Chapter 5: Parameter Determination

and the

Great Argument

What then are the conditions logically imposed on the choice of hypotheses to serve as the base of our physical theory? . . . [One condition is that] physical theory . . . is not to be resolved into a mass of disparate and incompatible models; it aims to preserve with jealous care a logical unity, for an intuition we are powerless to justify, but which it is impossible for us to be blind to, shows us that only on this condition will theory tend towards its ideal form, namely, that of a natural classification. Pierre Duhem, The Aim and Structure of Physical Theory(1)

Coincidences do occur, but we should not seek their complexities as favored modes of explanation. Stephen Jay Gould(2)


A considerable number of promissory notes remain from the preceding chapters. The principal epistemological challenge is to explain how major players in the Copernican episode, such as Galileo and Kepler, could rationally become Copernicans at a time when not many other scientists were, how their pursuit of heliostasis could occur prior to their discoveries, and how their discoveries could then eventually convince virtually a whole generation of scientists to become Copernicans prior to Newton's Principia. I have argued that the traditional polar opposites of Legend and psycho-social relativism are equally extreme and wrong; that an epistemological story can be told that answers the principal challenge of the Copernican episode by showing that what was occurring was a gradual clarification, strengthening and concomitant weakening of different hypertextual adjudicatory trails, with a major role played by the emerging theory choice constraint of parameter determination. The relativists are right that scientists often do choose to patch a hypertextual adjudicatory trail in the light of anomalies or apparent falsifications, and that in principle with enough creative investment of time and resources such patches can be successful in a purely logical sense. But they are wrong that such patches will always be successful in an ampliative sense, that such patches are incapable of being appraised objectively by well-supported criteria, and that there is always an incommensurability of such appraisal dependent upon theoretical allegiance.

Accordingly, what must now be defended in depth are the following:

1. Although Ptolemaic geostasis and Copernican heliostasis were both systems(3), the interconnected way that Copernicus explains the core problem situation of observational astronomy impressed both supporters and nonsupporters of heliostasis. In other words, key parameters in the heliostatic system are fixed and linked in such a way that they must produce an elegant solution to the "principle challenge" of observational astronomy.(4)

2. The impressive nature of heliostatic parameter determination became a principal motivating factor for nonsupporters of heliostasis to pursue a major auxiliary patch to geostasis, i.e., geoheliocentrism.

3. The pursuit of this auxiliary patch was successful, such that by the time the Church took a robust stand against realistic heliostasis, geoheliocentrism was the principal surviving geostatic alternative to the heliostatic challenge.(5) However, although defenders of geostasis won a major battle against the heliostatic challenge, the winning of this very battle caused them to lose the war.

4. Thus, from the standpoint of the strengthening and weakening of hypertextual adjudicatory trails, adoption of parameter determination as a constraint not only motivated geoheliocentrism, but this auxiliary patch in turn exposed many weak nodes in the general defense of geostasis. In fact, it is not an exaggeration to say that in the light of empirical developments (comets, novae, Galileo's telescopic results) and continuing successful conceptual development of heliostasis (Kepler's elliptical orbits and Galileo's work in dynamics), the very auxiliary patch that was supposed to save geostasis exposed geostasis as a "worm-eaten" system, as a hypertextual adjudicatory trail unraveling along many nodes.

In addition to defending these points, a crucial issue that must be discussed is the epistemic status of parameter determination itself. In other words, even if the above historical sequence is correct, that major players behaved this way, the question remains "ought" they to have behaved this way? Even if parameter determination ought to be a constraint on theory choice, what kind of constraint is it? Is the desirability of theories that display a greater comparative logical unity, an interlinking of postulates and parameters linked in turn with disparate but well-known observations, in the words of Duhem quoted above, only "an intuition we are powerless to justify"? Is its value purely pragmatic, heuristic, and prospective in that theories that fix key parameters are more fruitful in terms of ease of future testability? Or can something substantially more be claimed for this constraint? Can its value also be perceived as retrospective in providing a kind of empirical evidence for a theory?

In answering these questions one must be careful not to impose a modern perspective upon the Copernican episode players. In scientific practice today, parameter determination and intertheoretical consistency play major roles in motivating and constraining theoretical pursuit. As noted previously, the Standard Model of quantum field theory solves many problems, but when applied to explaining the first microseconds of the universe, it leaves numerous initial conditions flexible. Hence, we find large scale pursuit by physicists of a better theory that will solve the same problems, but lock in all the parameters at once. There is a suspicion that because of flexible parameters, the Standard Model has not quite got it right. Similarly, the fact that quantum mechanics and the general theory of relativity remain inconsistent has motivated the pursuit of numerous alternatives to Einstein's conception of gravity.(6) There is a similar suspicion that something is not right about the general theory, because as it is currently developed we do not possess a unity of treatment with quantum physics. However, assuming the meta-methodological standpoint that methodologies and theoretical constraints are themselves justified over time empirically, one must remember that modern scientists and philosophers of science have had an additional 400 years plus of experience testing methodologies.

My contention will be the following: Although attributing an oversimplified epistemic status to parameter determination is incorrect, and although the heuristic value of parameter determination in terms of ease of future testability is no doubt correct -- every test is potentially a "deadly test" if predictions are fixed -- something more can be said for parameter determination when it is not seen in isolation, when it is combined with the concepts of pursuit and hypertextual adjudicatory trails.

The Golden Chain Argument

We must first establish then what the major players, supporters and nonsupporters alike, found impressive about Copernican heliostasis. Why did it create an immediate stir?(7) Why was it pursued by some and at least studied carefully even by those who could not accept its cosmological implications? Prior to examining the technical details, it is important to let the major players speak for themselves.


"With regard to the apparent motions of the Sun and Moon, it is perhaps possible to deny what is said about the motion of the Earth, although I do not see how the explanation of precession is to be transferred to the sphere of the stars. But if anyone desires to look either to the order and harmony of the system of the spheres, or to ease and elegance and a complete explanation of the causes of the phenomena, by no other hypotheses will he demonstrate more neatly and correctly the apparent motions of the remaining planets. For all these phenomena appear to be linked most nobly together, as by a golden chain; and each of the planets, by its position and order and very inequality of its motion, bears witness that the Earth moves. . . .

I sincerely cherish Ptolemy and his followers equally with my teacher, since I have ever in mind and memory that sacred precept of Aristotle: "We must esteem both parties but follow the more accurate." And yet somehow I feel more inclined to the hypotheses of my teacher. This is so perhaps partly because I am persuaded that now at last I have a more accurate understanding of the delightful maxim which on account of its weightiness and truth is attributed to Plato: "God ever geometrizes"; but partly because in my teacher's revival of astronomy I see, as the saying is, with both eyes and as though a fog had lifted and the sky were now clear, the force of that wise statement of Socrates in the Phaedrus: "If I think any other man is able to see things that can naturally be collected into one and divided into many, him I follow after and 'walk in his footsteps as if he were a god.'" 1540, Narratio Prima(8)


"Certainly this is the great argument, viz. that all the phenomena as well as the order and magnitudes of the orbs are bound together in the motion of the Earth. (This is one of Maestlin's many annotations to his copy of Copernicus's De revolutionibus. Westman believes it was made between 1570 and 1580.)"(9)


". . . the ancient hypotheses clearly fail to account for certain important matters. For example, they do not comprehend the causes of the numbers, extents and durations of the retrogradations and of their agreeing so well with the position and mean motion of the sun.

Copernicus alone gives an explanation to those things that provoke astonishment among other astronomers, thus destroying the source of astonishment, which lies in the ignorance of the causes." 1596, Mysterium Cosmographicum(10)



"In the Ptolemaic hypotheses there are the diseases, and the Copernican their cure. . . . With Ptolemy it is necessary to assign to the celestial bodies contrary movements, and make everything move from east to west and at the same time from west to east, whereas with Copernicus all celestial revolutions are in one direction, from west to east. And what are we to say of the apparent movement of a planet, so uneven that it not only goes fast at one time and slow at another, but sometimes stops entirely and even goes backward a long way after doing so? To save these appearances, Ptolemy introduces vast epicycles, adapting them one by one to each planet, with certain rules about incongruous motions -- all of which can be done away with by one very simple motion of the Earth.


I should like to arrive at a better understanding of how these stoppings, retrograde motions, and advances, which have always seemed to me highly improbable, come about in the Copernican system.


Sagredo, you will see them come about in such a way that the theory of this alone ought to be enough to gain assent for the rest of the doctrine from anyone who is neither stubborn nor unteachable. I tell you, then, that no change occurs in the movement of Saturn in thirty years, in that of Jupiter in twelve, that of Mars in two, Venus in nine months, or in that of Mercury in about eighty days. The annual movement of the Earth alone, between Mars and Venus, causes all the apparent irregularities of the five stars named. . . . (explains Jupiter's motion, then follows with)

Now what is said here of Jupiter is to be understood of Saturn and Mars also. In Saturn these retrogressions are somewhat more frequent than in Jupiter, because its motion is slower than Jupiter's, so that the Earth overtakes it in a shorter time. In Mars they are rarer, its motion being faster than that of Jupiter, so that the Earth spends more time in catching up with it.

Next, as to Venus and Mercury, whose circles are included within that of the Earth, stoppings and retrograde motions appear in them also, due not to any motion that really exists in them, but to the annual motion of the Earth. This is acutely demonstrated by Copernicus . . .

You see, gentlemen, with what ease and simplicity the annual motion -- if made by the Earth -- lends itself to supplying reasons for the apparent anomalies which are observed in the movements of the five planets. . . . It removes them all and reduces these movements to equable and regular motions; and it was Nicholas Copernicus who first clarified for us the reasons for this marvelous effect." 1632, Dialogue Concerning the Two Chief World Systems(11)

Gemma Frisius

"While at first glance the Ptolemaic hypotheses may seem more plausible than Copernicus', nevertheless the former are based on not a few absurdities, not only because the stars are understood to be moved nonuniformly in their circles, but also because they do not have explanations for the phenomena as clear as those of Copernicus. For example, Ptolemy assumes that the three superior planets in opposition -- diametrically opposite the sun -- are always in the perigee of their epicycles, that is, a "fact-in-itself." In contrast, the Copernican hypotheses necessarily infer the same thing, but they demonstrate a 'reasoned fact.'" 1560(12)


"Now . . . everyone approves the calculations of Copernicus . . . . (and) this symmetry of all the orbs appears to fit together with the greatest of consonance . . . . (so) we follow Ptolemy, in part, and Copernicus, in part." 1592(13)


"[In examining the Ptolemaic hypotheses] . . . it gave me great concern that no necessary cause or natural combination explained why the superior planets are bound to the sun in such a way that at conjunction they always occupy the top of their epicycles, at opposition the lowest point of the same, and that the two planets that are called inferior always have the same mean position with the sun and are close to it at apogee and perigee of their epicycles." 1588 Letter to Casper Peucer(14)

"The testimonies of the planets, in particular, agree precisely with the Earth's motion and thereupon the hypotheses assumed by Copernicus are strengthened." (Tycho's annotation of De revolutionibus -- approximately 1575 -- regarding the more "exquisite order" implied by the heliostatic arrangement.)(15)

"I considered that the old Ptolemaic arrangement of the celestial orbs was not elegant enough, and that the assumption of so many epicycles by which the appearances of the planets towards the Sun and the retrogradations and stations of the same, with some part of the apparent inequality, are accounted for, is superfluous. . . . At the same time I considered that newly introduced innovation of the great Copernicus . . . by which he very elegantly obviates those things which occur superfluously and incongruously in the Ptolemaic system, and does not at all offend against mathematical principles. (Upon introducing his geoheliocentric alternative in his De Mundi Aetheri Recentioribus Phaenomenis (Uraniborg, 1588), explaining why, although he continued to believe "the Earth, large, sluggish and inapt for motion," he became convinced that "the simple motion of the Sun is necessarily involved in the motion of all five planets," that "the Sun regulates the whole Harmony of the Planetary Dance."(16))

And, of course,


"We find, then, in this arrangement the marvelous symmetry of the universe, and a sure linking together in harmony of the motion and size of the spheres, such as could be perceived in no other way. For here one may understand, by attentive observation, why Jupiter appears to have a larger progression and retrogression than Saturn, and smaller than Mars, and again why Venus has larger ones than Mercury; why such a doubling back appears more frequently in Saturn than in Jupiter, and still more rarely in Mars and Venus than in Mercury; and furthermore why Saturn, Jupiter and Mars are nearer to the Earth when in opposition than in the region of their occultations by the Sun and re-appearance . . . . All these phenomena proceed from the same cause, which lies in the motion of the Earth.

(In contrast with the Ptolemaic models) . . . although they have extracted from them the apparent motions, with numerical agreement, nevertheless . . . . They are just like someone including in a picture hands, feet, head, and other limbs from different places, well painted indeed, but not modelled from the same body, and not in the least matching each other, so that a monster would be produced from them rather than a man. Thus in the process of their demonstrations, which they call their system, they are found either to have missed out something essential, or to have brought in something inappropriate and wholly irrelevant, which would not have happened to them if they had followed proper principles. For if the hypotheses which they assumed had not been fallacies, everything which follows from them could be independently verified." 1543(17)

See Figures 3,4,5,6; especially 5 & 6.

