Chapter 6
The Dialogue on the Two Chief World Systems (1632)
Resuming the Copernican Discussion
For the next several years, Galileo did refrain from defending or explicitly discussing the geokinetic theory, although he did discuss it implicitly and indirectly in the context of a controversy about the nature of comets in The Assayer (1623). Even the publication of the corrections to Copernicus’s book in the Index’s decree of 1620, which gave one a better idea of what was allowed and what not, did not motivate him to resume the earlier struggle. The death of both Cardinal Bellarmine and Pope Paul V in 1621, and the election of Pope Gregory XV did result in some encouragement, for example when Galileo was consulted about astronomical matters by the cardinal nephew and Vatican secretary of state; but those developments were not enough for a significant change.
The event that put an end to the interlude took place in 1623, when Gregory XV died and Cardinal Maffeo Barberini was elected Pope Urban VIII (see Figure 14). Urban was a well-educated Florentine, and in 1616 he had been instrumental in preventing the direct condemnation of Galileo and the formal condemnation of Copernicanism as a heresy. He was also a great admirer of Galileo, and in 1620 he had even written a poem in praise of Galileo. He now employed as personal secretary one of Galileo’s closest acquaintances, Giovanni Ciampoli (1589–1643). Furthermore, at about this time, Galileo’s book on the comets, The Assayer, was being published in Rome by the Lincean Academy, and so it was decided to dedicate the book to the new pope. Urban appreciated the gesture and liked the book very much. Finally, as soon as circumstances allowed, in the spring of 1624, Galileo went to Rome to pay his respects to the pontiff; he stayed about six weeks and was warmly received by Church officials in general and the pope in particular, who granted him weekly audiences.
Figure 14. Maffeo Barberini (1568–1644), Pope Urban VIII (1623–44)
The details of the conversations during these six audiences are not known. There is evidence, however, that Urban VIII did not think Copernicanism to be a heresy, or to have been declared a heresy by the Church in 1616. He interpreted the Index’s decree to mean that the Earth’s motion was a rash or dangerous doctrine whose study and discussion required special care and vigilance. He thought the theory could never be proved to be necessarily true, and as we saw earlier, his favorite argument for this skepticism was the divine-omnipotence objection: God being all powerful, he could have created a world in which the Earth did not move, so asserting that the Earth must move is to wish to limit God’s power.1 This argument, together with his interpretation of the decree of 1616, must have reinforced his liberal inclination that, as long as one exercised the proper care, there was nothing wrong with the hypothetical discussion of Copernicanism, with treating the Earth’s motion as a hypothesis and studying its consequences, and its utility for making astronomical calculations and predictions.
At any rate, Galileo must have gotten some such impression during his six conversations with Urban, for upon his return to Florence he began working on a book. This was in part the work on the system of the world which he had conceived at the time of his first telescopic discoveries, but it now acquired a new form and new dimensions in view of all that he had learned and experienced since. His first step was to write and circulate privately a lengthy reply to the anti-Copernican essay written in 1616 by Francesco Ingoli. This Galilean “Reply to Ingoli,” as well as his earlier “Discourse on the Tides,” were incorporated into the new book. After a number of delays in its writing, licensing, and printing, the work was finally published in Florence in February 1632, with the title Dialogue on the Two Chief World Systems, Ptolemaic and Copernican.
The author had done a number of things to avoid trouble, to ensure compliance with the many restrictions under which he was operating, and to satisfy the various censors who issued him permissions to print.
To emphasize the hypothetical character of the discussion, Galileo had originally entitled it “Dialogue on the Tides” and structured it accordingly. It was to begin with a statement of the problem of the cause of tides, and then it would introduce the Earth’s motion as a hypothetical cause of the phenomenon; this would lead to the problem of the Earth’s motion, and to a discussion of the arguments pro and con, as a way of assessing the merits of this hypothetical explanation of the tides.2 However, the book censors, interpreting and acting on the pope’s wishes, did not like such a focus on the tides, which suggested a realistic interpretation of Copernicanism and the potential reality of the Earth’s motion. Instead, they wanted to make the book look like a vindication of the Index decree of 1616. Thus, the book’s preface, whose content must be regarded as originating primarily from the pope and the censors and only secondarily from Galileo, claimed that the work was being published to prove to non-Catholics that Catholics knew all the arguments and evidence about the scientific issues, and so their decision to believe in the geostatic theory was motivated by religious reasons and not by scientific ignorance. It went on to add that the scientific arguments seemed to favor the geokinetic theory, but that they were inconclusive, and thus the Earth’s motion remained a hypothesis.
Galileo also complied with the explicit request to end the book with a statement of the pope’s favorite argument, the objection from divine omnipotence. Such compliance reflected in part Galileo’s readiness and willingness to be cooperative and accommodating. It also reflected his judgment and recognition that there was something right about the pope’s favorite objection.
Moreover, to make sure he would not be seen as holding or defending the truth of the geokinetic thesis (which he knew he had been forbidden to do), Galileo wrote the book in the form of a dialogue among three speakers: Simplicio, defending the geostatic side; Salviati, taking the Copernican view; and Sagredo, who is an uncommitted layperson who listens to both sides and accepts the arguments that seem to survive critical scrutiny. Again, this aspect of the book also corresponded to Galileo’s deeply held views about the nature of knowledge. It reflected his view that knowledge is a process that requires such things as critical reasoning, argumentation, open-mindedness, fair-mindedness, etc. In this regard, Galileo’s epistemology overlapped (without, however, being identical) with that of the ancient Greek philosopher Plato, who also wrote all his works in dialogue form.
Likewise, in many places throughout the book, usually at the end of a particular topic, the Copernican Salviati utters the qualification that the purpose of the discussion is information and enlightenment, and not to decide the issue, which is a task to be reserved for the proper authorities. This, too, was partly prudential precaution, and partly logical or methodological judgment. Galileo did not want to be seen as contradicting either the Index’s anti-Copernican decree or Bellarmine’s personal warning to him, but he also judged that the case against the geostatic thesis and in favor of Copernicanism, however strong and probable, was not conclusive and decisive.
Galileo moreover obtained written permissions to print the book, first from the proper Church officials in Rome (when the plan was to publish the book there), and then from the proper officials in Florence (when a number of external circumstances dictated that the book be printed in the Tuscan capital).
