true it is that, when heavy bodies are rapidly turned around a motionless center, they acquire an impetus to move away from that center, even if they have a propensity to go toward it naturally.”5
Even more striking is that Galileo makes an essential clarification. He points out that as usually formulated, the argument is improperly stated: its crucial step should be stated to say that if the Earth were rotating then there would now be no loose bodies on its surface, since they would have all been extruded long ago, rather than claiming that if the Earth were in rotation we would see bodies on its surface extruded off toward the sky.
Finally, Galileo makes a third fair-minded point by defending the extrusion argument from the unfair criticism that it commits the classic Aristotelian fallacy of ignoratio elenchi.6 This would mean in effect that the argument alleges to be proving one conclusion (that the Earth is not in rotation), which is indeed controversial, but instead at best proves another (that the Earth did not recently begin to rotate), which nobody is claiming; in other words, the argument reaches an irrelevant conclusion—a proposition that is not being disputed. Such a criticism would be unfair because once it is made, it becomes immediately obvious how the original argument should be restated and was intended to be stated.
These improvements in the extrusion argument are so many and so important that, together with the fact that it is hard to find this particular argument in the texts of Aristotle or Ptolemy, they have led at least one critic to claim that the argument was largely invented by Galileo so that he could refute it!7 This claim is advanced as a criticism that exposes another one of the alleged sophistical tricks in Galileo’s bag, that he was setting up a “straw man.” But such criticism again inverts the truth, by attempting to portray negatively a technique that is actually sound and valuable.
Formulating arguments against your own position is a powerful method for the discovery of the truth. It is neither common nor easy, and certainly not for the faint-hearted; and it is usually a task to be left to one’s opponents. But if one can pull it off, and if one can then undertake an evaluation and criticism of such counter-arguments, this procedure provides another indication of where the truth lies, as our own position is being made to overcome additional obstacles. Galileo may not have invented a novel argument, but there is little doubt that he greatly strengthened and amplified an existing one.
Another example of Galilean fair-mindedness concerns the anti-Copernican argument from the apparent position of fixed stars, which was based on the fact that no annual stellar parallax could be observed. We have seen on many occasions that Galileo could not really refute this argument for the simple reason that even the telescope did not reveal a stellar parallax. I pointed out that Galileo was explicit in the Dialogue that the parallax argument could not be refuted, and the main point of his discussion was to sketch a research program designed to measure the parallax if it really existed. But Galileo also did something else. He began his discussion by clearing up some common misconceptions about the kind of stellar changes that would be produced by the Earth’s annual motion, in order to make sure that one understood the nature of the anti-Copernican argument.
One misunderstanding was that the elevation of the celestial pole above the horizon would change; this betrayed a failure to understand that if the Earth revolved around the Sun, the celestial pole would be defined by the terrestrial pole around which the Earth would rotate, and the elevation of the latter can change only by moving around the Earth’s surface, and not by any motion of the whole Earth. Another confusion was that the annual change in the apparent position of fixed stars would be comparable to the large changes in stellar elevation above the horizon resulting by moving around the Earth’s surface; this misunderstood the difference between moving on a curved surface (the Earth’s) while measuring stellar elevations relative to that surface, and moving on a plane (the ecliptic) while measuring stellar elevations relative to that plane. A third misconception was that the annual changes for the fixed stars would be comparable to the large changes easily observable in the elevation of the Sun over the horizon, which generate the cycle of the seasons; such thinking failed to appreciate the difference between moving in an orbit around a body—the Earth around the Sun—and moving in an orbit far away from a body—the Earth’s motion against the fixed stars.8
A Conceptual Framework
So far in this chapter, I have argued that nothing compares with the Copernican Revolution as a vivid illustration of the possibility and importance of criticism. The lesson here extends far beyond science: everyone may be mistaken, and everything is and ought to be open to criticism.
However, man is indeed, as Aristotle declared, a rational animal. Universal human beliefs are normally rational and reasonable, and such was certainly the geostatic belief before Copernicus and Galileo. Therefore, criticism would lack judgment if it did not recognize the importance of reasoning.