It is crucial to note from these assessments that there is no incommensurability of appraisal regarding the comparative harmony, symmetry, elegance, and, what we have called, the parameter determination capability of the Copernican system. All of the above, whether supporters or nonsupporters of heliostasis (Frisius, Praetorius, and of course Tycho, were not supporters) were impressed with the heliostatic ability, not only to produce the core problem observations as a necessary consequence of the model, but to link the observations and the parameters in such a way that there is relatively little flexibility in what they must be. For instance, the Copernican system not only elegantly produces retrograde motion, but fixes the number, size, and frequency of retrogressions for each planet. (Figure 6)

True, as Kuhn has noted, there was a different weight attached to this harmony. Copernicans tended to see it as discriminating evidence for heliostasis. However, it is clear that, contra Kuhn, supporters and nonsupporters of heliostasis were not "talking through each other." As Tycho noted, the testimony of the core observational problem and the linking of the details strengthened heliostasis. This feature achieved independent recognition as a desirable constraint on theory choice. A gestalt switch was not needed for this recognition; one did not need to be a Copernican to recognize and appreciate the parameter determining features of heliostasis.

Praetorius, a member of the Wittenberg circle and a supporter of geostasis, was one of the first astronomers to begin experimenting with geostatic transforms of heliostatic parameters, because he recognized that it was necessary to follow Ptolemy in part (the Earth does not move) and Copernicus in part (the interlinking features of Copernicus's models are too appealing to be ignored). And by the time of Tycho, we see that he is convinced based on "the more exquisite order" of Copernican models that the Sun must regulate "the whole Harmony of the Planetary Dance."

In the light of major debates regarding scientific change and the notion of hypertextual adjudicatory trails discussed in this thesis, we see an example of piecemeal change: the appeal of parameter determination became a node on both the geostatic and heliostatic webs of belief. Although one can see a continuity of concern for a unitary account from the time of the ancient Greeks, in Ptolemy's Planetary Hypotheses, through the medieval Arab astronomers, and up to the Renaissance, the story told here is that the appeal of a unified treatment in terms of linking parameters that fixed the observations of the core astronomical problem situation became more vivid upon the challenge of heliostasis. Just as defenders of heliostasis eventually recognized that they needed a much stronger dynamical story in response to the challenge of geostasis than the pitiful tale told by Copernicus in De revolutionibus, so defenders of geostasis recognized that they needed a much stronger account regarding the many linkages of planetary motion with the sun than the "fact-in-itself" coincidences of Ptolemy noted by Frisius above.

Although we will consider more of the technical details in depth shortly, it is important to note the point both Frisius and Tycho are making regarding one superior technical feature of linking planetary motion with the sun. When the superior planets are at opposition, they are not only in the middle of a retrogression, but they are noticeably brighter and thus presumably closer to the Earth as well. Hence, there is an apparent link between the positioning of the sun, the Earth, the superior planet, and the latter's brightness and direction of motion. The basic difference between the Ptolemaic and Copernican systems regarding these observations is that they are geometrically required by the latter (Frisius's "reasoned fact"). In other words, although these observations are handled remarkably by Ptolemaic geometry ("well-painted," according to Copernicus), one realizes upon comparison with Copernican geometry that the linkages are a coincidence for Ptolemy in the sense that the linkages are separable from the geometry. In the basic geostatic deferent-epicycle system the opposition observation of a superior planet is saved by having the planet revolve on its epicycle at just the right rate such that it reaches its closest approach to Earth at the moment that the Earth is positioned between the superior planet and the sun. However, it was now recognized that there is nothing in the Ptolemaic geometry that necessitates this result; at the moment of opposition the position of the planet could be, a priori, at any position along its epicycle. (Figures 5& 6)

This difference is perhaps best understood in terms of what each model would predict regarding the discovery of a new superior planet. Although there may have been a strong inductive reason to expect a continuation of a very notable pattern, there is no requirement in the Ptolemaic system that the new planet follow the same pattern of the previously known superior planets. Whether the planet is retrogressing and brighter at opposition or not, the Ptolemaic parameters can be adjusted to match the observation. Although in the Ptolemaic system the epicycle radius vectors of the known superior planets are made parallel to the Earth-sun radius vector, and turn at the same rate of time as the sun's radius vector, such that the planets are positioned so that at opposition they are at the bottom of their radius vectors (see Figure 4), as Tycho notes above, there is no requirement ("no necessary cause") for this, i.e., there is neither an a priori requirement for the bottom positioning nor the parallelism. Hence, there is no clear implication for what a new superior must display.(18) On the other hand, in the Copernican system, because retrogression is an illusion caused by the swifter moving Earth bypassing a slower moving superior planet, the superior planet must not only be closer to the Earth but be in a direct line with the sun, with the Earth between the planet and the sun (Figure 6). Accordingly, there is no flexibility for Copernicus in this regard: A new superior planet must follow the same pattern as the known superior planets.

Should this inflexibility have constituted a kind of decisive "second-order" empirical evidence for heliostasis? Can we double-count what we observe in favor of Copernicus? Lakatos, as we have seen, has argued affirmatively; being able to explain well-known observations in this special way was a kind of novel fact. I have argued in the previous chapter that this is to make too much of parameter determination. We can add to that analysis here by noting the obvious point that prior to the observation of additional superior planets that fit the same pattern, this might only mean that heliostasis was "rigidly wrong"!(19) Furthermore, that major players were impressed with certain features of the Copernican system neither provided an overwhelming evidential context that the whole system was correct nor eliminated the possibility that those same features could be incorporated into a modified geostatic model. However, it is clear that from the perspective of pursuit and fruitfulness, Praetorius, Frisius and Tycho believed that the impressive Copernican links with the sun were an indication that the basic geostatic position must be adjusted. The lack of necessitated links created the suspicion that the basic geostatic system just did not have it right. In the light of many other developments affecting various nodes along the Ptolemaic web of belief, it provided an evidential context such that one had a distinct suspicion that the basic Ptolemaic arrangement just would not do and something else was needed; that significant problem solving progress would be made by incorporating Copernican links with the sun into a geostatic system. In short, the significance of parameter determination should neither be seen as "mere aesthetics,"(20) nor as decisive empirical evidence for Copernicus at this time.

Another mistake related to making too much of parameter determination in isolation, is to couch the impressive difference between geostasis and heliostasis in terms of a radical discontinuity in the latter's attempt to create a system.(21) In other words, so this mistaken story goes, the defenders of geostasis were not concerned with a requirement of internal logical consistency or a unified broad-based explanatory theory, such that the problem context for each planet could be solved piecemeal without regard to needed adjustments in the models for other parts of the system.(22) Hence, to cite one feature of Ptolemaic geostasis discussed earlier, little concern resulted from the fact that Saturn's equant point must be positioned within the nested sphere of Mars.

Indeed, one can find statements from Ptolemy himself apparently supporting this radical discontinuity.

"The heavenly bodies suffer no influence from without; they have no relation to each other; the particular motions of each particular planet follow from the essence of that planet and are like the will and understanding in men." Ptolemy, Planetary Hypotheses(23)

Massively problematic for this interpretation, however, are the following:

1. Ptolemy's Planetary Hypotheses is clearly an attempt to wed Aristotelianism and the evolved geostatic planetary models into a complete system. In this work, Ptolemy attempts to show how the entire geostatic entourage of deferents, epicycles, eccentrics, and equants can be embodied in an Aristotelian plenum universe of nested, incorruptible celestial spheres surrounding, of course, a corruptible Earth.

2. Throughout the middle ages, Arab natural philosophers commented and struggled with the unhappy systemic marriage between Ptolemaic models and Aristotelian cosmology.(24)

3. Ptolemy's statement above is not an acknowledgment of disinterest in a complete cosmological system; rather it is a statement regarding the systemic relationship between Aristotelian philosophy and geostatic astronomy! In other words, it must be remembered that in Aristotelian celestial dynamics an individual planet moves the way it does, not because it is a physical place influenced by outside gravitational forces, but because like the will in an individual person, it is "striving" (as a celestial object, not a physical object) to achieve a goal, the goal of perfect circular motion. Galileo and Kepler proposed a different explanation, but they were clearly not the first to be interested in a broad-based explanatory linking of dynamics and kinematical models. To propose otherwise is to impose a modern cosmological perspective upon an ancient historical context.

4. In this light, the supporters of geostasis quoted above are best seen as being interested in "patching" the geostatic system, precisely because they believe that realistic heliostasis as argued for in De revolutionibus by Copernicus is a terribly weak system! In other words, Copernican dynamics was woefully inadequate, giving one little reason to believe, in the words of Tycho, that "the body of Earth, large, sluggish and inapt for motion . . . (could be) disturbed by movement, especially three movements..." According to Tycho, from the point of view of systemic considerations, "both these hypotheses (the Ptolemaic and Copernican) admitted no small absurdities." De Mundi Aetheri Recentioribus Phaenomenis(25)

From the standpoint of this thesis, to claim that only Copernicans became interested in a logically unified system is tantamount to claiming that prior to De revolutionibus, pre-Copernicans were not interested in problematic relationships between the hypertextual adjudicatory linking of theories, auxiliaries, methodologies, and experience. Although one can find such a claim being made by historians and philosophers of science,(26) from the standpoint of this thesis we see much more continuity. Just as we do not see a radical gestalt incommensurability, we are not forced to see a radical discontinuity in terms of overall rational skeletal structure. Both pre-Copernicans and post-Copernicans were concerned with arguments and reasoning trails. Both were concerned, trans-culturally and trans-temporally, with adjudicatory relationships between core theories, auxiliaries, methodologies, and observations. The discontinuity that existed was piecemeal in the sense that there was a dissimilarity between some of the nodes of developing adjudicatory trails, between the clarifying and justifying moves made in supporting and developing different, but at times overlapping, webs of belief.

Before leaving this section, one more prefatory matter must be discharged. In the previous chapter, against Lakatos, the work of Westman was cited to show that if the parameter determining features of heliostasis, matched with the core problem situation, ought to have constituted immediate and decisive empirical evidence favoring this theory, then contra Lakatos's own methodological claims the initial reception of Copernicanism must be seen as irrational and relegated to external explanatory sources. In other words, since the initial reaction to Copernican linkages was met with "silence," too much scientific behavior must be relegated to external psycho-social causation. Yet, in this chapter I have claimed that the parameter-determining linkages highlighted by Copernicus created an immediate stir, impressing both supporters and nonsupporters alike. Is this a massive inconsistency?

No. Moreover, the apparent tension in these claims and its resolution reveal the central value of the distinctions made in this thesis. We must be able to drive a wedge between the extreme interpretations of

1. Psycho-social relativism and claims that the unique behavior of Rheticus can be explained by an "anything goes" scenario -- that the situation was so confusing that pursuit of anything could not be seen as irrational -- and that his particular response was due to his unique personal history, i.e., he had a disparate need for unity because of his father's beheading.


2. Legend and methodological scenarios that leave us puzzled why every rational, technically proficient scientist did not immediately jump ship to what proved to be from hindsight the more successful theory.

A reading of Westman might lead one to object that there must be something wrong with any methodological scenario that highlights Copernican linkages, because the initial phase of reception was not marked by "intense debates and polemics" in general, and the linkages themselves were met with distinct silence in particular.(27) The only exception to the response of the majority of technically proficient astronomers and natural philosophers was that of Rheticus. But, according to Westman, Rheticus was unbalanced; he had a traumatic childhood experience to deal with and was not seeing the evidence more clearly.

My response is two-fold. Rheticus was not acting that much different than the other Wittenberg astronomers, and a correct analysis of the attitudes of the Wittenberg astronomers must be seen not so much in what they said, but what they did. According to Westman, the reception of Copernicanism was marked by two phases:

(1) A first phase, 1543-1570, and the Wittenberg interpretation -- silence regarding the symmetrical linkages displayed in heliostatic models and a view that Copernicanism should be seen "merely as a useful set of auxiliary mathematical hypotheses and tables to be exploited by the practitioners of geostatic astronomy."(28)

(2) A second phase, beginning in the 1570s, in which there is a "new appreciation" for the work of Copernicus in general, and the symmetrical linkages in particular.(29)

My quibble with Westman's phases is that this interpretation leaves too much discontinuity between the phases. Why the all-of-a-sudden appreciation of Copernican linkages? According to Westman with time Copernicus's own realistic intentions were becoming clearer, and the occurrence of the 1572 nova and the 1577 comet rocked the Aristotelian boat sufficiently to force a greater appreciation of Copernicanism in general, such that the linkages were then finally recognized as important by Tycho and others.

However, by Westman's own admission the Copernican system began to be studied immediately(30) at the master's level at the University of Wittenberg, Rheticus is not reprimanded by any member of the Wittenberg circle, including the strict Lutheran leader Melanchthon, for his "golden chain" emphasis on Copernican models, and an "important plank of the Wittenberg program" was to translate Copernican devices into "a geostatic reference frame."(31) How is the latter possible without an appreciation of the distinctive features of Copernican models?