The Dialogue is essentially a critical examination of all scientific and philosophical arguments on both sides of the Copernican controversy. The discussion thus includes all the astronomical, mechanical, physical, epistemological, and methodological arguments for and against the Earth’s motion. It usually consists of a statement or formulation of the argument, often a quotation from some author whom Galileo intends to criticize; an interpretation or clarification designed to convey a deeper understanding of the argument; an evaluation or assessment of whether the argument is valid or cogent, and of its strengths and weaknesses; and an analysis meant to explain and justify his interpretations and evaluations.
On the other hand, the book’s critical examination does not include the religious, theological, and biblical objections to the Earth’s motion. Galileo had not forgotten that, in light of the earlier Inquisition proceedings, he was not supposed to defend Copernicanism from these objections; and it was also obvious that the more liberal atmosphere resulting from Pope Urban VIII did not extend to this topic. The book’s ending does mention the divine-omnipotence argument, as required by the pope and the censors; and, accordingly, there is no critical analysis of that argument. (The Dialogue also contains one brief passage mentioning the biblical objection, in the context of reporting the arguments advanced by an anti-Copernican author; but Galileo summarily drops any critical discussion of this topic, and instead briefly expresses his reverence for the Bible and his unwillingness to mix science and religion.)
The book is divided into four parts or chapters, called “Days” to reflect the fiction that the three interlocutors met on four different days to focus on four distinct but interrelated problems. The First Day examines the Earth–heaven dichotomy, whose truth would have made the Copernican system impossible. The Second Day considers the diurnal motion, whether it belongs only to the Earth or to all heavenly bodies except the Earth. The Third Day focuses on the annual motion, whether it belongs to the Earth or to the Sun. The Fourth Day discusses the problem of the tides, why they take place and how the Earth’s motion can cause them to come about.
First Day: Earth–Heaven Dichotomy
In the First Day, Galileo criticizes the Aristotelian arguments in favor of the Earth–heaven dichotomy and elaborates an argument showing that there is no essential difference between terrestrial and heavenly bodies. Bear in mind that the contradiction between the Aristotelian thesis and Copernicanism was explicit, direct, and palpable. The primary evidence for the similarity between Earth and heaven had been available since the telescopic discoveries, but Galileo had not had the occasion to elaborate the argument explicitly. He argues as follows.
The telescopic observation of the Moon shows that its surface is not perfectly smooth, but rather rough, full of mountains and valleys, made of a substance that is opaque, non-luminous, and casts shadows; this is very much like the Earth. The observation of sunspots points in the same direction: they are not previously unknown planets circling the Sun, but phenomena on the surface of the Sun; they appear as dark spots, grow in size, and then gradually fade away; they occur somewhat irregularly, but while a particular sunspot lasts, it appears to move across the solar disk in such a way as to indicate that the Sun undergoes an axial rotation with a period of about one month. In the First Day, Galileo also briefly mentions some naked-eye observations that did not require a telescope: the novas that became visible in 1572 and in 1604 and that appeared to be instances of generation and decay in the heavens. Moreover, later (in the Third Day) Galileo analyzes at great length the observations of the 1572 nova by a dozen astronomers, to refute the attempt to show that this nova was located below the Moon, in the sublunary region.
Galileo is clear that to establish the similarity between Earth and heaven does not amount to proving the key Copernican thesis that the Earth moves. It remains to be shown whether the similarity between terrestrial and heavenly bodies extends to motion.
Galileo is equally clear that his observational argument for the Earth–heaven similarity merely refutes the dichotomy thesis, thus depriving the Aristotelians of a reason to reject Copernicanism. The argument as such does not even tell us what is wrong with the reasoning which led the Aristotelians to believe in the Earth–heaven dichotomy. However, Galileo thinks that it is equally important to understand how their reasoning went wrong, and about half of the First Day is devoted to such a critical analysis.
For example, one of their arguments was itself an observational argument: the heavenly region is devoid of physical changes (other than regular circular motion) because no such changes have ever been observed in the heavenly bodies. Galileo points out that this argument presupposes that what is observed by the senses normally corresponds to reality. He also points out that Aristotle himself explicitly asserted such a principle on many occasions. Galileo can thus formulate the memorable criticism that “it is more in accordance with Aristotle to philosophize by saying ‘the heavens are changeable because so the senses show me’ than if you say ‘the heavens are unchangeable because theorizing so persuaded Aristotle’.”3
But Aristotle also had some theoretical arguments in support of the Earth–heaven dichotomy, and they too deserve critical scrutiny. In fact, Galileo begins the First Day with a critical analysis of those theoretical arguments.
At the most fundamental and abstract level, the Earth–heaven dichotomy was based on Aristotle’s distinction between two kinds of natural motions. He claimed that there are two distinct kinds of natural motions: the first is straight, toward or away from the center of the universe, and characteristic of elementary terrestrial bodies such as earth, water, air, and fire; the other is circular, around the center of the universe, and characteristic of heavenly bodies made of a fifth substance named aether.
This Aristotelian distinction between straight and circular natural motions was the key element of the Earth–heaven dichotomy, insofar as the distinction per se divided the universe into two regions where bodies behaved in accordance with radically different laws. Moreover, the distinction helped to generate other differences between the two regions. The most crucial of these other differences involved the alleged non-occurrence in the heavenly region of any of the physical changes that are ubiquitous and continual on Earth. To reach such a conclusion about the unchangeability of the heavenly bodies, the Aristotelians combined the doctrine of two natural motions with another doctrine, about change and contrariety: that change does not occur unless there is contrariety. They argued that there is no contrariety in the heavens, because the natural motion of heavenly bodies is circular, and natural circular motion has no contrary; but there is contrariety among terrestrial bodies, because their natural motion is two-fold, straight downwards and straight upwards; therefore, heavenly bodies are unchangeable and terrestrial bodies are changeable.
Galileo criticizes the doctrine of two natural motions as conceptually incoherent. One objection is that from the point of view of geometrical simplicity, there is a third simple line, that of the cylindrical helix or spiral, and yet Aristotle ignores it. Moreover, even if we limit ourselves to straight and circular lines, any straight line is simple regardless of whether it intersects the center of the universe; and similarly, circular motion around any point is simple, even if that point is not the center of the universe. Third, it is arbitrary to equate the spontaneous downward motion of heavy bodies with motion toward the center of the universe, rather than toward the center of the Earth; equally arbitrary is to equate the spontaneous upward motion of light bodies with motion away from the center of the universe; and the same applies to the apparent motion of heavenly bodies. Finally, there is an ambiguity in the Aristotelian concept of natural motion, insofar as it has two incompatible meanings: potentially everlasting motion, as in the case of heavenly bodies; and spontaneously free motion, as in the case of terrestrial bodies.
