The Epistemological Stew: 1543-1616
In the preceding analysis of Feyerabend's claims and the application of the notion of intelligent inference along hypertextual adjudicatory trails of reasoning, there is no intention to endorse an historical chauvinism. Although the notion of a hypertextual adjudicatory trail is meant to preserve the logical-historical approach to epistemology against the psychological-sociological, no slide is intended that sees individual scientists as always algorithmically calculating the cost-benefit analysis of endorsing a particular node along an adjudicatory trail, such that the decisions they made appear inevitable given our present conception of successful theories. As was noted in the previous chapter, in the work of Galileo and Kepler inferential sagacity should not be overlooked as an important element in theory competition. It is seldom immediately clear which auxiliaries are consistent, and hence needed, with a core hypothesis. Although Kepler, unlike Galileo, became aware that allegiance to circular uniform motion must be given up to be a consistent Copernican, also unlike Galileo, he was initially inhibited from endorsing the validity of celestial telescopic observations because of a residual allegiance to aspects of Aristotelian cosmology.
As Stanley Jaki has noted, "History is the great equalizer. Sooner or later it cuts all things and all men down to their true size."(1) The notion endorsed in this thesis of hypertextual adjudicatory trails is not meant to deny that refined historical analyses of the Copernican episode have revealed a messy, vague, "circuitous, mazelike" road full of "blind alleys" and "wrong paths."(2) As Koyré has noted, the history of scientific thought should not be treated as "a catalogue of errors or achievements, but as the entrancing, instructive history of the efforts of the human mind."(3) The rational scaffolding I have proposed, however, is intended to avoid such extreme psychological conclusions as that of Koestler,
"The history of cosmic theories. . . may without exaggeration be called
a history of collective obsessions and controlled schizophrenias; and the
manner in which some of the important individual discoveries were arrived
at reminds one more of a sleepwalker's performance than an electronic brain's."(4)
Koestler's stance has, of course, much in common with Feyerabend's anything-goes relativism. The initial review of Koestler's book by Santillana and Drake(5) was equally extreme, prompting further shrill responses in defense of Koestler. According to Santillana and Drake, Koestler depicts the founding fathers of the Copernican revolution as "antisocial schemers, cowards, liars, hypocrites, irresponsible cranks or contemptuous snobs." In portraying the revolution this way, they claim Koestler has the "unique inability to understand what Galileo wrote" and "the distinction of being the first writer to misunderstand (Galileo's sunspot argument) entirely," that Koestler's book is full of "insolent misrepresentations" and his "ulterior motive" is the "blackening of science as the destroyer of 'spiritual values'," and finally that his thesis is "repugnant to everything we have written, and in contradiction with all that we have learned in the course of years devoted to these studies."(6) According to Santillana and Drake, one of the many things we have learned is that "Galileo seems to have been practically the only man of his age who was fully aware of what was happening and what would follow."(7)
For a response to this review, consider Mark Graubard's summation after noting that Santillana's and Drake's attack of Koestler was "hostile to a degree rarely encountered in academic literature":
". . . history shows reason and scientific rightness to have been with
Bellarmine and not with Galileo, who truly had no evidence besides the
phases of Venus which disproved Ptolemy, but not Brahe. There was indeed
no real proof. . . . The overall work of traditional historians such as
Santillana, compares to the contribution of Koestler much as the work of
rat-psychologists compares to the contribution of a Sophocles, Dostoyevsky,
Tolstoy or Faulkner to our knowledge of the human psyche, even though here
and there Santillana does point to a slight inaccuracy of no genuine relevance."(8)
In this exchange we see the same questionable dilemma noted previously. Rationality is either to be the algorithmic calculation of a computer combined with an input process analogous to the mundane and unproblematic observational tabulations of the rat psychologist, with the historical actors completely aware of all the needed auxiliary nodes in their webs of belief, or it is nothing at all.
My notion of a hypertextual adjudicatory trail is similar in concept to the insights gained recently in neural net theory regarding learning, the functioning of the human brain, and artificial intelligence. Learning and understanding do not involve merely making crisp deductive connections that occur all at once based on fixed rules, but the gradual strengthening and articulation, via the test of experience, of a very involved net of neural nodes with the rules emerging from the interaction of the network. Unlike current digital computers based on the assumptions inherent in propositional logic, the brain does not seem to be a discrete state system. The model of a symbol manipulating system that maps discrete elements of a data-structure to features of the world is replaced by a much more "holistic system."(9) Similarly, the acceptance of a theoretical structure must be viewed as a gradual, comparative strengthening of a vast network of theories, auxiliaries, methodologies, and experimental results. Furthermore, our meta-methodological judgments regarding the strengthening or comparative weakening are hypertextual in the sense that they are not entirely transcendent of the networks in question but are a non-linear node on potentially several networks.(10) As we will see, we must replace such extreme notions of deductive fit of theory and experience on the one hand, and framework gestalt switches on the other hand, with concepts of comparative reliability, gradual reinforcement or erosion, and threshold illumination.(11)
In this way one can endorse the overall rationality of science without endorsing the rationality of every move of individual scientists. One can endorse wholeheartedly the relevance of the sociological, psychological, and cultural contexts for understanding theoretical allegiance, arguing in fact that such messy, complex milieus are necessary conditions for the creation of ideas and the articulation of adjudicatory trails, and still capture a supervising reasonableness to scientific change. For instance, that individual scientists may have interests that affect their attempts to prove other scientists wrong contributes to the criticism and competition necessary for the creation and eventual thorough analysis of the nodes of a hypertextual trail. Similarly, changes in allegiance of theoretical structures may also be causally related to interests. An individual scientist may realize that it is not in his or her best interest in terms of career and institutional support to appear stupid and dogmatic in the light of overwhelming evidence that shows that one's former position is crumbling.