On the other hand, reasonableness and rationality are matters of degree, and they are contextual. What is reasonable under certain conditions need not always remain so. Still, a change will not occur arbitrarily, but rather only when a prevailing idea is shown to be less reasonable than a new idea. Again, judgment is required to ensure that reasonable ideas are not discarded arbitrarily, but only in the light of more reasonable ones.
These claims about the Copernican Revolution and Galileo’s contributions can in turn be reinterpreted as conclusions about the nature of human rationality in general. For if we take these events as a defining instance of human rationality in science, then our account also enables us to see that and to see how human rationality involves three elements: criticism, reasoning, and judgment. These notions now require some clarification, definition, amplification, and systematization,
By reasoning, I mean a form of thinking consisting of the interrelating of thoughts in such a way as to make some thoughts dependent on others, and this interdependence can take the form of some thoughts being based on others or some thoughts following from others. Here we are defining reasoning in terms of thinking, and taking thinking as an undefined primitive notion.
“Criticism” can have several different meanings. In the narrow sense of negative evaluation, as used earlier in this chapter, we could speak of criticism as thinking that is aware of and open to the possibility of the falsehood or refutability of a proposition, including one’s own view. We can give the label principle of fallibility to a key lesson of the Copernican Revolution, that everyone may be mistaken and everything is and ought to be open to criticism. Then, criticism in this narrow sense is thinking guided by or aware of the principle of fallibility.
But there is another meaning of criticism, which refers to self-awareness or self-reflection. In this sense, criticism is thinking that displays an awareness of what one is doing. When what we are doing is searching for the truth or trying to acquire knowledge, such criticism is equivalent to methodological (or epistemological) reflection: that is, thinking aimed at the formulation, analysis, or application of principles about the proper procedure to follow in the search for truth and the quest for knowledge.
A third common meaning of criticism is evaluation, in the general sense of either favorable and positive assessment or unfavorable and negative assessment. This is the meaning one has in mind when one speaks of art criticism or aesthetic criticism.
Now, going back to reasoning, a special case, argument, is reasoning that aims to justify a conclusion by supporting it with reasons and/or defending it from objections. This enables us to focus on another special case of crucial importance, critical reasoning, which I would define as reasoning aimed at, or consisting of, the interpretation, evaluation, or self-reflective formulation of arguments. Such self-reflection may involve not only the principle of fallibility, but also others, such as open-mindedness, fair-mindedness, rational-mindedness, and judicious-mindedness (or, more simply, judiciousness, or judgment).
These, in turn, may be defined as follows. Open-mindedness is the ability and willingness to know, understand, and learn from the arguments, evidence, and reasons against one’s own views. Fair-mindedness is the ability and willingness to appreciate the strength of arguments and reasons against one’s own view, even when one is attempting to criticize or refute them. Rational-mindedness is the ability and willingness to accept the views justified by the best arguments and strongest evidence; so defined, it should not be equated with rationality in general, but is rather a particular (although important) intellectual trait that is part of rationality.
Next, judiciousness is the willingness and ability to be impartial, balanced, and moderate; that is, to avoid one-sidedness (by properly taking into account all distinct aspects of an issue) and to avoid extremism (by properly taking into account the two opposite sides of any one aspect). This does not mean that anything goes, that one indiscriminately accepts all points of view as equally good, or that one does not accept any one point of view as better; nor does it mean that one mechanically splits the differences separating the several aspects and the opposite sides. Instead, the view which one accepts must be “properly” balanced and moderate.
Finally, critical thinking may then be considered a special case of critical reasoning that stresses such principles. That is, critical thinking is reasoning aimed at, or consisting of, the interpretation, evaluation, or self-reflective formulation of arguments, and guided by such ideals as the principles of fallibility, open-mindedness, fair-mindedness, rational-mindedness, and judiciousness.
Let’s see how this conceptual framework corresponds to Galileo’s contributions to the Copernican Revolution. Before the telescope, he was keenly aware of the strength of the anti-Copernican arguments based on the Earth–heaven dichotomy, the appearance of Venus, the apparent brightness and size of Mars, and the apparent position of fixed stars. This appreciation exemplifies his open-mindedness, fair-mindedness, and judiciousness. After the telescope, his critical reasoning about these arguments and the new evidence, together with his rational-mindedness, enabled him to re-assess and to seriously and actively pursue the Copernican theory.