In any case, Galileo objects, the contrariety argument is self-contradictory. If you accept it, then you could give an analogous argument showing the opposite—that the heavenly bodies are changeable. Such an analogous counter-argument could be stated as follows: heavenly bodies have contraries, since they are unchangeable, but terrestrial bodies are changeable, and changeability and unchangeability are themselves contraries; now, all bodies that have contraries are changeable, since change does not occur unless there is contrariety; it follows that heavenly bodies are changeable.
If these criticisms seem abstract, keep in mind that here Galileo is examining the theoretical arguments for the Earth–heaven dichotomy, and so he is trying to expose their theoretical and conceptual flaws. Moreover, this theoretical criticism is made in addition to the observational criticism of the Aristotelian observational argument.
Second Day: Diurnal Motion
Most of the Second Day consists of a lengthy critical examination of the many arguments against the Earth’s daily axial rotation. However, it begins with a very brief discussion elaborating the simplicity argument in favor. This argument was common and well known, not only since Copernicus but also in earlier times. We considered it earlier (Chapter 3). Recall that there were two main ways in which terrestrial rotation was widely recognized to be simpler than universal geocentric revolution: the former involves (thousands) fewer moving parts, and only one direction of motion (eastward) rather than two (eastward for planetary revolutions, but westward for the diurnal motion). The main novelty of Galileo’s discussion is the clarity and explicit awareness that this argument is not conclusive but merely probable, and the addition of a new and significant simplification embodied in the Copernican system compared to the geostatic one. Let me explain.
Galileo’s general formulation of the simplicity argument is as follows. He states that it is more probable that the Earth rotates, rather than the heavenly bodies rotating around it, because while apparent diurnal motion can be explained by either the Copernican or the Ptolemaic hypothesis, given the principle of relativity of motion, the Copernican one is simpler for at least eight reasons, and nature usually operates by the simplest means.
Let’s focus on the third of Galileo’s reasons for the greater simplicity of the Copernican explanation of diurnal motion: that the periods of revolution have a uniformity in the Copernican system which they lack in the geostatic one. To show this, Galileo begins with a claim which I call the law of revolution: it is probably a general law of nature that, whenever several bodies are revolving around a common center, the periods of revolution become longer as the orbits become larger. He then supports this by the well-known fact that the planets revolve in accordance with this pattern, and by his own discovery that Jupiter’s satellites also follow the pattern. The important point here is that, although this feature of planetary revolutions was known to the Ptolemaics and incorporated into their system, before the discovery of Jupiter’s satellites it would have been rash to generalize a single case into a general law; however, the completely different and unexpected case of Jupiter’s satellites suggested that this was not an accidental coincidence but had general systemic significance.
Given the law of revolution, Galileo goes on to point out that, whereas the Earth’s diurnal motion in the Copernican system is consistent with the law of revolution, the diurnal motion of the universe in the Ptolemaic system is not. This is because in the geostatic system the diurnal motion corresponds to the revolution of the outermost sphere (whether stellar sphere or primum mobile) around the central Earth, but this outermost sphere involves both the largest orbit and the shortest period. So the Copernican system has a uniformity or regularity lacking in the Ptolemaic system.
Let us now go on to the arguments against terrestrial rotation. These were arguments that had accumulated for two millennia, starting with ancient thinkers such as Aristotle and Ptolemy, and being repeated and updated by such great contemporaries of Galileo’s as Tycho, and by lesser contemporaries such as Johann Georg Locher and Scipione Chiaramonti. In the Second Day, Galileo sometimes quotes explicitly from their works (especially from Aristotle, Locher, and Chiaramonti), sometimes indirectly attributes an argument to them (especially with regard to Ptolemy), and sometimes is silent about the source (especially for the case of Tycho). However, Galileo is always concerned to elaborate, clarify, and strengthen their arguments before refuting them.
Some of their arguments were philosophical, specifically epistemological, the best example being the objection from the deception of the senses. Recall that this argument claimed that if the Earth rotated, our senses would not be telling us the truth. For example, our eyes clearly see falling bodies move vertically, but on a rotating Earth such an observation would mean that their motion was actually slanted eastward; our sense of touch perceives no constant westward wind, which would have to exist on a rotating Earth; and our kinesthetic feeling of rest would be mistaken if the Earth were rotating.
Galileo denies that such cases are genuine instances of deception of the senses.
First, it would be no deception of the senses if on a rotating Earth we perceived bodies falling vertically and failed to perceive any lateral component of their motion due to terrestrial rotation. For motion exists only relative to things that do not share it, and so motion shared by an observer and an observed object does not exist for the observer and is imperceptible to him. But on a rotating Earth, the eastward component of the motion of the falling body would be shared by the observer, and hence it would not be there to be perceived. Note that here Galileo is exploiting the principle of the relativity of motion to elaborate his criticism.
Second, Galileo objects that there would be no wind deception on a moving Earth because there would be no wind for us to perceive; wind is, by definition, air moving relative to the observer, and on a moving Earth the air as well as the observer would be carried along.
Third, our inability to feel the Earth’s motion is not a deception either. For our experience with navigation shows that we can feel only changes of motion and not uniform motion, and so the Earth’s constant rotation is not something susceptible of being felt. It would be improper to speak of deception in this case.
Besides such a refutation of the premises of the deception argument, Galileo also elaborates a more general criticism that undermines the validity of the argument; such a flaw would be present even if the cases just considered were indeed deceptions, or other cases were found. He points out that if and to the extent that there would be sensory deception on a moving Earth, that would be no reason to conclude that knowledge is impossible; the more correct conclusion would be that knowledge is difficult, that it cannot rely solely on the senses, and that reason plays an equally crucial role.
Here Galileo elaborates a methodological principle that may be called critical empiricism and may be contrasted with the naïve empiricism of the Aristotelians in general. They make the acquisition of knowledge so dependent on sensory experience that if the senses are not completely reliable, then there is no reliable guide in the search for truth, and knowledge is impossible. By contrast, Galileo stresses that if the senses are not always reliable, then we should learn to distinguish situations in which they are reliable from situations in which they are not, and this task can only be performed by reason. So if and to the extent that there is a deception, it would be a deception of reason, the reason of those who from the fact that certain things appear in a certain way conclude mechanically and uncritically (and incorrectly) that they are really that way.