A good example of the more gradual nature of parameter appreciation is the education and work of Johannes Praetorius (1537-1616), one of the first astronomers in the 16th century to tinker with geoheliocentrism.(32) He appears to have started his affiliation with the University of Wittenberg in 1555, received a copy of De revolutionibus in 1560 when he began the master's level, met Rheticus in 1569, and no doubt contemplated how to fulfill the Wittenberg plank during this time. Another example, is that of Erasmus Reinhold. Even prior to the publication of De revolutionibus, we find him writing in 1542 that he knows (through Rheticus) of an "exceptionally skillful" astronomer who "has raised a lively expectancy in everybody."(33) Later, via annotations of his personal copy of De revolutionibus, we see Reinhold clearly appreciating Copernican models.(34) This appreciation culminates, of course, with Reinhold's systematization and recalculation of planetary motions, published as the Prutenic Tables (1551), based upon Copernican models. According to Westman, Reinhold's work had the "full moral and financial support of Melanchthon. . ."(35)

Westman claims that the Wittenberg interpretation was a "split interpretation," and his main concern is to educate Kuhnians to the fact that the initial period of heliostatic reception was not marked by revolutionary cosmological debates and incommensurable standoffs between two clearly demarcated paradigms. With this I readily concur. However, two important points must be added to this account to underscore the gradual and piecemeal nature of eventual full appreciation of the parameter determining features of heliostasis. First, recall that it was not conclusively clear that the Prutenic Tables were more accurate than the Alphonsine Tables, and that "ease of calculation" is often confused with "superior accuracy."(36) What impressed Reinhold was the ease of calculation of planetary positions given the technical features of heliostasis. Second, one cannot appreciate the ease of calculation capability of heliostatic models without an early study and appreciation of the technical parameters of the models. We must now examine those technical features in depth.(37)

Technical Treasures

To fully understand the appreciation of Copernican parameters experienced by supporters and nonsupporters of heliostasis, we must now flesh out with greater detail what I have called the core observational problem. First, one finds in the literature consistent references to anomalies or inequalities, specifically the first and second anomalies or inequalities.(38) The first observational anomaly is that the rate of motion of each planet through the zodiac is irregular. The second observational anomaly is that each planet displays retrograde motion; that is, in addition to an overall eastward motion through the zodiac in the course of a year, planets also "wander" by changing directions and looping backwards in a westward direction. It is important to note that these anomalies are observationally connected in the sense that as a planet is in its retrograde phase, it appears to be moving faster than when not in this phase.

Articulating these anomalies in fine detail, ancient astronomers also recorded comparative regularities and differences in the size, shape, and frequency of planetary retrogressions. The eastward motions of the planets occur, of course, at different rates. Saturn as the slowest is thus presumed to be farthest from Earth. However, Saturn also displays 28 retrogressions in the course of a Saturn year, while Jupiter moves a little faster but only shows 11 retrogressions in a Jovian year. While Mercury moves much faster, it shows a retrogression only once every 116 Earth days. Mars, while displaying fewer retrogressions than Jupiter, has larger retrogressions than Jupiter, and Jupiter's are larger than that of Saturn. Moreover, in the course of a planetary year the shape of the retrogressions of any particular planet will not be the same. Sometimes the loop will be thin and sometimes relatively fat.

Also observed were several important relationships with the sun. The inferior planets, Mercury and Venus, have a bounded elongation, whereas the superior planets do not. That is, the inferior planets always appear to move in relation to the sun within certain limits; whereas the superior planets can obtain any elongation from the sun. However, the superior planets do show another type of a distinct linking with the sun. As each superior planet retrogresses it appears brighter, achieving maximum brightness at the midpoint of its retrogression. At this midpoint the planet is said to be in opposition, because the sun will always be located such that the Earth is situated in a direct line between the sun and the planet. The inferior planets also show a relationship between retrogression and the sun. Although greater illumination is not observed, at the midpoint of retrogression the planet is said to be in conjunction because it will be situated on a direct line between the Earth and the sun.

In addition to these core phenomenal features, a successful geometric model had to give an account of other complex relative motions, and do so while predicting the location of all the astronomical bodies throughout the year. In addition to the planets, the sun has three motions: its daily motion, east to west: an eastward motion in relation to the stars; and a yearly north-south motion, noticeable as a change in seasons, where in northern latitudes the sun is higher (more northerly) in the summer sky and lower (more southerly) in the winter sky. Furthermore, any explanation had to account for the sun completing these motions and returning to any given position in just over 365 days. The moon not only has an east-west nightly motion, a monthly eastward motion, and an even larger north-south motion than the sun but phases as well. The appearance of the moon changes perceptively as it moves, such that successive full moons will not occur in the same place.

If all of this makes you dizzy, then you can well appreciate any geometric solution that accounts for all these motions qualitatively, quantitatively predicts locations relatively accurately, is able to link these predictions such that lunar and solar eclipses are also foretold, and can be used to estimate distances to all the major astronomical bodies. It is no small wonder that the Ptolemaic system was accepted for 1500 years. Combined with Aristotelian physics and a cosmology of nested spheres, and matched by no serious alternative in terms of a different hypertextual adjudicatory trail, Ptolemaic geostasis was an "elegant cosmology."(39) How does Ptolemy save all these phenomena?

The basic Ptolemaic geostatic arrangement involves deferent and epicycle circles with eccentric and equant devices. That is, a planet revolves on an epicycle circle around a point that lies on a deferent circle that in turn revolves around a centrally located Earth. The deferent circle marks the midpoint of a planetary epicycle that is nested and revolving within a sphere, such that the epicycle radius marks off the thickness of the sphere. The Earth (the center of observations), however, is not in the exact center of the deferent circle, but is displaced some distance from (eccentric to) the central point of deferent revolution. An equant point, oppositely displaced than the Earth from the central point of the deferent, is the geometric location of uniform motion for a planet. That is, the latter is not observed; it is geometric only in the sense that if an observer could be placed at the equant point, uniform motion would be observed. The equant point is not a mere a priori requirement, used by Ptolemy to haphazardly harmonize his system with the pythagorean requirement of uniform circular motion. It plays a crucial role in adjusting the degree of eccentricity of the deferent orbit from the point of astronomical observation (the Earth), since the midpoint of the deferent orbit (called the eccentric point) will lie at the midpoint of a line connecting the Earth and the equant.(40) See Figure 3.

Ptolemy solves the core problem situation in the following way. As a planet revolves on its deferent in relation to the background stars (also moving in Ptolemy's system), the planet also revolves around its epicycle in such a way that at various times during the year it will be moving (looping) in the opposite direction of its overall eastward motion. By adjusting the radius ratios and periods of revolution of the epicycle-deferent arrangements for each planet, Ptolemy can match the frequency and extent of planetary retrogressions. Variable speeds are accounted for by combining the effects of the eccentric, equant, and direction of motion of the epicycle compared to the direction of motion of the deferent. For instance, Saturn's epicycle radius will be smaller than that of Jupiter's and adjusted to account for the planet's 28 epicyclic loops in the course of its overall movement around the Earth. Jupiter's epicycle radius will be larger, thus accounting for larger loops, and so on. Shape is handled by inclining the orbits of the planets to the sun's orbit about the Earth. When these adjustments are combined with eccentric deferents and the displaced equant point, the core problem situation is solved by Ptolemy: irregular speed and retrogressions along with the latter's extent and frequency.

Recall, however, that these solutions must also be linked with the sun. A geostatic Ptolemaic system saves these linkages by first fixing the epicycle centers for both Mercury and Venus on the same line from the Earth to the sun, and then keeping the epicyclic radius-vectors of the superior planets parallel to this line at all times. In this way, the motion about the sun of the inferior planets is limited (bounded elongation), and although the superior planets can attain any elongation, their motion on epicycles can be fixed with the motion of the sun such that the retrogression, opposition, brightness relationships will be saved.(41) This is accomplished by making sure that not only does the epicyclic radius vector remain parallel to the Earth-sun line for each superior planet, but that any given superior planet is at its lowest point at opposition (perigee, closest approach to the Earth). See Figure 4.

We are now in a position to summarize Ptolemaic parameters and to comment on their a priori flexibility.

1. The ratio of the epicycle and deferent radii.

2. The period of the revolution of the deferent.

3. The period of the revolution of the epicycle.

4. The directions of the revolutions of the deferent and epicycle.

5. The positions in the deferent and the epicycle for any given starting date.

6. The eccentricity of the orbit and equant. The extent of displacement from the exact center, of the Earth and equant point.

7. The direction in which the equant-eccentric line lies.

Of paramount importance for understanding the quotes above, particularly those of Frisius, Tycho, and Galileo, the Ptolemaic scheme offers a very flexible solution to a large part of the core problem situation. For instance, to return to the superior planet example discussed above, the geostatic arrangement does not absolutely require that a superior planet be in a perigee position in its epicyclic revolution when at opposition. Even if the epicycle-radius-vector-sun-Earth parallelism was a geometric requirement (it is not), there is nothing in the Ptolemaic system forbidding a newly discovered superior planet from being at apogee (farthest point from Earth) in its epicycle at opposition. In other words, other than the strong inductive expectation based on what had already been observed, and the dramatic success of Ptolemy's standard geometric arrangement to save it, there is nothing in the Ptolemaic overall machinery that forbids the discovery of a new superior planet that becomes noticeably dimmer at opposition and the mid-point of its retrogressions.

There is no necessity for the parallelism as well. Independent of observation, a superior planet could be at any position on its epicycle in relation to the sun's position, such that a superior planet could, a priori, show retrogression at opposition, conjunction, or in-between opposition and conjunction.(42) Figure 5.

Consider next the inferior planet Venus. Ptolemy had measured the elongations from the sun to be 47 20' and 44 48'. From these observations he was able to set the eccentricity of the deferent circle and the radius of the epicycle by making them fit the appropriate angles of observation. Other than the relationship of Venus's epicycle to that of the sun -- recall that the epicycle centers for both Mercury and Venus are fixed on the same line from the Earth to the sun -- and distance relationships -- recall that once the length of the radius is fixed for an epicycle this determines the thickness of a sphere -- the results are "not linked to those of the other planets in any other way."(43) In other words, the elongation observations dictate the parameters, and these parameters have no effect on the frequency, extent, and brightness relationships of the retrogressions of other planets.

Of the seven parameters listed above, five are independent. From this perspective, it is no small wonder that upon introduction of Copernican parameters we see even the Wittenberg astronomers jumping ship to Copernicus in terms of calculation (Reinhold and the Prutenic Tables). As Owen Gingerich has noted,

Given the parameters and the geometry of the [Ptolemaic] model, we could find the longitudinal direction of the planet for some specified time, but in the days before pocket calculators this would have been rather hard work. Even with a small calculator the procedure is tedious enough to ruin a morning.(44)

As Kepler noted, but was not alone in so noting, there is much astonishment in the match of Ptolemaic parameters and observations. Why is the elongation of the inferior planets bounded? Ptolemaic silence. Why do the planets show particular retrograde sizes? Ptolemaic silence. Why do the superior planets show a steady progression in terms of retrogression size from Saturn to Mars? Ptolemaic silence. Why do they show different retrograde frequencies? Ptolemaic silence. Why does the mid-point of retrogression always occur at opposition? Ptolemaic silence. In fact, why are all these phenomena so intimately linked with the sun? Ptolemaic silence.

There are, of course, parameter matters the Copernican system is silent about as well. Why are all celestial motions in one direction and basically in the same plane? Why is the Earth-sun distance what it is? Before Galileo's observations of the moons of Jupiter, why was the Earth's moon apparently an exception in terms of motion about the center of the universe? But Copernicus is not silent regarding the features of the core problem situation, the problem situation of the greatest concern since antiquity. All of the above Ptolemaic perplexities receive a dramatic response in a basic heliostatic system. By placing a revolving Earth between Venus and Mars, all inferior planets must have bounded elongation, all superior planets must show retrogression only at opposition, and the observed frequency and extent of retrogression are precisely linked with distances (Figure 6). Galileo may have been wrong that this argument alone -- the "great argument" (Maestlin), the "golden chain" argument (Rheticus) -- should have convinced all to accept Copernicanism, but it was appropriate that he gave it such prominent attention in his Dialogue. It impressed everyone, and convinced the majority of technically proficient astronomers, in the words of Tycho, that the Sun must regulate "the whole Harmony of the Planetary Dance."


So impressive were the Copernican linkages with the sun that Margolis claims that by the last decade of the 16th-century "astronomers began to openly abandon Ptolemy," such that by the opening decades of the 17th-century "the only coherent choice available to a competent astronomer became Copernicus versus Tycho."(45) Furthermore, according to Margolis, sense can be made of an "otherwise bewildering situation" only if it is understood that the arrangement made between Galileo and the Pope, regarding the content of Galileo's Dialogue, was to leave the Tychonic system "undiscussed, and hence . . . unchallenged."(46)

Accordingly, the Pope's rage and consequent action are best understood by realizing that after thoroughly discussing the content with Galileo and personally approving the project after a thorough year-long review by Church censors, thinking, as the title page suggests, that only the Ptolemaic and Copernican systems would be discussed, nevertheless "Galileo's identification of the Tychonic arrangement (in his Dialogue). . . as the surviving alternative is unambiguous and emphatic, but discrete. . ."(47) Worse, after publication and dissection by a wider and more technically proficient audience, the Church became aware of Galileo's grand trick, that Galileo not only had made clear to any knowledgeable reader that the alternative to heliostasis was geoheliocentrism, but alluded to the latter in just those contexts that would then make such readers puzzle over how it might actually work.(48) In other words, Galileo's silence is deafening on how complicated the Tychonic motions would need to be. He embarrassed the Tychonic system without mentioning it directly. According to Margolis, it is as if one were to criticize the physical layout of the city of New York with persistent reference to a large city at the mouth of the Hudson river, without ever using the words 'New York' in the criticism.(49) Finally, according to Margolis, the Pope and censors failed to foresee this potential embarrassment because no one had worked out the details of the Tychonic system. To cite the bare observational equivalence of the Copernican and Tychonic systems was one thing, dealing with dynamical issues (raised constantly by Galileo in his Dialogue) was quite another.