Similarly, we have seen that the Letter to Christina provides a clear statement, an appreciative interpretation, and a nuanced evaluation of the scriptural argument against the Earth’s motion. Galileo’s essay should be seen as an instance of critical reasoning, not an abstract treatise on hermeneutics.
And Galileo’s critique in the Dialogue of the anti-Copernican arguments likewise exemplifies these concepts. The discussion of the argument from the extruding power of whirling is first and foremost an instance of critical reasoning. It also carries open-mindedness to a new height, for it stresses an objection to Copernicanism that is more powerful than most of those advanced by the anti-Copernicans themselves. And it displays fair-mindedness by ensuring that this anti-Copernican argument is properly stated, before it is refuted. Nevertheless, it is ultimately invalid, and rational-mindedness dictates its rejection.
Finally, the criticism of the argument from vertical fall is obviously a piece of critical reasoning. The analysis leads not only to rejecting vertical fall as evidence against the Earth’s motion (as demanded by rational-mindedness), but also to a better understanding of the objection than one finds in the proponents of geocentrism themselves (thus exemplifying open-mindedness and fair-mindedness).
These concepts and principles correspond not merely to Galileo’s practice, but also to his reflections. In the Third Day of the Dialogue, in the context of the criticism of the empirical astronomical objections to the Earth’s motion, he expresses amazement at “how in Aristarchus and Copernicus their [aprioristic] reason could have done so much violence to their senses, as to become, in opposition to the latter, mistress of their belief.”9 On the other hand, he confesses that in his own case, if telescopic observation “had not joined with reason, I suspect that I too would have been much more recalcitrant against the Copernican system than I have been.”10 These pronouncements express the importance of being judicious with regard to the contrast between theoretical speculation and sensory observation.
An eloquent statement of Galileo’s open-mindedness is found in the Second Day of the Dialogue, in the course of the presentation of the many objections to Copernicanism. The Copernican character Salviati is keen to point this out to the Aristotelian Simplicio: “you will hear the followers of the new system produce against themselves observations, experiments, and reasons much stronger than those produced by Aristotle, Ptolemy, and other opponents of the same conclusions; you will thus establish for yourself that it is not through ignorance or lack of observation that they are induced to follow this opinion.”11
And with regard to rational-mindedness, in a set of notes meant to provide replies to the objections in Bellarmine’s letter to Foscarini, Galileo states:
Not to believe that there is a demonstration of the earth’s mobility until it is shown is very prudent, nor do we ask that anyone believe such a thing without a demonstration. On the contrary, we only seek that, for the advantage of the Holy Church, one examine with the utmost severity what the followers of this doctrine know and can advance, and that nothing be granted them unless the strength of their arguments greatly exceeds that of the reasons for the opposite side.12
On the principle of fair-mindedness, Galileo found the occasion to formulate it with words that are memorable for their clarity, elegance, and eloquence. The context was the complex and problematic one of the Inquisition proceedings of 1633. In the second deposition, he pleaded guilty to having, in the Dialogue, violated Bellarmine’s warning not to defend the truth of Copernicanism. But he justified his violation as being the unintentional result of his wanting to critically examine the pro-Copernican arguments: “when one presents arguments for the opposite side with the intention of confuting them, they must be explained in the fairest way and not be made out of straw to the disadvantage of the opponent.”13
The Copernican Revolution, then, required that the geokinetic hypothesis be justified not only with new theoretical arguments but also with new observational evidence; that the Earth’s motion be not only constructively supported with theoretical arguments and observational evidence, but also critically defended from many powerful old and new objections; and that this defense include not only the destructive refutation but also the appreciative understanding of those objections in all their strength. One of Galileo’s major accomplishments was not only to provide new evidence (from telescopic observation) supporting the Earth’s motion, but also to show how the anti-Copernican objections could be refuted, and to elaborate their power before they were answered. In this sense, Galileo’s contribution to the Copernican Revolution was rational-minded, open-minded, fair-minded, and judicious. He was and remains a model of critical reasoning and critical thinking. This is an everlasting and universally relevant intellectual lesson that can be learned from Galileo.