The heart of the Second Day is Galileo’s critique of the many mechanical objections, which were based on the observed behavior of falling bodies, of projectiles, and of bodies undergoing whirling and extrusion, and on the principles of Aristotelian physics concerning natural motion, violent motion, and the motion of simple bodies. Galileo’s criticism usually involves a combination of an exposure of flaws in reasoning, a correction of observational claims, and an articulation of a new and better physics based on such principles as conservation, superposition, and relativity of motion. One of the most instructive examples of these critiques deals with the anti-Copernican argument based on the ship’s mast experiment, and we will look at it shortly. Two other important examples, to be discussed later, involve the objection from vertical fall, which is a related but distinct argument, and the objection from the extruding power of whirling.
As we saw earlier, the ship’s mast experiment amounts to dropping a body, such as a rock or ball, from the top of a ship’s mast. The experiment is to be done both when the ship is motionless and when it is advancing forward. The experimental claim was that on a moving ship the rock falls to the deck away from the foot of the mast, toward the back of the ship. And the argument was that on a rotating Earth, a rock dropped from the top of a tower would land away from the foot of the tower, toward the west; and since this does not happen, the Earth does not rotate.
Galileo’s main criticism of this argument is that its key premise is false: on a moving ship, the rock is not left behind but rather falls at the foot of the mast, the same as it does on a motionless ship. He has two reasons for this. One is an experimental report; the other is an indirect theoretical argument. In this passage of the Dialogue, he elaborates only the theoretical argument, whereas the experimental report is found only in his “Reply to Ingoli” (1624).4 However, the argument in this passage is theoretical not in the sense of being a priori, but rather in the sense that its empirical conclusion is based partly on more easily observable phenomena, partly on more easily ascertainable facts, and partly on some theoretical claims that are not arbitrary but can be justified in various ways.
This theoretical argument may be reconstructed as follows. The more easily observable phenomena are that: (1) the undisturbed downward motion of bodies on an inclined plane is accelerated; and (2) their undisturbed motion up an inclined plane is decelerated. The more easily ascertainable fact is that (3) the cause of projectile motion is not the motion of the surrounding air. The reasons for this are that: (3a) wind moves cotton more easily than rocks, and yet rocks can be thrown farther and more easily than cotton; (3b) lead pendulums oscillate much longer than cotton ones; (3c) if the force cannot be impressed directly by the thrower to the projectile, then it cannot be impressed directly by the thrower to the air; and (3d) arrows can be shot against the wind.
From (1) and (2) one may infer that (4) the motion of bodies on a horizontal plane is conserved if undisturbed, and consequently that (5) the horizontal motion which the rock has before being dropped on the moving ship continues even after being dropped, if undisturbed. Now from (3) one can infer that (6) the cause of the motion of projectiles is the impulse conveyed to them by the projector, and consequently that (7) the cause of the horizontal motion of the rock, after it has been dropped, is the horizontal impulse given to it by the hand holding it before dropping. But (8) there is no way in which this horizontal impulse could be disturbed by the vertically downward tendency due to the weight, because (9) the two are not opposed, but are at right angles, to each other, and (10) they have distinct causes (the projector and gravity, respectively). It follows that (11) the horizontal motion of the dropped falling rock is undisturbed, and hence that (12) that motion will continue, and therefore that (13) the rock will end up at the foot of the mast on the moving ship.
This argument is ingenious and plausible, although not completely conclusive and compelling. It presupposes the principle of the superposition of motions, which is lurking around in the justification of proposition (8) by (9) and (10), and which needs more elaboration; and it presupposes the principle of conservation of motion, a version of which is stated in proposition (4). So it is not surprising that Galileo would seek a direct experimental test of the claim that on a moving ship the dropped rock still falls to the foot of the mast, thus refuting empirically the key premise of the anti-Copernican argument based on the ship’s mast experiment. Nor is it surprising that Galileo goes on to elaborate and justify these two principles in the next section of the Second Day. Finally, needless to say, Galileo is well aware that his critical argument merely refutes the anti-Copernican objection, but does not provide support for the Earth’s motion.
Third Day: Annual Motion
The Third Day considers the annual motion and also has a two-fold focus: a part that elaborates some arguments in favor of attributing this motion to the Earth, and a longer part criticizing arguments against it (that is, in favor of attributing such a motion to the Sun instead).
One of the arguments in favor of the Earth’s heliocentric revolution is, as we have seen, based on retrograde planetary motion, claiming that the geokinetic explanation of this phenomenon is more coherent and better than the geostatic explanation. This was a well-known argument since Copernicus, and Galileo adapts it from him. Another of the arguments was partly old and partly new. It was based on the heliocentrism of planetary motions, that is, the claim that the planets (Mercury, Venus, Mars, Jupiter, and Saturn) revolve in orbits centered at the Sun, rather than at the Earth. This had become a widely accepted claim, especially since Tycho, whose system combined it with the traditional geostatic thesis: the Earth stood still at the center of the universe, but the Sun with the whole Solar System of the planets revolved daily and annually around the motionless central Earth. Although Galileo presented some new evidence in support of planetary heliocentrism, he also devised a new argument on that basis in favor of the Earth’s annual motion.
The heliocentrism of the five planets says nothing about the motion or rest of the Earth. However, it does say something about the location or position of the Earth: the Earth is located between Venus and Mars, because Venus (and Mercury) are never observed to be on the opposite side of the Sun in the sky, whereas Mars (and Jupiter and Saturn) are sometimes in opposition; thus, the orbit of Mars encloses the Earth (as off center) as well as the Sun (at the center), but the orbit of Venus encloses only the Sun but not the Earth. And then Galileo advances three reasons for the Earth’s motion: it is more fitting to have the center (the Sun) rather than a point off center (the Earth) be motionless; the Earth is positioned between two other bodies (Venus and Mars) which perform orbital revolutions; and the period of the Earth’s orbital revolution (one year) would be intermediate between the periods of Venus and Mars (nine months and two years, respectively), just as the size of its orbit would be intermediate between the sizes of theirs. This is a kind of simplicity argument, ingenious and plausible; but of course it is not conclusive.
Finally, there is an argument in the Third Day that is novel with regard to both the evidence used and the reasoning arising from it. The new evidence analyzed by Galileo concerns the annual pattern of sunspot paths. And the reasoning is basically that this phenomenon is better explained geokinetically than geostatically.
The observational evidence about sunspot paths had been described in detail in a 1630 book published by Jesuit astronomer Christoph Scheiner, but he gave a geostatic explanation of the phenomenon. This was the same Scheiner with whom in 1612–13 Galileo had had a bitter dispute over the priority of discovery and the interpretation of sunspots in general, although at that time neither had yet observed the annual cycle of sunspots. Although Galileo says in the Third Day that he had observed this annual cycle before and independently of Scheiner’s book, Galileo had never mentioned the phenomenon before; moreover, there is no question that he was led to understand its Copernican significance by Scheiner’s book. This is the important point for us here.