What is the evidence for this startling claim?

First, there is the intellectual environment. As early as 1601, Kepler is able to say, "today there is practically no one who would doubt what is common to the Copernican and Tychonic hypotheses, namely that the sun is the center of motion of the five planets . . ."(50) By the second decade of the 17th-century the Jesuit astronomers of the Collegio Romano had clearly abandoned Ptolemaic geostasis in favor of the Tychonic system, such that by the time of publication of the Dialogue, the Tychonic system had been taught for many years in a Jesuit introductory textbook on astronomy. This endorsement of geoheliocentrism was made quite clear by the Jesuit Grassi in his polemic against Galileo's theory on comets. According to Grassi, "Tycho remains the only one."(51)

In response to Grassi, Galileo had written that he regarded the Tychonic system as an unfulfilled promise and a "null" system because of its lack of articulation and physical impossibility,(52) and he had made his intention clear that he would demonstrate this in the Dialogue.(53) Why would he change his mind? Would Galileo, who loved to argue, who was obviously very aware of the state of cosmological discussion in the astronomical community, acutely aware of the position of his arch enemies, the Jesuits, and who had been stewing in frustrated contemplation for many years seeking a forum for his ideas, despondent that he would soon be totally forgotten, finally, when he got his big chance, spend 465 pages ignoring his most worthy opponent and leave himself vulnerable to such a simple charge of questionable dilemma sophistry or the appearance of an old man out of touch with modern positions? Margolis's insight is that Galileo would not open himself to such a perception and criticism unless he was prohibited from mentioning the Tychonic compromise, and unless he had brilliantly figured out a way to embarrass the compromise without directly mentioning it. Koestler may be right that we sometimes give our historical heros too much credit by ignoring their fallibility and foolishness, but to think that Galileo would either deliberately ignore Tycho or think that no one would notice if he did ignore him, is to give this historical figure much too little credit.

Next there is the political situation. Why allow Galileo to publish at all? How could the Pope think that publication of the Dialogue would serve Church purposes in any way? The Church was involved in a massive struggle for the hearts, minds, and pocketbooks of the European community. It was perceived to have taken a harsh stand in its 1616 Edict against the Copernican planetary linkages with the sun. (Actually, De revolutionibus was only edited in a minor way to eliminate any reference to heliostatic referential commitment.) Those linkages had now received widespread acceptance and praise, and the Church needed to clear up misperceptions by sending a positive message of its forwardness and openness regarding this matter in particular and its relationship with science and astronomy in general. In other words, pressure had been building for almost two decades to reconcile the Edict of 1616 with the continual progress and consequent acceptance by most competent astronomers throughout Europe of linking planetary motion with the sun. What better way was there than to allow the major spokesperson involved in the 1616 Edict to come forward and straighten things out?(54)

Then there is the textual evidence. Massively curious is the fact that a book personally approved by the Pope and scrutinized carefully by censors for a year would be allowed publication when the traditional Ptolemaic position is so promptly dismissed when the issue finally arises whether the planets revolve around the sun or the Earth. The issue is not even raised in a substantive way until well into Day 3. Significant is that the discussion of this day is introduced by a defense of Tycho's position, and other "assailers of the sky's inalterability,"(55) on the celestial location of novas. Next there is an apparent puzzling discussion on the meaning of "center of the universe." Is the center (1) the place that stands still while everything else moves, or (2) the place around which every other celestial body moves in circular motion? It is crucial to realize that in (1) that place need not be anywhere close to being the exact center of circular planetary motion. In (2) the place around which every other celestial body moves in circular motion would also be the place that stands still. This discussion makes no sense if the debate is only between Copernicus and Ptolemy, because although they have a different object in this center, both Copernicus and Ptolemy are advocating (2). According to Margolis, "It is only in the Tychonic system that there are two different candidates for the body (Sun or Earth) which is the center."(56) Bottom line: Galileo is alerting his discerning readers that there is a third possibility, the Tychonic system. He is also embarrassing supporters of that system as we will see below.

Next Galileo has Salviati refer to the well known planetary linkages to the sun. If we define 'center' as that place around which the celestial bodies move in circular motion, then "it is certain that the sun not the Earth is at that center."(57) Why would Galileo be allowed to make this statement? Because the consequent of this statement, if true, does not eliminate all geostatic systems. Furthermore, one need not define 'center' in this way. One can acknowledge that the planetary linkages with the sun are so overwhelming as to dictate that the planets revolve around the sun, but still have the sun revolve around a stationary Earth, i.e., the Tychonic system. According to Margolis, what follows at this point in the discussion -- Simplicio's expected objection and then Salviati's having Simplicio himself draw a diagram -- is best understood as Simplicio not objecting necessarily to the notion of the planets revolving around the sun (it is a realization on his part as well as for the reader), because even if the planets revolve around the sun, the center of the universe could still be the stationary Earth around which the sun revolves.(58)

Galileo would not have been allowed to claim that it is "certain" (pp. 321, 455), "true" (p. 326), "indubitable" (p. 340), and that planetary revolution around the sun is "the true arrangement" (p. 455) in a book personally approved of by the Pope and in which he was clearly forbidden to argue for a realistic interpretation of heliostasis, unless these statements meant that it is certain that the planets revolve around the sun, and it was still left open what stationary object is in the center and at rest. It is very hard to accept the traditional interpretation -- that the Pope and the censors were buffoons -- when it would have been obvious to anyone who could read that these statements would be an obvious violation of the Church injunction for publication. These statements were not perceived to be a violation, because the intention (at least Galileo's intention for passing the scrutiny of the Pope and censors; he also had another intention) was to refer to the settled matter that the planetary linkages with the sun are so overwhelming that it is no longer an issue whether the planets revolve around the sun. What remained was whether the Earth moves or the sun. Bottom line: When the Ptolemaic perspective of the planets revolving around the Earth is finally brought up, it is dismissed quickly; what follows from this point on (the discussions of sun spots and tides) address the main issue of whether the Earth moves.

Finally, a major corroboration of Margolis's controversial thesis is that the Inquisition's condemnation of Galileo never raises the obvious objection that he has blundered astronomically as well as theologically by failing to consider geoheliocentrism. It cannot make this complaint, because the members are no doubt aware that Galileo was prohibited from explicitly debating this alternative.

As noted above, with the Tychonic system so well known, it is very hard to believe that Galileo would think that he could get away with such questionable dilemma sophistry of framing the debate so simply, as only between Ptolemy and Copernicus, or that discerning readers would not jump all over him for such an obvious omission. By the time of the Inquisition proceedings it is clear that Galileo had alluded to geoheliocentrism repeatedly and in such a way as to embarrass holders of this position. But the Inquisition cannot refer to this matter, because it cannot refer to a private agreement made between Galileo and the Pope, even though Galileo has violated that agreement.

The Pope thought he had an agreement that Galileo would not attack the Tychonic system. Perhaps he even thought that this would be a way of embarrassing Galileo for this omission, drawing attention to the Church's forward-looking acknowledgement of the sun-planet linkages, but at the same time discrediting heliostatic supporters for their poor logic. Knowing what the Pope's agenda was, knowing how a simple presentation of Ptolemy vs. Copernicus would be perceived, wanting to display the full support for heliostasis and discredit all versions of geostasis, Galileo not only eliminates Ptolemy (which the Church has no problem with at this time) but embarrasses geoheliocentrism as well without even mentioning it by name. The Pope thought he was using Galileo; he ended up realizing he was used by Galileo. When he is asked, a few days before handing the matter over to the Inquisition, what Galileo has done, the Pope responds furiously that he has been deceived, that it is not any particular passage that is offensive but the whole book, and that Galileo knows perfectly well what he has done, "since we [i.e., the Pope] have discussed . . . [these issues] with him . . .(59) Galileo was able to signal to discerning readers that he was fully aware of geoheliocentrism as an alternative, pass the scrutiny of the censors by never mentioning it, and yet embarrass it at the same time.

How does Galileo embarrass geoheliocentrism? By repeatedly linking astronomical matters with dynamics. Returning to the key exchange noted above between Salviati and Simplicio, Simplicio, the defender of geostasis, himself draws a diagram that has the planets revolving around the sun (for his "greater satisfaction and . . . astonishment").(60) He is portrayed by Galileo as being most impressed by this arrangement,(61) but he is then appropriately silent about whether the sun revolves around a stationary Earth or the Earth revolves around a stationary sun. Salviati, of course, completes the diagram by having the Earth revolve around the sun. However, before he does so, he makes it clear that he has trapped Simplicio by referring to a remark Simplicio has made earlier.

Earlier, in what appeared to be an abstract, almost irrelevant discussion concerning the definition of 'center,' Simplicio admits that if our choices are that 'center' means either the stationary place around which key celestial objects move (but not necessarily in circular motion), or the central location around which key celestial objects move, then

"If we could stop with this one assumption and were sure of not running into something else that would disturb us, I should think it would be much more reasonable to say that the container and the things it contained all moved around one common center rather than different ones."(62)

But Galileo now makes it clear that there is much to disturb us about any system that has multiple centers. He has allowed Simplicio himself to acknowledge the planetary linkages with the sun, and then has Salviati say,

". . . it seems most reasonable for the state of rest to belong to the sun rather than to the Earth -- just as it does for the center of any movable sphere to remain fixed, rather than some other point of it remote from the center."(63)

Galileo's move here is quite subtle, but very clear once read from the standpoint of Margolis's thesis. Galileo has Simplicio the Aristotelian admit that from a dynamical perspective the concept of multiple centers does not seem reasonable. From a purely dynamical perspective, there is apparently no problem on this point for an Aristotelian. In fact, this was often cited as a reason against the Copernican system, because the moon revolves around the Earth rather than the center of the universe. Then Galileo has Simplicio acknowledge the planetary linkages with the sun while framing the discussion from a purely astronomical perspective. Now there is no problem for a defender of some altered version of geostasis. Then Galileo combines the two perspectives, but without great fanfare, demonstrating to the very careful reader that there are major problems when the two perspectives are combined.

Compare this exchange, which never mentions Tycho, with Kepler's direct criticism of Tycho many years earlier.

". . . many reasons render it likely that the Sun remains in one position at the center of the universe, most of all because in it is the source of motion for at least five of the planets. Whether you follow Copernicus or Brahe, the source of motion for the five planets is located in the Sun. . . . However, it is more likely for the source of all motion to remain in one place than to move."(64)

Galileo is repeating the same argument against Tycho made by Kepler!(65) But unlike the freedom Kepler enjoyed, Galileo cannot attach this criticism openly to the Tychonic system. Thus, Galileo's entrapment must be very subtle. Salviati does not remind Simplicio that the unreasonableness of multiple centers is his position. This would be like saying, "But earlier my dear Simplicio you said X. Do you not now realize that this is a criticism of Tycho?" Galileo, in a most subtle way, has drawn attention to the cumbersome arrangement of a geoheliocentric system and its multiple centers, and planted a major seed of doubt for any "discerning reader" who would begin to wonder how such a system would work.(66)

At this point, Galileo is not allowed to develop this argument by raising more explicitly the issue of exactly how the Tychonic system would work. He has only drawn attention to this next stage of discussion. It is most significant that Kepler, after using the same argument, does proceed to draw out the complexities of the Tychonic arrangement. According to Kepler,

". . . the motions were vainly multiplied by Brahe as they were by Ptolemy before him. . . . (and) the following schema for physics would have to be set forth: the Sun with all this great burden of the five eccentrics . . . being moved by the Earth, or the source of the motion of the Sun and the five eccentrics attached to it residing in the Earth."(67)

What is the "great burden" in the Tychonic system that Kepler is referring to? First, the sun moves in an eccentric orbit around a much smaller Earth, producing variation in speed and a faster motion as it is closer to the Earth. Second, each planet also has an eccentric orbit around the sun, producing variation in speed.(68) Third, combining these motions, the eccentric motion of each planet linked with the sun is in turn linked with the eccentric motion of the sun around the Earth. Fourth, to account for the core observational problem, like a ferris wheel, each planet must have a counter-revolution in the direction opposite that of the sun around the Earth, with the period of the counter-revolution being equal to the period of the sun's revolution around the Earth. Fifth, all other celestial objects in the universe besides the Earth must revolve around the Earth once a day, such that they "must turn in the opposite direction from the Sun's annual motion, 365 times as fast as that motion, along an axis tilted back from the axis of the annual motion."(69)

According to Kepler, a heliostatic system is able to strip the five planets of these "coiled" courses and "extraneous"(70) motions by adding only a few motions to the Earth and having a single motion for each planet (a single motion around the sun). Even Tycho seemed prepared to lessen this great burden by having the Earth rotate daily!(71) Logomontanus, Tycho's principal disciple, continues the auxiliary patch by making the Earth's rotation explicit, and by the time of Kepler's Astronomia Nova this no longer seems to be an issue.(72)

But what has happened? The auxiliary patch has become more trouble than it is worth. The very patch introduced to save the Biblical, Aristotelian, and common sense position that the large and sluggish Earth could not move has ended up undermining that position. The very auxiliary patch that was supposed to save geostasis has exposed geostasis as a "worm-eaten" system, as a hypertextual adjudicatory trail unraveling along many nodes. The relativists are right in principle. We can patch away to our heart's content. They are even partially right in terms of historical fact -- scientists will often attempt to patch their theories in the light of problems. But they are conspicuously wrong that just any patch will be accepted in the long run, that all patches can be made to work given effort and resources, and that scientists do not abandon adjudicatory trails for very good reasons, being fully capable of seeing their positions crumbling and the proverbial writing on the wall.

The social-psychological relativist would assert that a scientist may change his or her mind at such a point, because they do not want to be embarrassed and consequently socially excluded from a new emerging consensus group. From the standpoint of this thesis, a trivial point. What causes the recognition of potential embarrassment is recognition of the epistemic situation, and relativists have their own regress problem unless we postulate that at least some psychological states are caused by a reaction to epistemic explorations. Psychological states may predispose a scientist to view the world in a particular way, to defend or explore initially a hypertextual adjudicatory trail, but different psychological states may emerge after such exploration. A young Tycho apparently felt no embarrassment in defending Ptolemy, but the mature Tycho, after a lifetime of debate and detailed study, was experiencing many doubts and would have surely experienced embarrassment if he were still defending the basic Ptolemaic system.

Tycho hesitated for a long time in publishing his system (at least 10 years(73)). When he finally did introduce the geoheliocentric system it was only a sketch as part of a brief three page digression in a treatise on comets and novae. Even this introduction seems to have been offered reluctantly due primarily to the fear that someone else (Ursus) would get the credit.(74) In the light of the above analysis, his hesitation is most likely due not only to his acknowledged, transitional struggle with crashing celestial spheres, but that jettisoning these spheres is another slap at Aristotelian cosmology and dynamics. Without the spheres there is now no obvious means of generating the motions of the planets, of transmitting the motion from the celestial sphere on down to the moon.

Relativists will often make much of the fact that just because Tycho and others gave up on celestial spheres does not mean that they ought to have done so. Aristotelian cosmology could still have been saved with enough effort.(75) Comets and novae were observed before. Observations are just "stimulations"; they require interpretations before they acquire meaning.(76) If our theories clash with observations, we can always reject the offending interpretation of the observations. But this purely logical argument, disconnected as it is from the actual scientific and historical context, ignores the ampliative basis for accepting the observations. It ignores the vast difference in evidential contexts. For instance, the comet of 1577 was very bright and located in a well known constellation (Cassiopeia). Tycho's observatory at Uraniborg was well established, and his instruments and instrumental techniques were far superior to any previously used. Furthermore, from the late 16th- to the early 17th-century a significant number of comet and nova sightings occurred (1577, 1580, 1582, 1585, 1590, 1602). Holes were literally being punched into Aristotle's celestial sphere. Aristotelian cosmology was under pressure along many fronts.

The very title of Tycho's book, On the Most Recent Phenomena of the Aetherial World, is a challenge to the orthodoxy of the Aristotelian world view. The very world view that Tycho set out to preserve. Tycho may have set out to rescue "the Copernican harmonies . . . from the Copernican heresies,"(77) but he ended up showing that orthodoxy had just as many problems if not more than the heresies.

Parameter Determination

According to Philip Kitcher in his recent book The Advancement of Science, "A central problem of scientific inference consists in showing how endeavors to find paths through escape trees yield various types of modifications of practice."(78) Scientists routinely experience "Duhemian predicaments" and must address the "costs" of amending such situations.(79) Put in terms of this thesis, much of intelligent scientific inference involves probing and pursuing, adjusting, testing, perceiving a strengthening or weakening, and ultimately accepting or rejecting hypertextual adjudicatory trails. These activities have constraints, but these constraints are themselves part of the developmental process. They are not a priori, transtemporal fixed principles, but emerge as hypertextual nodes that may be linked with conflicting adjudicatory trails. Furthermore, they can be argued about and accepted or rejected independent of theoretical allegiance.

I have argued that one of the standard defenses of scientific rationality during the Copernican episode is an historical myth. It is not true that by the time of Copernicus's De revolutionibus the Ptolemaic system was so patched up and in crisis, that rational people clearly saw that the Copernican system was so simple that it must be right. It is not true that only the heliostatic system had a basis for rational pursuit in the 16th-century. I have also argued that a finer-textured analysis shows the traditional view to be partly right. The Copernican system displayed an order, unity, and parameter fixity that gradually impressed every competent player. The supporters of heliostasis repeatedly raised this issue. Should not our theories display an overall unity and fix as many parameters as possible? And like a red flag that could not be ignored, the defenders of geostasis responded, not by rejecting the importance of this general aim, but by accepting it and pursuing a geostatic patch that would fulfill it.

The key epistemological question that can now no longer be postponed is, "What normative basis is there for judging this to have been a rational move on the part of the geostatic and heliostatic participants?" There are usually three answers to this question, all of which I will reject.

First, relativists respond to this question by claiming, of course, that there was no normative basis. Heliostatic and geostatic supporters agreed simply because of the cultural milieu in which they were embedded. It was "mere" agreement due to the neoplatonic and neopythagorean metaphysical ambience that permeated the renaissance. It was merely "aesthetics" backed by a world view. The participants had some silly anthropocentric views about the relationship between God and human intellects: God had created everything according to some elegant mathematical floor plan; the most elegant astronomical system therefore must be true, and participants saw their lives as a religious and scientific race to be the first to read the mind of God.

Second, defenders of Legend would argue that this was not mere agreement. That logical unity, order, and parameter determination are a priori, fixed principles that have always governed rational scientific practice. When they are not recognized as such, then those involved are acting irrationally. Hence, Copernicus, Rheticus, Galileo, and Kepler were acting rationally; all defenders of Ptolemaic geostasis were acting irrationally, even from day one of the introduction of his system -- they should have known better.

Third, we have learned over time that theories that display a high degree of logical unity, order, and parameter determination are not only easier to test, but also generally have a long term reliability. A scientist today would not be very comfortable supporting or pursuing a theory analogous to that of Ptolemy, where a model explaining some individual feature of observation was not consistently linked with another model explaining another feature of observation.(80)

My response to the first view has been similar to that of Lakatos. That an external, historically contingent feature helps participants to see a particular internal feature as important does not unequivocally indict the internal feature as not important. A methodology or a theory is perfectly capable of possessing long term reliability, and can display features indicative of long term reliability, even if the motivating factors for their origin are later abandoned. The reliability of the current species classification scheme used by evolutionary biologists is not called into question because Linneas believed he had discovered God's floor plan for life on Earth.

My response to the second view is that it makes too much of parameter determination. If parameter determination and associated concerns of theoretical unity are fixed, a priori principles, then large tracts of history must be seen as consisting of irrational participants. Ptolemy must be seen as a poor scientist who should have known better right away that his system could not be true. Yet Ptolemy was obviously a great scientist, and we need a story of scientific change that captures this appraisal. Popper may have taught us that a good theory should prohibit as much as possible, but this is 20th-century advice. Such a constraint is something we have learned over a vast stretch of time by observing the success and failure of competing theories. We can hardly expect that such advice was fully formed at Ptolemy's time, especially without a robust competing theory.

Of the three views, this thesis has the most sympathy with the third view. Constraints, I have argued, emerge as part of a learning process over time. However, what applies to Ptolemy still applies to a certain extent to the formative stages of the Copernican episode. Problematic for this third view is its hindsight perspective that does not help us very much in explaining the rational moves made in the late 16th- and early 17th-centuries. Even if there is agreement that parameter determination has been important in the 20th-century science, modern scientists have had the backing of almost 400 years of experience with theories succeeding and failing. So, why should parameter determination have been considered normatively important in say 1590?

As noted previously, there would have been no expectation in the Copernican episode for any new planets. However, theories make predictions, and whether one is a realist or an instrumentalist one is interested in backing a theory that makes the most successful predictions. To make the most out of a theory's predictive potential it must be linked with as many nodes on a hypertextual adjudicatory trail as possible. In this light consider the following cases.

Case 1: A theory T1 that models a feature F1 that predicts an observation O1, and a theory T2, with F2, that does not predict O1 or ~O1, but is compatible with either O1 or ~O1 occurring. If ~O1 occurs, comparatively, this is discriminating evidence for T2. On the other hand, if O1 occurs, this is discriminating evidence for T1.

As we have seen, for Ptolemy a future observation of a new superior planet need not show increased brightness at opposition. In the late 16th-century if a new superior planet had been discovered and there was clear observational agreement that it did not show increased brightness during opposition, this would have been well-defined evidence for Ptolemy. I want to claim now that if a new superior planet was discovered in the late 16th-century and it did show increased brightness at opposition, defenders of heliostasis would have had an easier time claiming that this was evidence for their system, even though defenders of Ptolemy would have had little trouble in covering the observation once it was already made.

A defender of geostasis or a relativist might object to my last claim. They might respond that the new observation is perfectly compatible with the planetary linkages with the sun already established by Ptolemy's models, i.e., that superior planets are always at perigee in their epicycle orbits at opposition. It is simply a fact of the matter that the epicycle radii of superior planets have the orientation that they do in relation to the sun. It is simply a basic principle of epicycle theory that the motion of the radius vectors are linked with the sun such that they turn at the same uniform rate as the sun's radius vector.

Accordingly, there are two problems with using Copernican parameter determination as discriminating evidence. First, the above scenario is purely prospective. No new observations were available to show definitively whether the Copernican system was surprisingly correct or rigidly wrong. The observed pattern could have been only a coincidence; it could have been discovered that superior planets need not continue to show the same pattern of retrogression frequencies, brightness, and orientation in terms of the Earth and sun. Second, an established pattern is relative to the eye of the beholder; that the Ptolemaic system is compatible with O1 or ~O1, and O1 occurs, can be seen as a continuation of a pattern nevertheless.

There is a robust response to the second objection. Ptolemy's prediction is at best strongly inductive; whereas that of Copernicus is rigorously geometric. There ought to be an uneasiness over any theory that does not make a precise prediction relevant to a core observational problem. All the superior planets had shown a particular pattern in terms of frequency, brightness, and relationship with the Earth and the sun. Does Ptolemy predict that this pattern will continue? If so, then in what sense? We ought to be uneasy about a theory that lets its supporters hedge on the answer to this important question, supporters who could say, "I'll let you know after we make the observation." Although their way of putting the matter was different than my new planet example, I contend that what was being realized by the major players, after a comparison was available, was that the basic principle of epicycle theory cited above had been invoked (albeit elegantly) to cover only the current observational situation. If Ptolemy is not making a precise prediction about future observations, an uneasiness is engendered about how the models match current observations. As we have seen, the "looseness" of Ptolemaic fit between models and observations was now apparent to supporters and nonsupporters.

Consider the planet Mercury in the Ptolemaic system. Ptolemy's model for the inferior planets is consistent with Mercury being either the closest planet to the sun or the second closest to the sun. Furthermore, if a new inferior planet were observed, the observation of its degree of elongation would leave us with the same indeterminacy. In fact, the indeterminacy would now be compounded. We would not be able to tell which interior planet -- Mercury, Venus, or the new planet -- was closest to the sun. For Copernicus, elongation observations rigorously determine that Mercury must be the closest to the sun, and the placement of any future inferior planet would be rigorously determined by the observation of its degree of elongation compared to that of Venus and Mercury. So, suppose that during the peak of the Copernican episode debates Tycho had figured out some independent means for determining that indeed Mercury was the closest planet to the sun? A clear evidential plus for Copernicus, even though Ptolemaic supporters could easily adjust once the determination was made. On the other hand, if Tycho had been able to detect that Venus was the closer planet to the sun, the Copernican system would have been in serious trouble.

Although none of these observations or determinations could be made, the story told here is that the major players are starting to realize that the indeterminateness inherent in the Mercury-Venus ordering problem permeates much of the Ptolemaic system when it is compared to that of Copernicus. As noted previously (note 18), realizing that Ptolemy has a more flexible response to surprise changes in the core observational problem, helps us realize that the major players were beginning to see that Copernicus had a more fixed response to the known core observational problem.

Today we would be just as apprehensive about a theory that predicts the next car that enters my college's parking lot will be red or blue, black or white, or green or yellow. If our domain of inquiry was my college parking lot and the core observational problem was that an observational pattern has been established regarding the colors of cars, their frequency and timing of appearance -- red, black, and green cars at a certain times -- should one have a very high motivation for pursuing a theory that makes such a vague prediction, provided also that another theory existed that predicted only the red, black, and green pattern?(81) The reason a Copernican would have had an easier time claiming predictive success, if the pattern regarding superior planets continued for a new superior planet, is that Ptolemaic supporters would have had to face the fact that the real prediction that the Ptolemaic system was making is that the pattern need not continue. Ptolemaic supporters cannot have it both ways. They cannot argue that a future ~O1 is compatible with the basic geostatic model and simultaneously argue that O1 is a requirement.