Galileo summarizes the observable facts about the trajectories followed by sunspots by means of some diagrams, which may be adapted with slight modifications as follows. Figure 155 represents four views of the solar disk and of sunspot paths at roughly three-month intervals. MN is a line perpendicular to the line of sight of a terrestrial observer and located in the plane of the ecliptic, which plane we can imagine to be perpendicular to the plane of the paper, while we regard the observer to be located in this plane. Most of the time, the trajectories are both inclined and curved with respect to the plane of the ecliptic.
Figure 15. Annual cycle of sunspot paths
However, twice a year, at about six-month intervals, the curvature of the sunspot trajectories is absent and their inclination is maximum, so that sunspots appear to follow a slanted rectilinear path (views A and C). In the first of these views (A), the slant is upwards; a spot that first becomes visible at E appears to move along line EG toward G. In the third view (C), the slant is downwards, with spots first visible at G appearing to move toward E along line GE.
Moreover, the curvature is maximum at two other times of the year (views B and D), also separated by six-month intervals from each other, but interspersed at three-month intervals with the two other views (A and C). At one of these times of maximum curvature (B), the curvature is upward from the plane of the ecliptic, but six months later (D), the curvature is downward. And at these times there is no slant—the spots are seen to begin and end their path at points equally distant from the ecliptic (near F and H in view B; and near H and F in view D). At these times, the direction of motion is the same as for all other times, namely from left to right of the observer.
Aside from these four special times, the paths of sunspots usually appear both curved and slanted and are continuously changing, with the curvature being upward for half a year and downward for the other half, and with the slant also alternating in a similar manner.
Galileo’s geokinetic explanation of such sunspot paths is best stated in terms of another diagram (Figure 16).6 This represents the Earth’s annual orbit ABCD, or ecliptic, around the central Sun, represented by the sphere KELG. (The Earth’s daily axial rotation is not represented here, and plays no role in this part of the argument. And although the Earth’s orbit is drawn in an elliptical shape, this is not a reference to Kepler’s first law of planetary motion, but reflects the convention that we are looking at a circle from an angle.) AC and DB are diameters of the Earth’s orbit. NS is the axis of the Sun’s monthly rotation, N corresponding to its north pole, and S corresponding to its south pole; note that axis NS is inclined to the plane of the ecliptic. Circle EFGH is the solar equator, equidistant from the poles, and perpendicular to the axis. KFLH is a great circle of the solar sphere, at the intersection of the solar body and the ecliptic plane.
Figure 16. Geokinetic explanation of annual cycle of sunspot paths
As the Earth revolves around the Sun in a counterclockwise direction (through points A, B, C, D), terrestrial observers get different views of the path of sunspots. When (from D) the Sun’s north pole is tilted toward us, sunspots rotating along the solar equator (or circles parallel to it) will appear to bend southward (i.e., downward), along curve HEF; whereas from B, when it’s the Sun’s south pole that is tilted toward us, sunspots (still rotating counterclockwise over the solar body) will appear to bend northward (i.e., upward), along curve FGH. On the other hand, about a quarter of a circle after D, from A, we will see the greatest inclination northward (along EFG) but no bending or curving; and from a point reached six months after A, namely from C, the path will again appear straight, still left to right or counterclockwise, but now inclining southward. These visualizations become easier if we compare Figure 16 with Figure 15 embodying the observed path of the sunspots across the Sun (note that the letters in the two figures correspond).
In short, the Earth’s annual motion around the Sun explains in a simple, coherent, and natural manner why we observe sunspot paths to exhibit an annual cycle. By contrast, to explain the phenomenon geostatically, the Sun would have to be attributed an additional motion, besides its diurnal and annual motions and monthly axial rotation. Such a fourth motion would have to be one of the following: if the Sun is rigidly attached to its own orb in accordance with the traditional geostatic system, then there must be an annual precession of the solar axis of monthly rotation in a direction (clockwise) opposite to its rotation, to ensure that the north pole of this axis points in the proper sequence relative to a terrestrial observer—left, away, right, and toward; or if the traditional orbs are discarded and solar rotation is conceived in a Galilean manner as an inertial phenomenon, then the Sun’s axis must have a daily precession in the same direction as the diurnal motion, to ensure that in the course of a single day the solar axis points always in the same direction relative to the terrestrial observer, and that the pattern of the annual cycle is not repeated on a daily basis. Such a fourth solar motion would increase complexity; it would be ad hoc; and it would be inexplicable.
As I mentioned, the Third Day devotes more space to the criticism of the anti-Copernican arguments than to the presentation of the pro-Copernican ones. But here we will have to reverse that space allocation and deal with the objections more briefly.
One group of objections to the Earth’s annual motion had already been answered 20 years earlier, at the time of the original telescopic discoveries. This is the case, for example, for the arguments based on the non-observation of Venus’s phases and of the eight-fold variation in Mars’s apparent diameter. As we saw earlier, these arguments are unanswerable as long as one is limited to naked-eye observations, but are easily answered once the telescope reveals the phenomena in question. Galileo had never found the occasion to discuss these issues explicitly and systematically, and he does so in the Third Day.
Galileo makes a methodological confession in this passage to the effect that he personally judged these observational arguments to be so strong that, without the telescope, he (unlike Copernicus) could have never taken the Earth’s motion seriously. In memorable words uttered by Salviati, Galileo reveals:
These are so clearly based on our sense experience that, if a higher and better sense than the common and natural ones had not joined with reason, I suspect that I too would have been much more recalcitrant against the Copernican system than I have been since a lamp clearer than usual has shed light on my path … These are the difficulties that make me marvel at Aristarchus and Copernicus; they … were unable to solve them; and yet … they trusted what reason told them so much that they confidently asserted that the structure of the universe can have no other configuration but the one constructed by them.7
Finally, Galileo also discusses in the Third Day an objection which he could not really refute: the argument from the apparent position of fixed stars, also known as the argument from annual stellar parallax. Recall that this objection argued that if the Earth revolves around the Sun, then in the course of a year the apparent position of any one fixed star (measured, for example, by its angular elevation above the ecliptic) should change; in other words, there should be an annual stellar parallax. But no such parallax was observed, even with the telescope. Galileo’s lengthy discussion amounts to a clarification of the argument, an analysis of the relevant issues, and a description of a research project designed to detect the parallax if it exists.