As to the first objection consider the following case.

Case 2: T1, having features F1, F2, and F3, predicts O1, O2, and O3. Furthermore F1 is such that it could not exist unless F2 and F3 also exist, F2 could not exist unless F1 and F3 exist, and F3 could not exist unless F1 and F3 exist. Thus, T1 predicts O1, O2, and O3 as a unified sequence. The occurrence of ~O1 would significantly and negatively affect the ability of T1 to take credit for saving O2 and O3, even if they occur. Comparatively, T2, having features F1', F2', and F3', is compatible with O1 or ~O1, O2 or ~O2, and O3 or ~O3. If ~O1 occurs, T2 is not significantly impaired in terms of covering O2 and O3.

T1 is of course the Copernican system. Although many other features could be selected, O1, O2, and O3 can represent, respectively, superior planetary brightening at opposition, frequency of retrogressions, and degree of elongation of inferior planets from the sun, the latter in the Copernican system implying a definite commitment on planetary ordering of these planets.(82) T2 represents the Ptolemaic system. The Ptolemaic system is not committed a priori to the necessity of planetary brightening at opposition for the superior planets, nor a particular frequency of retrogressions. Furthermore, there is no simple relationship between observations of degrees of elongation and the ordering of Mercury and Venus. Ptolemy's geometric models are compatible with either Mercury or Venus being the closest planet to the sun. Ptolemy was fully aware of this, but also knew that he needed to make a choice. (It is obviously one way or the other in reality.) He chose Mercury as being closer to the Earth than Venus by invoking an aspect of Aristotelian cosmology. Venus must be closer to the sun, because Mercury had the most erratic orbit of the two, so it must be closer to the corruptible, vaporous sublunary realm.

Again the obvious objection to make against Lakatos and others who view this comparison as representing decisive empirical evidence for Copernicus is that the situation is still prospective. Parallax measurements of Mercury and Venus were not possible, nor were any new inferior planets discovered showing bounded elongation consistent with Copernicus's prediction. However, a case can still be made as to why the Copernican system impressed everyone, and continues to impress us to this day when one fully appreciates all the initially appearing, discordant observable details it ends up linking. But what is it? And why should we be rationally impressed? What is it, in Duhem's words, that it is impossible for us to be blind to?

Consider carefully the difference between Cases 1 and 2 above. In Case 1, the fact that T1 fixes one observation may be interesting, but not overly impressive. At this point in any investigation of a rivalry between two theories, it could simply be a coincidence that T1 fixes this observation, whereas T2, although compatible with O1 and ~O1, does not. From the perspective of the 16th-century, and without any other information, the world could have indeed been such that although superior planets to date had increased brightness at opposition, future ones may not have.

However, the paramount difference between Cases 1 and 2 is that in Case 2 the fixation of observations is no longer just individual fixations. They are now not only beginning to add up in a purely quantitative sense, but they are linked. What is operative here in terms of our "astonishment," to use Kepler's portrayal, is that when faced with such unity, we are less likely inclined to be believe the features are a coincidence. Contra the philosophical positions of the likes of Lakatos and Glymour, I am not suggesting that such linkages can be counted as extra empirical evidence for the Copernican system, nor that prior to other matters being settled along a hypertextual adjudicatory trail can such linkages be decisive relative to acceptance. What I am suggesting is that we find such unity impressive because it supports the primary aim of intelligent ampliative inference -- our desire to obtain long-term reliable beliefs -- and as such, one can clearly see the very good reasons a 16th- or early 17th-century scientist would have for a robust pursuit of heliostasis.

We make use of ampliative inference knowing full well that we cannot achieve certainty for our conclusions. As such, we develop methodologies attempting to tease from nature her secrets, by testing those methodologies over time, hoping to find those that produce conclusions that are less likely to be wrong. Of paramount importance in this endeavor is to get nature to respond in such a way that the response is less likely to be a coincidence. We know, from painful past experience, that she is in the business of fooling us with her responses, of displaying what we think are regularities initially only to find later that they were coincidences.

For instance, consider the use of the technique of a controlled study that has exposed the relationship between cigarette smoking and lung cancer. We do an initial study, setting up two groups of say 100,000 people to follow, controlling as many variables as possible, attempting to limit the major difference between the two groups to the fact that one group consists of cigarette smokers and the other does not. After ten years we find that in the group that smokes cigarettes almost 5,000 people have developed serious cases of lung cancer; whereas, in the non-smoking group only 34 cases of lung cancer exist. We are impressed, but the tobacco companies, to use Kitcher's language, have an escape tree. Some major variables have not been controlled. At this stage it is possible that nature's response is a coincidence, that the 5,000 people in the smoking group and the 34 in the non-smoking group have something in common other than prolonged exposure to cigarette smoke. Perhaps lung cancer is very common in their family histories. Perhaps they have inherited a tendency to develop lung cancer and it matters little whether they were in the smoking group or not. We could repeat the study with different people and might find the numbers reversed, and that the real common denominator was heredity. Or, perhaps all of the cancer victims lived in homes with high concentrations of radon gas, and it was just a coincidence that our study placed so many people in such homes in the smoking group. So, the ampliatively intelligent thing to do is to repeat these studies, using different investigators, different people, and control for variables left out in the first study.

Suppose we conduct such studies literally thousands of times.(83) If the results are virtually the same in every case -- a significantly (140 times) higher incidence of lung cancer cases in the smoking groups -- it is still possible that these results are a massive coincidence. But the ampliatively intelligent inference to make is that it is not a coincidence, and it is very unlikely that most of these people have something in common causing the cancer other than cigarette smoking. It is possible that the thousands of people with lung cancer did something on their third birthdays that eventually produced lung cancer. It is possible because this and many other lifestyle behaviors have never been controlled for. However, there are no rational grounds for pursing any of these escape trees. Nor, if we were to start worrying about classical confirmation problems at a purely logical level (Goodman's emerald paradox), is there any rational reason to believe that although smoking may be the cause of lung cancer now, this will change in the year 2010. We do not have any ampliative reason to believe that nature's causal laws work one way in the 20th- century and then work a different way in the 21st-century.

Consider another example. If one was overly impressed with a strictly logical approach to confirmation theory, one could make a case that we should not be too impressed with how Darwin's theory of natural selection predicts and explains the massive amount of extinction in the fossil record. One could see it as no more than simple and highly suspect induction by enumeration. Each example of species extinction is seen as a positive case for Darwin's theory, but since such simple generalizations have been wrong so many times before, and because the set of possible species outcomes is infinite, the positive cases of extinction already observed confer zero probability on Darwin's theory. However, even without bringing to the table other substantial support for Darwin's theory and the fact that competing theories do not predict massive amounts of extinction (Lamarckism and Scientific Creationism), when one comes out of one's lofty logical tower and gets paleontologically dirty with the actual observational situation, seeing how difficult it is to explain anything,(84) one does not see just individual positive cases for Darwin, but rather thousands of linkages of species extinction, mutation and variation, and environmental change, such that we are left with the ampliative feeling that it is very unlikely that the connection between natural selection theory and this evidence is a coincidence.

According to Kepler, if one looks at "only the numbers" -- the ability of the Copernican and Ptolemaic systems to predict planetary positions -- then we cannot provide any rational grounds to pursue or accept heliostasis. However, if we are also interested in how the world works and/or in possessing theories with long term reliability, we must be also interested in a unified theoretical approach. We must be interested in how our geometric theory works with other fields of study, not the least of which is physics. Furthermore, even within the purely geometric models we ought to be concerned with how the various aspects of the models link up with the observations. We ought to be concerned with such unity, because realists and instrumentalists alike concur that it is most likely that the world we are dealing with is one world, one world of universal, objective features and regularities that do not show one face on Mondays, Wednesdays, and Fridays, and a different face on Tuesdays and Thursdays.(85) If we believe that there is an objective world, we also believe that its fundamental features are locked together in a functioning whole (Duhem's natural classification), that the different faces nature shows us are only apparent, that behind the scenes are natural mechanisms of some sort that stay the same. Thus, even if we are instrumentalists we must be concerned with unity and linkages, because if our metaphysical hypothesis of the general nature of reality is true, then those theories that show such unity and linkages are more likely to have staying power in terms of long term reliability. Merely having this unity does not guarantee truth or reliability, but without it, it is very unlikely that our theories will have staying power; it is a goal we seek because of our general belief about the nature of reality.(86)

Very much related to this metaphysical justification is the pragmatic and heuristic value of finding theories that, if reliable, will have ramifications for future and/or collateral domains of experience. According to the astrophysicist Neil de Grasse Tyson,

In scientific inquiry, the answer to one simple question often fortuitously explains the answers to many others; it may even answer questions that have yet to be conceived. Powerful ideas also unify concepts or phenomena that were previously thought to be unrelated.(87)

Once we think we have found a pattern shown by nature, we desire a theory that not only captures that pattern but provides some distinct leads about what we should find "down the road" so to speak. We are uneasy about any theory that captures a pattern already observed, and then predicts that next we might observe O1 or ~O1, O2 or ~O2, or O3 or ~O3, and so on. We have learned from experience that such theories are not helpful and we believe that they are unlikely to be helpful, because we do not believe the world works this way. We believe that the patterns we observe are linked with many other distinct features and patterns not yet observed.

Today physicists are unhappy simply knowing that the fundamental constants of matter have the values that they do. Why is a proton 2,000 times more massive than an electron? Why is the force of gravity so much weaker than the other forces of nature? They do not believe that such parameters are coincidences, but must be linked by some fundamental process. Thus, they pursue a logically consistent theory of everything in which all such constants would be derived, in which all such constants would be fixed as having these values and no others. They do so, not only because the fruitfulness of such a theory would be enormous -- from a seamless linking of every stage of the Big Bang, to why we have the kind of universe that we do rather than a very different one, to interactions of matter heretofore undreamed of -- but also because of our justifiable suspicion that reality works this way, i.e., we live in one world and the patterns that nature shows us are linked. Our metaphysical theory could be wrong, but ampliatively speaking, it is the best we have at present.

There is no puzzle then why rational human beings during the Copernican episode began to pursue either the Tychonic or Copernican systems. Once the Copernican supporters drew attention to the unity that could be achieved by modifying the geometrical account of the linkages with the sun (and how this unity extended to the settings of other parameters), there was no going back. It would not have been rational to pursue a theory that had theoretical unity but could not deal successfully with the core observational problem, but it surely was rational to pursue a theory that could match another observationally and had greater overall unity. Thus, we see that Duhem was partly right -- it is impossible for us to ignore the need for unity; but he was also partly wrong -- we are not powerless to justify using it as a constraint. We are powerless to justify this goal of unity from some transcendental perspective -- our metaphysics, of course, could be wrong, and our ampliative methodologies may have been tricked all these years. We may not be part of one world and all our experience of repeatable patterns may not be indicative of a unity behind nature's complexity. We could simply be brains in a vat of preservative chemicals connected to a computer via electrodes simulating the reality of a unified external world, and our ampliative goal of using methodologies that pierce through the top layers of nature's tricks and coincidences thus totally quixotic. But we have little reason to believe such skeptical scenarios.(88)

A large part of the interpretation of scientific practice defended in this thesis appears clearly in Kepler's philosophy of science. First of all, according to Kepler, the oft cited empirical equivalence of various hypotheses used by skeptics is merely the result of appraising such hypotheses in isolation. For instance, one historical source of empirical equivalence arguments is Hipparchus's demonstration that the motion of the sun can be saved by either an epicycle-deferent or eccentric device. But according to Kepler, such hypotheses are "small change" and are not "truly astronomical hypotheses."(89) This demonstration was for one astronomical object only, and was neither linked with many of the other details of the core observational problem nor a complete set of auxiliaries.

In other words, as in Case #1 above, the interpretation of evidence for an individual hypothesis is misleading if we do not consider all sources of evidence; specifically, how each hypothesis is linked with other hypotheses in a full web of belief, both within a particular field, such as astronomy, and related sciences, such as physics, and the ramifications that result for the whole system in accepting the particular hypothesis. According to Kepler, it is a mistake to ignore "the diverse outcomes which weaken and destroy [the] vaunted equipollence when one takes account of related sciences."(90)

Secondly, "that which is false by nature betrays itself as soon as it is considered in relation to other matters."(91) In the language of this thesis, accepting a particular node along an adjudicatory trail has ramifications. Although from a purely logical point of view with sufficient imagination and creativity, any particular node can be defended "come what may," in actual practice this can only be done by ignoring well supported hypotheses in related fields and accepting a possible but highly unlikely support structure. According to Kepler, this can only be accomplished if "you would willingly allow him who argues thus to adopt infinitely many other false propositions and never, as he goes backwards and forwards [in his arguments], to stand his ground."(92)

To return to an example from the Introduction, most astronomers of antiquity were convinced that the observed variation in planetary brightness was best explained by variation in distance from the Earth, and hence eccentric orbits of some kind. However, a defender of homocentric orbits could appeal to the auxiliary hypothesis that planets oscillate in size, and that during opposition planets swell up, becoming brighter, providing the illusion of approach to and variation in distance from the Earth. As a mere possibility, there is no absolute way to block this escape tree, but it is not without significant costs. If we ask the defender of homocentrics "to stand his ground," he must explain how this auxiliary is consistent with the then prevalent conception of planets. Even within an Aristotelian cosmology, such a conception of the nature of planets would have massive negative ramifications. It is possible given sufficient creativity and imagination to tinker further with this save, to patch the patch, and possibly find a way of making the patch consistent with Aristotelian cosmology. However, the rational move taken by the vast majority of astronomers was to assess the situation ampliatively and conclude that such a trail was unworthy of pursuit due to its great likelihood of failure.

Similarly, although tobacco companies can continue to safely state on purely logical grounds that the link between cigarette smoking and lung cancer has not yet been proved, no scientist today would propose a grant to examine what all the lung cancer victims, in all the studies of the last 40 years, were doing on their third birthdays. Without an examination, it is possible that chewing a particular type of gum on a third birthday was the real common denominator of lung cancer victims in both groups.(93) Such a variable, and many like it, have never been tested. But the scientific community knows full well that grant money will not be forthcoming for such studies. This response is not a mere conservative consensus. There is no ampliative basis for opening up this escape tree; we have no reason to believe that chewing a particular type of gum on one's third birthday is causally linked with eventual lung cancer.

Note that the situation was notably different in the late 16th and early 17th centuries for supporters of geostasis and heliostasis. For the defenders of geostasis, the relative merits of its empirical strengths and weaknesses were well known, and a major rival had been proposed that was not only able to match the empirical success of geostasis but propose, unlike the tobacco companies, auxiliary nodes that had to be taken seriously. As we have seen, there was a sufficient ampliative basis for defenders to pursue geoheliocentrism. Furthermore, the very reasons that supported pursuit of an escape tree for geostasis, also supported heliocentric pursuit. The nodes on the various hypertextual adjudicatory trails were not mere logical possibilities, but serious contenders based on the total empirical and conceptual developments of the time.

The misleading point that relativists consistently flaunt is that from a purely logical point of view the development of empirically equivalent hypertextual adjudicatory trails is "an easy matter." In his attack on Tycho, Ursus made use of this point to claim that priority in the development of geoheliocentrism was not a big deal.(94) In his Apologia pro Tychone contra Ursus, Kepler seizes upon this point and responds that only "a thoughtless man who pays attention only to the numbers will think that the same result follows from different hypotheses and indeed that the truth can follow from falsehoods."(95) Scientists do not propose solutions to problems while ignoring the linkages that a particular hypothesis has with many other nodes along an adjudicatory trail. Such a characterization underrepresents what scientists do, and ignores "the long and tortuous course" of real science.(96) According to Kepler,

To predict the motions of the planets Ptolemy did not have to consider the order of the planetary spheres, and yet he certainly did so diligently. To predict and expound a method of calculation for the heavenly motions Copernicus and Lord Tycho after him did not have to ask why it is that the planets at their evening risings become nearest to the Earth. For they could have produced the same results even by using the Ptolemaic form of the heavens with the dimensions corrected. But love of finding out about nature made astronomers take up the exploration of this part of physics on astronomical grounds. . . . What about Copernicus? He censored a certain non-uniformity of the motion of the epicycle in Ptolemy, not on the grounds that this motion conflicts with what is seen and with our experience or observations of the stars, but because it is in conflict with the nature of things; so from this, he declared, he derived his motive for parting company with Ptolemy.(97)

For Kepler, even if the numbers in terms of celestial coordinates are the same, even if one can make neat mathematical models and elegantly demonstrate their equivalence in the cozy confines of pure geometry, systemic linkages with other considerations produces a whole host of ramifications in terms of present and future evidence. To cite, according to Kepler, only a few examples: In comparing the Ptolemaic and Copernican systems, there is a different treatment of the superior planets in terms of distance to the Earth during opposition providing the possibility of discrimination by a parallax effect. The Copernican system predicts that Mars should show a greater parallax than the sun.(98) In comparing the Ptolemaic and the Tychonic systems, on the one hand, with the Copernican, on the other hand, there is a significant difference in prediction of stellar parallax.(99)

The fact that Tycho would initiate a systematic attempt to observe these projected parallax discriminations shows that the astronomers of the time were well aware of many of the ramifications of different hypertextual adjudicatory trails and were testing the nodes along those trails.

To sum up. The major virtue of emphasizing the role of parameter determination in the light of scientific practice as pursuit, adjustment, and acceptance of adjudicatory trails is that we are allowed to see the majority of players during the Copernican episode, both supporters and nonsupporters of heliostasis, as rational. Furthermore, although the major players had many nonepistemic influences, these influences not only helped articulate the competing adjudicatory trails, thus producing variety of practice and a robust debate, but also, in the end, the nonepistemic factors did not overwhelm epistemic considerations. If nonepistemic influences had been paramount, it is most likely that the Copernican revolution would have never taken place, that at least some version of geoheliocentrism would have been defended for far longer than it was. But as we have seen the position of geostasis crumbled in the light of its own articulation and competition from heliostasis.

Notes for Chapter 5

1. Duhem, 1954, p. 220.

2. Gould, 1994, p. 9.

3. Below I will deal with the issue of whether or not Ptolemaic astronomy was a complete theoretical system. My contention will be that it was not only intended as such by its author, but it is a misrepresentation of the debate to assert that Ptolemaic astronomy was not a system and that of Copernican astronomy was. By the end of the 16th-century, it was clear that both sets of astronomical models had an uneasy marriage with their respective supportive physics, and major questions were being raised concerning the implied cosmologies of both theories.

4. According to Gingerich and Lightman, "The principal challenge for the astronomers of antiquity and the Renaissance was to account for the seemingly irregular motions of the planets among the stars, especially the so-called retrograde motion. . . . In the sun-centered system of Copernicus, this phenomenon is easily explained." 1991, p. 691.

5. This claim, of course, appears massively inconsistent with the date and content of Galileo's Dialogue. However, I will argue below that Howard Margolis is correct: The long standing puzzles of the Galileo affair can best be explained by seeing that one of Galileo's main targets in his Dialogue is not Ptolemaic geostasis, but rather Tychonic geoheliocentrism.

6. Peterson, 1994. Recall from the Introduction that I am claiming that there is a very close relationship between parameter determination and at least one type of theoretical unity.

7. One response to this question is that it did not. In this regard I will comment on Westman's Wittenberg Interpretation below.

8. Rosen, 1971, pp. 164-165; 167-168. Emphasis added. These paragraphs show the connection perceived by Copernican supporters between parameter determination, explanation, and theoretical unity. The phenomena, according to Rheticus, of the core observational problem are not only saved but linked in a rigorous geometric way, and the details of each planet -- position, order, and details of inequalities (retrogressions) -- bound up "into one" theoretical unity. Note also that Rheticus "sincerely cherish(es)" what Ptolemy had accomplished, but is arguing that upon comparison of the two systems there is more unity in the Copernican treatment.

9. Westman, 1975c, p. 333. Emphasis added. Again, the "great argument" was viewed to be that the "order and magnitudes" of planetary parameters are fixed and "bound together" in a heliostatic model.

10. Jardin, 1979, p. 157; Gingerich, 1993, p. 327. Emphasis added. Here we see the connection between fixing key parameters and explanation, the latter being Kepler's main concern.

11. Galileo Galilei, 1632, Drake translation, 1953, pp. 341-342; 344-345. Emphasis added. Here Galileo lists the details the others are referring to -- the qualitative and quantitative details of the anomalies (inequalities) in the motions of all the planets -- and repeats the connection with explanation and theoretical unity.

12. Gingerich and Lightman, 1992, p. 692. Here Frisius refers to an example of parameter determination that figured prominently in the persuasiveness of heliostasis. All the planets show increased brightness at opposition and this is geometrically required by heliostasis. It is debatable whether this is required by Ptolemy (see below), but Frisius is drawing attention to the fact that none of the historical players perceived it as required ("a reasoned fact") in geostasis.

13. Gardner, 1983, pp. 239-240. Emphasis added. Praetorius's "symmetry of the orbs" is equivalent to Rheticus's "golden chain." Here Praetorius expresses the ambivalence of many nonsupporters of heliostasis: calculations were easier and heliostasis surely possessed a desirable theoretical feature, but the motion of the earth conflicted with accepted auxiliaries.

14. Blair, 1990, pp. 359-360. Here Tycho repeats the fixation of planetary oppositions and refers to another parameter that featured prominently in the minds of those who supported planetary linkages with the sun, i.e., bounded elongation of the inferior planets (Mercury and Venus).

15. Westman, 1975c, p. 317, 319. Read "exquisite order" as "golden chain" and "symmetry of the orbs."

16. Translation by Boas and Hall, 1956, pp. 258-259. Emphasis added. Here Tycho makes clear that the superior elegance of the Copernican linkages with the sun should not be couched simply in terms of the number of epicycles. Rather, it is the synchronized fixation of the details of planetary motion by Copernicus that is most impressive.

17. Book. I, chap. 10, and prefatory letter to the Pope. Emphasis added. (1939 edition, Wallis translation) Note Copernicus's reference to symmetry, harmony, and linkages just prior to listing in detail the parameters of the core observational problem. Although Ptolemy can save the numbers, and his models are "well-painted," they link together, claims Copernicus, like the body parts in a Frankenstein monster.

18. According to Gingerich, "(I)n an Earth-centered system, such a coincidence (parallelism and bottom positioning) is not required by the geometry." (1991, p. 691).

This needs an important qualification. Although Ptolemy does not explain the parallelism and bottom positioning, they are required in his system to save the known observations. What the major players are realizing ("no necessary cause or . . . explanation," according to Tycho; no "reasoned fact," according to Frisius) is that if the observations of linkages with the sun had been different, Ptolemy has the geometric machinery to adjust. No one, of course, at the time would have expected any other planets to exist, but my appeal to this thought experiment is a way of showing the dramatic difference between the two systems recognized by those who carefully studied the two models.

The flexibility inherent in the Ptolemaic system is often misinterpreted to mean that the geometry is full of ad hoc jiggery. This interpretation fails to recognize the elegant response Ptolemy provides to the core observational problem when viewed (as it was for over 1400 years!) with no competitor. However, realizing that Ptolemy has a more flexible response to surprise changes in the core observational problem, reveals that Copernicus has a more fixed response to the known core observational problem.

19. Both Laudan (forthcoming) and Margolis (1987, p. 237, n. 2) make this point against the strong epistemic interpretations of Lakatos and Glymour (1980, chapter 5). According to Glymour, although the evidence is relatively equal empirically,

"The question is whether the (same) evidence provides better grounds . . . for the Copernican theory than for the Ptolemaic. I believe it does. There are several respects in which the bearing of the evidence is different for the two theories. (p. 193, emphasis added)

My way of rendering (developed below) how I differ from Glymour is to admit that the new planet examples are counterfactual, and hence, cannot consist of crucial tests of the two theories and a basis for acceptance of one theory over the other. Furthermore, that one theory T1 determines key parameters while another theory T2 treats them as coincidences, does not decisively tell us that T1 has got things right. The question of whether we are dealing with coincidences or fundamental processes is often the fundamental ampliative issue to be decided by further testing. However, we desire knowledge of fundamental processes because we have learned from experience that such theories have staying power and lead fruitfully to many other discoveries, providing connections to many other fields and answering questions that we did not even know we had. So, we pursue theories that tell us stories about fundamental processes.

20. Kuhn, 1957, p. 180. In his 1957, Kuhn can not seem to make up his mind on how much weight to give parameter determination. While acknowledging that overall the Copernican ability to fix key parameters related to the core observational problem is the "the single most striking difference" (p. 141) between Copernicus's system and that of Ptolemy, that heliostasis offers "a simpler and more natural account" (p. 171) of the phenomena, that it possesses "a naturalness and coherence" (p. 176) not possessed by geostasis, and that the "sum of the evidence drawn from harmony is nothing if not impressive" (p. 180), he nevertheless concludes with his famous claims that "it may be nothing" (p. 180), that the "apparent economy" was simply "a propaganda victory" and "largely an illusion" (p. 168), and that the appeal of aesthetics was only persuasive to a "perhaps irrational subgroup" of neoplatonic mathematicians (p. 180). This indecisiveness on Kuhn's part is due to a flawed holistic interpretation of scientific change, and the fact that Kuhn makes no attempt to unpack the notions of harmony and coherence, as I have attempted to do.

Shapere is certainly correct when he writes (1975, p. 102 n4), "Nothing is gained in illumination, and much is lost because of highly misleading associations, by referring to such considerations (unity and linkages in the Copernican system) as 'aesthetic'."

21. Goldstein, 1987, 1988; Hanson, 1973.

22. According to Goldstein (1988, p. 317),

. . . up to the time of Copernicus, and for a short time thereafter, modifications in the Ptolemaic system were made piecemeal. When one part was changed no modification of any other part was required precisely because the whole was not yet regarded as subject to the requirement of internal logical consistency. The new mode of criticism, where systems could be rejected because of defects in their parts, may be found in Kepler and Galileo.

23. Quoted from Gardner, 1983, p. 207. Emphasis added. Gardner uses this quote to show the realistic foundation for instrumentalist sentiments in Ptolemy. See p. 208.