In fact, the anti-Copernicans had many confusions and misconceptions about exactly what the stellar changes should be. Galileo argues constructively that the Earth’s heliocentric revolution should cause changes such as the following (Figure 8, in Chapter 3): stars lying on the ecliptic plane would exhibit a change in apparent magnitude but no change in angular elevation; stars near the pole of the ecliptic would show a change in elevation but no change in magnitude; stars located in-between (the pole and the ecliptic) would display both types of changes; the amount of such changes would depend on the angular position of a star, such that lower positions would cause bigger changes in magnitude and smaller changes in elevation; finally, the amount of both such changes would vary inversely with the distance of a star. Moreover, because of the extremely large distances involved, all such changes would be extremely small.
Galileo also points out that the objection assumes that the failure to observe annual changes in stellar appearances implies that there are no such changes. And he thinks that this assumption is precisely the weak point of this argument. Perhaps they are not observed because they do not exist, but their absence may also be because no one has searched for them seriously or systematically enough, or with the appropriate instruments, or with the necessary skill.
Accordingly, this passage also contains some practical suggestions about observational procedures and techniques, designed to detect such changes in stellar appearances. Galileo says that we need instruments whose sides are miles long, so that differences of seconds in stellar elevation correspond to distances of the order of cubits along the instrument. This would contrast with the capabilities of even the very best previous astronomical instruments, such as those of Tycho: in his apparatus, the celestial quantities being measured corresponded to differences of a hairsbreadth on the instrument. Galileo is talking about using topographic features on the Earth’s surface, such as mountains. The idea is, for example, to observe the changes in the way a particular star would be hidden by some beam on top of a building, at the top of a mountain, by carrying out observations from the valley below, and at different times of the year.
In this discussion, unlike all other critiques of anti-Copernican arguments, Galileo is not really refuting the argument. Rather, he is admitting that the changes in stellar appearances due to the Earth’s heliocentric revolution are not observed, and he is elaborating a research program designed to detect them if they exist. His elaboration consists of a theoretical analysis of the details of such observational consequences, and of practical suggestions for making the observations. Such a research program was indeed followed in part by subsequent astronomers, such as the Englishman James Bradley, who discovered stellar aberration in 1729; and the German Friedrich Bessel, who measured an annual stellar parallax in 1838.
Fourth Day: Tides
The Fourth Day examines a topic which Galileo had been hinting at in several previous passages—the problem of explaining why tides occur. He makes it clear at the outset that he is going to explain this phenomenon on the basis of the Earth’s motion, and that this explanation will provide a novel argument in favor of the Copernican hypothesis that the Earth moves.
Galileo also makes it clear that this tidal argument for the Earth’s motion is different from his previous pro-Copernican arguments because it involves physical considerations about terrestrial phenomena, whereas those others have all involved astronomical considerations about the heavenly bodies.
Terrestrial physical phenomena had been extensively discussed in the Second Day, in the context of the criticism of the mechanical objections to the Earth’s rotation. But that criticism showed only that the physical phenomena being appealed to could take place on a moving Earth, not that they provide evidence in favor; in other words, that criticism merely refuted the anti-Copernican arguments, without yielding pro-Copernican ones. On the other hand, the tidal motion of the sea is different from the other terrestrial mechanical phenomena: according to Galileo, whereas the latter could occur on both a motionless and moving Earth, the former could only occur on a moving Earth; and this is what yields a pro-Copernican argument.
The discussion begins with a description of the most basic facts about the tides. The phenomenon consists of three kinds of basic motions of seawater: up and down motion, such as the vertical rising and falling of the water level visible inside a harbor, along the sides of a pier; back and forth motion, such as the horizontal water currents observable in certain straits or narrows; and a combination of these two, such as the ebb and flow that takes place in some beaches and shallow coastlines, in which the water alternates between both rising and flowing inland, and dropping and flowing outward to sea. Moreover, these basic tidal motions occur in accordance with various cycles, the most important and noticeable one being the diurnal period: the water usually rises or flows in one direction for about six hours, and then it drops or flows in the opposite direction for another six hours. So during the twenty-four hours of a single day, there are two high and two low tides separated by six-hour intervals, and there are two full cycles of 12 hours during each of which the water exhibits all the motions that characterize a particular location.
This phenomenon had puzzled mariners and thinkers from time immemorial, and various attempts had been made to explain why seawater exhibits such motions. Galileo gives a brief critical review of the main alternative explanations. Some had tried to explain the tides as a result of an attraction exerted by the Moon toward the water directly below. This explanation was in part supported by the well-known and undeniable fact that there is a correlation between the daily motion of the Moon and the tides. Yet Galileo dismissed such an explanation for two reasons. First, lunar attraction would produce the same tidal motion in all parts of a given sea, for example, both in Venice at the northwestern end of the Adriatic Sea and in Dubrovnik at the southeastern end of the same sea; but that is not the case. Second, he regarded the lunar-attraction account as methodologically inappropriate, insofar as attraction was an “occult” property involving a magical view of nature and the resulting explanation would be tantamount to explaining a phenomenon by giving a name to it. At one point, he even chides Kepler for his “childish” belief in a lunar-attraction theory. The irony is of course that the lunar-attraction explanation turned out to be essentially correct; Isaac Newton explained the tides in 1687 in terms of the law of universal gravitation and the different gravitational forces exerted primarily by the Moon (but also by the Sun) on different parts of the oceans and land.
The first step in Galileo’s own explanation is to show that when a container of water undergoes acceleration or retardation, the water experiences vertical up and down motions at the extremities and horizontal back and forth motion in the middle part of the container. Labeling such movements tidal-like motions, and taking the term acceleration in the strict general sense that includes retardation as negative acceleration, the first step is to state and support the generalization that acceleration causes tidal-like motion.
To see this, consider a boat with a large rectangular tank full of water, going from one seaport to another over a calm sea, such as one of the boats that deliver fresh drinking water to the city of Venice from the nearby coast. Consider now what happens to the water in the tank as the boat begins its journey and starts moving. The acceleration imparted to the boat and the tank is not instantly communicated to the water in the tank. This water will tend to be left behind and flow backwards, so that its level will rise at the back end of the tank and drop at the front end. Being a fluid, the water will then tend to flow in the opposite direction, from the back to the front end of the tank; the water level will then rise in front and drop in the back. This process of oscillation will continue for a while, even though the boat may have reached a uniform cruising speed. Moreover, during this process, if we look at the middle part of the tank, the water there will mostly not rise or drop, but rather move horizontally backwards first, then forward, then backwards again, and so on. After a while, however, if the boat continues moving uniformly over a calm sea, the water in the tank will also calm down and no longer experience those motions within the tank; it will simply follow the forward motion of the boat.