24. Duhem's To Save the Phenomena (1959) is perhaps the best single source that depicts this struggle.

25. Translation by Boas and Hall, 1956, p. 258.

26. I would claim that both Drake and Duhem make this mistake. See notes 35 and 40, chapter 2, and chapter 3. Hanson also, 1973. Shapere comes close when he says (1975, pp. 102-103) that characteristic disunities in the Ptolemaic system "were not problems, facts requiring explanation, which were recognized as existing with regard to Ptolemaic theories; they were not, and certainly did not need to be, so recognized as long as astronomical theories were considered as mere collections of devices, to be applied to different cases in different ways according to need, for the sake of prediction." But Shapere qualifies this by saying that he only wants to emphasize that apparent Ptolemaic disunities "did not constitute a 'crisis' for Ptolemaic astronomy." (p. 103)

27. Westman, 1975c, pp. 286-287.

28. Ibid., p. 286.

29. Ibid., pp. 288-289.

30. We are not talking about e-mail here, but 'immediately' given the mid-16th century logistics of printing and transmission of important works.

31. Westman, 1975b, p. 395

32. In an annotation to a series of lectures, he drew a model of the inferior planets circling the sun while the sun revolved around a stationary Earth, but then crossed it out.

33. Quoted from Westman, 1975b, p. 402.

34. Ibid., p. 403.

35. Ibid., p. 404.

36. Here it is appropriate to make a major point regarding historiography. When is it appropriate to normatively appraise statements made by historical figures? Answer: when we see that they made mistakes by reliable standards, theirs and ours. Although statements can be found claiming a greater accuracy for the Copernican system, and this has been mistakenly picked up as authoritative by some modern commentators (see Kitcher, 1993, p. 206), Gingerich has shown that a recomputation of planetary positioning using Ptolemaic and Copernican models does not show superior accuracy for the latter. According to Gingerich, this is to be expected when one realizes that Copernicus was only trying to "match" Ptolemy's achievement observationally. (Gingerich, 1975a) Furthermore, using the best observational tools available for the time, Tycho also concluded that overall observational values given by Copernicus were not better than that of Ptolemy. (Schofield, 1981, pp. 36-37) Relativism has made us overly fearful of making any historical normative judgments "by our own lights."

That we do sometimes make mistakes imposing a modern perspective on ancient texts (eg. the misinterpretation of Ptolemy's statement on individuality and the planets above), does not mean that texts can mean anything we want them to mean.

37. There remains more to my quibble with Westman that we must pass over quickly. Westman claims that regarding the so-called Copernican linkages there was a remarkable silence during the first phase of reception. But it is clear from his papers that what he has in mind is a silence regarding the Copernican ability to fix planetary distances. But there is much more to the Copernican linkages than just an impressive ability to specify planetary distances. As I have argued, there is the Copernican ability to link parameters that necessitate a solution to the core problem situation, i.e., retrograde motion, frequency per planet and links with the sun. The latter, as shown below, is clearly linked with calculation and would be recognized by any competent astronomer immediately. Westman recognizes the Wittenberg astronomers appreciation of the Copernican elimination of the equant, but couches this in a purely philosophical way -- everyone objected to the equant a priori. He fails to see how the elimination of the equant is also linked with calculation based upon Copernican parameters.

Thus, the Copernican linkages created an immediate stir even if they were not fully appreciated in terms of linking the heliostatic retrogression connection with the sun and planetary distances. Viewed this way, a much more likely explanation than childhood trauma for Rheticus's awareness of this connection is that he was "a bright young man devoted to higher learning rather than money and profit." This characterization is due to Johannes Petreius, the printer of De revolutionibus. (Swerdlow, 1992, p. 270.) It is worth noting that Petreius, as part of the Nuremberg circle of "learned men," in writing to Rheticus as early as 1540, refers to the Copernican system as described by Rheticus in his Narratio prima (1540) as a "glorious treasure" even though "he does not follow the common system." (Ibid., p. 274.)

38. In the above quotations, Galileo refers to "anomalies" and Tycho refers to "inequalities." Both were using language common in discussing astronomical observations that models were required to save. The canonical description of these observational problems is in Dijksterhuis, 1961, p. 57.

39. Margolis, 1993, p. 94.

40. Ibid., pp. 96-97.

41. I say "can be" because a priori Ptolemy has the machinery to adjust if the well-known planetary linkages with the sun did not exist. I am not claiming that the linkages with the sun were an afterthought for Ptolemy. A posteriori, Ptolemaic geometry rigorously saves the qualitative features of the core observational problem.

42. According to Owen Gingerich, "in an Earth-centered system . . . a planet at the moment of opposition could, a priori, lie at any position on its epicycle. . . . a striking observational fact that would later have a completely natural explanation in the heliocentric system of Copernicus had to be accepted as a given, without explanation, in the geocentric system of Ptolemy." (1991, p. 691-692)

43. Van Helden, 1985, p. 43.

44. Gingerich, 1993, p. 123.

45. Margolis, 1987, p. 277. With this language Margolis does not mean to exclude Kepler's elliptical version of heliostasis or other versions of geoheliocentrism. It is clear in the original context of his argument that he means that the choice was between some version of heliostasis (Kepler introduced his elliptical orbits in 1610) and some variant of geoheliocentrism.

46. Ibid., p. 280.

47. Margolis, 1991, p. 266.

48. It would not be long before commentators would be referring to Galileo's book as discussing "the three systems of the world," and that the controversy was 'twixt Ticho Brahe and Copernicus." (Schofield, p. 250).

49. 1991, p. 266.

50. Jardine, 1984, p. 147.

51. Drake and O'Malley, 1960, p. 71.

52. In his The Assayer (1623). See Drake and O'Malley, 1960, pp. 184-185.

53. In a letter to Diodati (Schofield, 1981, p. 249).

54. Problematic for this claim is that from our perspective today it would seem that the Pope would have simply forced Galileo to discuss directly all three systems, allow the Ptolemaic to be destroyed, and then conclude with the Tychonic and Copernican systems as surviving equals.

Margolis does not address this objection. Let's help him a little. His response might be threefold. (1) This is indeed a puzzle, but there are a greater number of puzzles for the traditional view that Galileo was indulging in questionable dilemma sophistry. (2) This objection is the result of hindsight and we do not know what kind of detailed negotiations took place between Galileo and the Pope. It is possible that this requirement was suggested by the Pope, and Galileo, using his friendship with the Pope, was able to negotiate his way out of it. (3) It is also possible that Galileo was able to suggest to the Pope that this be postponed, because the details of the Tychonic system had not been worked out by anyone. Margolis does mention this lack of Tychonic articulation, but applies it to a different puzzle. Why did the Pope not foresee the embarrassment of the Tychonic system? See below. Concerning (3), however, the Pope and his close advisors were also probably unaware, and Galileo was unlikely to volunteer this information even if he was aware of it, of Kepler's devastating reasons to prefer heliostasis over geoheliocentrism, published much earlier in his Astronomia Nova (Gingerich translation, p. 313). If Galileo's plan was to indirectly embarrass the Tychonic system, he would not want to show his cards too soon. If the Pope was aware that the Tychonic system was in big trouble, Galileo would not be allowed to publish at all. Better would be to cut a deal that allowed Galileo to champion the planetary linkages with the sun, supporting Copernicus and Tycho over Ptolemy, but agree not to discuss the Tychonic system, leaving the impression that future articulation of this system could match Copernican successes.

55. Drake translation, 1953, p. 318.

56. Margolis, 1991, p. 262.

57. Margolis, 1991, p. 262.

58. Ibid., pp. 262-263.

59. Quoted from Margolis, 1991, p. 272.

60. Drake 1953 translation, p. 322.

61. To cite but one clear indication that Simplicio is not defending the Ptolemaic system, he says there is "no doubt" that Venus and Mercury circle the sun with the latter being closer to the sun (p. 324), a Copernican and Tychonic arrangement. In the Ptolemaic system, not only do these planets not circle the sun, of course, but Venus is closer to the sun than Mercury.

62. Ibid., p. 321. Emphasis added.

63. Ibid., p. 326. Emphasis added.

64. Gingerich translation (1983) of Kepler's Astronomia Nova, 1610b, p. 314, emphasis added.

65. I am not suggesting that Galileo has taken this argument directly from Kepler, although the pattern in both arguments is virtually identical. It is still unclear how much attention Galileo paid to Kepler. Galileo may well have arrived at this argument independently and/or it was a common argument used by Copernicans by this time against supporters of the Tychonic system.

66. Galileo's move here is not unlike writing an apparent positive letter of recommendation for a student while making clear to the discerning reader that your appraisal of this student's work is somewhat short of enthusiastic!

67. Kepler, 1610b, p. 314.

68. Rather than using a Ptolemaic eccentric, Tycho used Copernican epicyclets to achieve the eccentricity.

69. Margolis, 1991, p. 270.

70. Kepler, 1610b, Gingerich translation, 1983, p. 314.

71. Schofield, 1981, pp. 86-87.

72. Margolis, 1991, p. 270; Schofield, pp. 87, 180.

73. Boas and Hall, 1956, p. 254.

74. Gingerich and Westman, 1988.

75. Feyerabend, 1978a.

76. Rorty, 1991, p. 169.

77. Margolis, 1987, p. 268.

78. Kitcher, 1993, pp. 258-259.

79. Ibid., pp. 249-250.

80. Let's assume here that there is some truth to this caricature of Ptolemy. Recall that Ptolemy's model for Saturn must place the important equant point within the sphere of Mars. In isolation, in terms of just observational features, Ptolemy's models for Saturn and Mars work. Placed within a system they don't appear to work well together.

81. This example needs a time-indexed qualification to avoid appearing a clear case of questionable analogy. My point is not that Ptolemy's models are obviously atemporally ad hoc. (In fact, it is an implication of the notion of hypertextual adjudicatory trails that there is no such thing as atemporal ad hocness. In its place we have adjustments to hypertextual adjudicatory trails with nodes that fail or succeed.) If we had no other theory for comparison, we might find that our theory of car color patterns is doing a marvelous job when it always gets it right by predicting red or blue, black or white, yellow or green. The flexibility of the Ptolemaic models were perceived only after a comparison with Copernican models. Thus, the analogy is valid to this extent. Recall that in Ptolemy's system it is theoretically possible for any new superior planet to be anywhere in its epicycle orbit when its epicycle center is in opposition. Copernicus predicts that all superior planets must be at a precise position P1. Ptolemy makes no such essential prediction; we must wait to see if it is at position P1, P2, P3, etc. Recall Figures 5 and 6. Furthermore, because Ptolemy makes no essential prediction regarding the frequency of retrogressions, a new superior planet could have any number relative to the known planetary values.

It would even be possible for the known planets in Ptolemy's system to very slowly revolve out of their current linkages with the sun, such that a million years from now all planets are then at apogee positions in their epicycles! Recall that a similar move was made by Ptolemaic apologists to explain Ptolemy's original value for precession. See chapter 2, point 8 of Ptolemaic problems. Comparing this possible situation with Goodman's paradox, suppose T1 predicts that future emeralds will be green and T2 predicts that they will be green or maybe blue sometime in the future. Why should we give T1 greater credibility given current observations? Why would it be more fruitful to work on T1. Below I will argue that we give greater credibility to T1 because we do not believe we have any evidence that the fundamental objective features of the world are time dependent. Particular processes may change over time (continents drift, weather patterns change), but overwhelming ampliative evidence suggests that there is one world whose time-independent, fundamental objective features cause such changes.

82. We could also use the Copernican linking of the eccentricity of the Earth's orbit with the long standing problem of calculation of precession. According to Gingerich (1993, p. 35), this "impressed everyone."

83. In October of 1994 the Honolulu Advertiser reported that over 60,000 studies have been done on the relationship between cigarette smoking and health hazards. Probably an exaggeration, but there have been a lot. Basically, these studies can be seen as follow-up studies to the seminal work of Hammond and Horn, 1958.

84. According to Stephen Jay Gould, "It's hard enough . . . to find one way of accommodating experience, let alone many. And these supposed ways of modifying the network of beliefs are changes that no reasonable -- sane? -- person would make. There may be a logical point here, but it has little to do with science." Paraphrased by Kitcher, 1993, p. 247.

85. Taking a few days of rest and showing only quantum fuzz on Saturdays and Sundays!

86. In this way, according to Duhem, we can still side with Osiander and Bellarmine while appreciating the mathematical innovations of Kepler and Galileo. See Duhem's summation in his To Save the Phenomena, pp. 116-117.

87. Tyson, 1995, p. 18.

88. Note that even this skeptical scenario uses laws of nature and repeatable patterns!

89. Jardine, 1979, p. 164.

90. Ibid., p. 166.

91. Ibid., p. 157.

92. Ibid.

93. Even after an examination that produces a negative result, it would still be possible that the real common denominator is the use of a particular chewing gum. Our study could be flawed.

94. Jardine, 1979, p. 161.

95. Jardine, 1984, p. 141. For Kepler, "the numbers" means planetary positioning in celestial coordinates.

96. Ibid., p. 140.

97. Ibid., p. 145.

98. It is significant that Tycho, although supporting a different system than Kepler, also recognized the great importance of this non-equivalent feature of the two systems. Schofield, p. 56

99. Jardin, 1984, p. 141.