Now suppose the boat runs aground in shallow water, thus experiencing a strong reduction in speed until it stops. Such retardation will cause the water in the tank to start its oscillatory motion, like during the initial acceleration, except in reverse order. At first, the water will rush forward, increasing the level in front and lowering it at the back, then the other way, and the oscillations will continue for a while before dying down. Besides such acceleration on starting and stopping, merely increasing or decreasing the speed of the boat while cruising would have similar effects.
So Galileo’s first intermediate conclusion is that the acceleration or retardation of a body of water causes it to undergo tidal-like motions. Now, he applies this generalization to the case of a moving Earth in the Copernican system, making the key analogy that a sea basin, such as the Mediterranean Sea, is a container of water being carried by the moving Earth. And the generalization applies in the sense that the Earth’s axial rotation and its orbital revolution combine in such a way as to generate daily accelerations and retardations in the motion of such a sea basin. The second step in the Galilean explanation is precisely to show that, if the Earth were moving (with the two motions of axial rotation and orbital revolution), then every point on the Earth would regularly and alternately undergo a daily acceleration and a daily retardation.
In Figure 17,8 circle GEC is the orbit in which the Earth moves in a counterclockwise direction, around the central Sun at A. Circle DEFG represents the Earth, which rotates around its own center B, in the same (counterclockwise) direction. Here both motions are taken to be constant and uniform: the Earth’s center B moves around the Sun A at a speed that enables it to traverse the whole circumference of circle GEC in one year; while any given point on the Earth, for example D, in the period of 24 hours traverses the whole circumference of the Earth, DEFG.
Figure 17. Geokinetic explanation of daily tides
Now, consider how these two motions combine with each other. For a terrestrial point located on the opposite side from the Sun and experiencing midnight, for example D, the diurnal speed and the annual speed are in the same direction, toward the left; so they add up to give point D an actual speed that is the sum of the two, by reference to absolute space or at least to the center of the Sun A. But for a terrestrial point located on the side facing the Sun and experiencing noon, for example F, the annual and diurnal speeds are in opposite directions, the former still toward the left but the latter toward the right; thus they work against each other to give point F an actual speed that is the difference between the (greater) annual speed and the (smaller) diurnal speed. For intermediate midway points on the Earth’s surface, such as E and G, their diurnal speed has no effect on their annual speed, at least from the point of view of the west-to-east (i.e., right-to-left) direction; thus, such points move toward the left with a speed equal to just the annual speed.
At D the total actual speed is the maximum; at F it is the minimum. This applies to every point on the Earth’s surface in the course of 24 hours, and so any such point will alternate between such a maximum and a minimum speed. Moreover, in moving from D (through E) to F, a terrestrial point is undergoing retardation; whereas in moving from F (through G) to D, it is undergoing acceleration. This also applies to every point on the Earth, and so we may also say that every day every such point experiences acceleration for 12 hours and then retardation for another 12 hours, and so on. Furthermore, while moving from G to D and to E, every terrestrial point moves at a speed that is greater than the annual speed; whereas, when moving from E to F and to G, it moves at a speed that is smaller than the annual speed. So we may also say that every day every point on the Earth alternates between moving at a speed greater than the annual speed for 12 hours, and moving at a lower speed for the next 12 hours, and so on.
The daily accelerations and retardations just described constitute for Galileo the primary cause of the tidal motions of the sea. That is, he means partly that without such changes of speed there would be no tides; in this sense, they provide a necessary condition for the tides. He also means that such changes of speed get the whole process of the tides started; and in this sense, they contribute to the production of the tides. However, by itself the primary cause is not sufficient, and we need other concomitant causes, which he subdivides into secondary and tertiary causes. The secondary causes involve the fluid properties of water, which Galileo elaborates at length. The tertiary causes are such factors as the flow of large rivers into small seas, the action of winds, and the topographical interrelationships of sea and land.
Other complications stem from the fact that, besides the basic tidal motions, the phenomenon exhibits various features, secondary tidal effects, that also require explanation; an example being that there are no tides in lakes and small seas. Finally, besides the daily period of the tides, Galileo also tries to explain the monthly and annual variations in the tides.
It is obvious that the basic structure of Galileo’s tidal argument is explanatory, in the sense that its conclusion (the Earth’s motion) is supported by showing that it can provide an explanation of some facts (the tides) stated in the premises. In this regard, this argument is structurally similar to several others presented earlier in the book that provide explanations of various astronomical facts (some old and some new). However, in those previous arguments a key point was that the geokinetic explanation was simpler or more coherent than the geostatic. Instead, in the present case, Galileo believes and argues that there is no geostatic explanation; that there is no way of explaining the tides as long as the Earth stands still. So the complexities of his own geokinetic explanation do not really weaken it; they are needed because of the complexity of the phenomenon to be explained.
On the other hand, Galileo is aware that just because no satisfactory geostatic explanation of the tides has yet been devised does not mean that no such explanation is logically possible. Such a possibility cannot be ruled out; this is so partly for theological reasons stemming from divine omnipotence, but also for methodological reasons stemming from the logic of explanation. And Galileo mentions the theological argument at the very end of the Fourth Day, as required by the pope and the censors; and he elaborates the logic and methodology of explanation in several previous passages. Indeed, we can interpret the later elaboration of a gravitational explanation of the tides by Newton as providing an alternative and better explanation than Galileo’s, and thus weakening and invalidating his tidal argument in a straightforward manner.
Rhetorical Flourishes and Poetic License
The account just given provides a summary of the essential parts of the content and structure of the Dialogue from the point of view of astronomy, physics, and the Copernican controversy. I have also summarized a few of Galileo’s methodological or epistemological discussions that happened to be especially relevant to the argument and particularly incisive or memorable. Indeed, the book is full of such concrete philosophical reflections, so much so that they make it easy to see why, as I put it in the Introduction, Galileo may be rightly regarded as the Socrates of methodology and epistemology.
There is another aspect of the book which I have so far almost completely ignored. I refer to the book’s rhetorical dimension. Here, by rhetoric I mean the theory and practice of verbal communication, in all its variety of expression.
The book’s rhetoric derives in part from its universalist aim; Galileo is addressing several audiences at once. It derives in part from its dialogue form, which means that there is a certain amount of drama unfolding before the reader. It stems from the controversial character of the scientific and epistemological issues discussed, which means that we are witnessing a brilliant polemic. It also arises from the context of Galileo’s struggle with the Catholic Church: in writing the book he was taking considerable risks and could not always safely say what he meant or mean what he said. Finally, the rhetoric originates to some extent from the fact that the practice of science at that time was socially and financially dependent for the most part on the patronage of princes; this means generally that Galileo’s career was partly that of a courtier, and specifically that his book represented an action in an intricate and delicate network of patronage involving the Tuscan Medici court in Florence and the Vatican court of Pope Urban VIII in Rome.
I am not equating rhetoric with the art of deception, in particular the skill of making the weaker argument appear stronger. So understood, rhetoric would be an inherently objectionable activity, whereas my definition allows both good and bad rhetoric. Nevertheless, rhetoric does not easily mix or coexist with scientific inquiry, critical reasoning, and methodological reflection; it considerably complicates the proper understanding and evaluation of the book. Indeed, the book’s rhetoric is one of the things that led to the Inquisition proceedings against it, as we shall see.
The Dialogue also happens to be a great work of art, because Galileo was a gifted writer who poured his heart and soul into this work, so much so that many passages achieve a high degree of literary and aesthetic value. Indeed, Galileo is widely regarded to be one of the greatest writers in the (800-year) history of Italian literature, rivaled only by poet Dante Alighieri (1265–1321) and his Divine Comedy. If we define poetry in terms of expressiveness and imagery, rather than formalistically (in terms of verse, rhyme, and meter), we could say that the Dialogue is a scientific and philosophical poem. The book is full of passages which are best understood and appreciated in terms of artistic inspiration, aesthetic imagination, and poetic license. This aspect of the book also played a part, however small, in the trial proceedings, specifically in Galileo’s confession of some wrongdoing, stemming from literary vanity. Galileo is in places prone to rhetorical excess and poetic license.
We have already seen that the three speakers in the book’s dialogue are named Simplicio, Salviati, and Sagredo, and that they represent, respectively, the Aristotelian, Copernican, and layperson’s point of view. In the book’s preface, Galileo states that Salviati and Sagredo were names of recently deceased friends with whom he had discussed such topics; but Simplicio was the (Italian) name of a famous commentator to Aristotle’s works, who lived in the sixth century ad, and whose Latin name is Simplicius. This seems a reasonable choice. But the name Simplicio also has the connotation of simpleton. Moreover, recall that Simplicio is the interlocutor who loses all the arguments (although he is neither stupid nor simple-minded, and occasionally displays flashes of great logical insight,9 which are shared by Salviati and Galileo himself ). Hence, with the name Simplicio, Galileo seems to be engaged in a double entendre, to remind readers of the inferiority of the Ptolemaic system to the Copernican.
Take an example involving the Earth–heaven dichotomy. This thesis included the idea that the heavenly bodies (primarily the Sun, but also the planets and the fixed stars) cause physical changes in the terrestrial bodies, although they are themselves unchangeable. We saw earlier that Galileo criticizes the Earth–heaven dichotomy on substantive observational grounds, as well as on theoretical conceptual grounds. But he also could not resist the temptation of making fun of this particular idea. In the middle of the First Day, he points out that this is like “placing a marble statue beside a woman and expecting children from such a union.”10
Other aspects of the Ptolemaic system also lent themselves to ridicule. At the end of the Second Day, Galileo picks on its feature that the Earth is at the middle of everything, even though the heavens are noble, perfect, and incorruptible and the Earth is base and full of imperfections and impurities: “What a way of separating the pure from the impure and the sick from the healthy—to give those who are infected room at the heart of the city! And I thought that the pesthouse should be located as far away as possible!”11
Other types of rhetoric abound. For example, we have seen that some of the objections to the Earth’s diurnal motion were based on mechanical phenomena and the laws of motion. Some of these mechanical arguments dealt with the range and accuracy of gunshots in various directions on a rotating Earth, comparing and contrasting gunshots toward the east and west, toward the north and south, vertically upwards, and in a horizontally point-blank direction. Such gunshot arguments are not found in Aristotle’s works, since gunpowder had not been invented during his lifetime. However, after this invention, anti-Copernicans formulated new arguments against the Earth’s motion based on gunshots.
Now, at the beginning of the Second Day, Simplicio confesses his relative ignorance about such modern arguments, and Salviati volunteers to give full and detailed statements of them. After Salviati is finished, Simplicio expresses his joy at the fact that the truth (that the Earth stands still) can be supported by such irrefutable arguments and novel evidence (as compared with that available at the time of Aristotle). At this point, Sagredo interjects: “What a pity that there were no cannons in Aristotle's time! With them he would have indeed conquered ignorance.”12 The rhetorical service performed by this witticism is to insinuate that the anti-Aristotelians have such an understanding of the Aristotelian position as to be able to eloquently present new evidence in its favor, and thus to incline readers to think more highly of Copernicanism.
The Third Day does not lack its share of rhetoric. Here is a different kind of example. In the discussion of the heliocentrism of planetary motions, Galileo hurls an insult to some opponents of Copernicanism by calling them “men whose definition contains only the genus but lacks the difference.”13 In traditional logic, definitions were given by identifying the genus and the species (or specific difference) to which the thing to be defined belongs; the genus is a broader category of classification, and the species (or specific difference) is a subdivision within the genus. Modern biological taxonomy still follows this procedure. Modern humans, Homo sapiens, belong to the genus Homo and the species sapiens.
Now, traditional Aristotelian doctrine defined man as “rational animal,” namely as belonging to the genus “animal” and the species (or specific difference) “rational.” If from this definition of man the species is removed, we are left with “animal”; so a person whose definition contains only the genus is an alleged rational animal who is not really rational but only a mere animal. Galileo is here engaged in name-calling; subtle and not prosaic to be sure, but name-calling nonetheless.
Finally, here is an example from the Fourth Day. We saw earlier that, before elaborating his own geokinetic explanation of the tides, Galileo gives brief criticisms of alternative explanations. One of these explained the phenomenon as due to the Moon, and one version of the Moon theory claimed that, as the Moon moved above a particular sea on Earth, the Moon’s heat warmed the water below, causing it to expand and its level to rise. One of Galileo’s criticisms of this version is the empirical one of inviting anyone to test the temperature of water at high and at low tides, and see that there is no difference. To this he adds, referring to proponents of this theory, the following gem: “tell them to start a fire under a boiler full of water and keep their right hand in it until the water rises by a single inch due to the heat, and then to take it out and write about the swelling of the sea.”14 He does not elaborate, but I suppose the point is that the expansion of water due to heat is not that great, so anyone trying the boiler experiment would burn their hand waiting for the water to rise by an inch.