One need not be put off by Tycho's obsession for patronage, credit, and reputation, Kepler's wacky mysticism, or Galileo's egotistical social climbing unless one thinks of science as the sole creation of an "electronic brain" in Searle's Chinese room, and not by fallible human beings wanting to be right and successful in a social context. We need not jettison rational assessment just because we discover that individual pursuits and allegiances were powered in part by motivations other than the pursuit of truth. It is an elementary principle of informal logic -- one still worth defending against those who would advocate the existence of "alternate rationalities" -- that the circumstances of belief can be separated from the assessment of the reasonableness of belief. As Stephen Jay Gould has remarked, "People may believe correct things for the damnedest and weirdest of wrong reasons." In short, we can accept with Feyerabend without controversy in this post-positivist age that
". . . the development of knowledge is not well planned and smoothly running process; it . . . is wasteful and full of mistakes; it . . . needs many ideas and procedures to keep it going."(12)
but still celebrate along with Darwin that there is "grandeur" in a view of life that sees beautiful adaptation as the result of historical contingency and the vagary and happenstance of individual pursuit.(13) Furthermore, we can also identify, as did Darwin, a governing process that constrains and makes use of contingency.
This said, we need to distinguish this position from the socalled compromise model recently advocated by Philip Kitcher.(14) According to Kitcher, we need a model of scientific change, debate, and assessment that "embodies some of the ideas of rationalism and some of antirationalism," that recognizes the "crucial step" and "general moral . . . that epistemology should be psychologistic."(15) According to Kitcher, his model "may be viewed as making some rather obvious amendments to classical rationalism. . . . The central thrust of rationalism (being) that the power of the right kinds of inferences is sufficiently strong to overwhelm effects of interdependence of nonepistemic goals, or of background variations in practice and stimuli."(16) According to Kitcher, against this rationalist thesis we must acknowledge the thrust of the cognitive sociologists that scientists are moved by nonepistemic as well as epistemic goals, that there are causal relationships between beliefs and nonepistemic matters, that community decision is related to the relative power of subgroups, that there is variation within a scientific community as to practice, and that at certain stages in scientific debate reason is not necessarily on the side of the ultimate victors. Kitcher's main point is that it is a mistake to think that reason overwhelms nonepistemic concerns. Rather nonepistemic features often work with epistemic features, provided we promote the nonepistemic features that are conducive to cognitive progress.
Apparently, Kitcher thinks that the great insight behind his compromise model is that the work of Bloor and other sociologists poses no threat to rationality as long as we recognize that "there are important distinctions among the types of processes that generate and sustain beliefs, decisions, and actions." There are "processes that reliably generate true beliefs, while others . . . have a very small chance of yielding true beliefs."(17) In short, we can distinguish nonepistemic processes that favor good cognitive design and those that do not. Rule-based logical approaches do not sufficiently acknowledge that scientists are part of a social situation, that they have, for instance, "conversations" with colleagues, and that rules and reasoning must be supplemented by an "appropriate educational regime."(18)
There are many points of agreement between Kitcher and my thesis. According to Kitcher, "It is, I believe, equally wrong to insist on the presence of decisive reasons for being a Copernican in 1543 and to deny that there were decisive reasons after 1632,"(19) and "Legend (Kitcher's categorization of logical positivism, but also sometimes any apsychologistic approach to epistemology) does not require burial but metamorphosis."(20) But have the sociologists provided us with "deep and important insights"?(21) His key thesis is trivial (he admits that it can be viewed as "rather obvious amendments") once one recognizes a simple questionable dilemma that he sets up with the help of the sociologists. He claims that we must get psychology into the "meliorative epistemological project," that the biggest mistake positivists and even all post-positivists, who have emphasized ampliative reasoning and fallibilism, have been making is to see the epistemological enterprise as basically one of logical analysis. In other words, he sets up a false dilemma between the defenders of Legend and all uses of psychology and then shows how we need a compromise model: to wit, the sociologists are right, sociological and psychological causative factors are heavily implicated in theory choice and transition, but the sociologists are also wrong -- it is a mistake to not make a distinction between good sociological processes and bad ones.
What defender of Legend ever disagreed with this? What defender of Legend ever disagreed with the belief that we should strive for optimal sociological conditions for knowledge acquisition? That good science requires conversations with colleagues and an "appropriate educational regime"? Once one translates Kitcher's "preferred idiom,"(22) all he is saying is that we have learned that scientists should go to college, learn to read, speak more than one language, know how to communicate with colleagues via journal articles, and so on. Furthermore, that we have learned that such conditions are better at activating the "right propensities" for theory choice and progress than "lexographically ordering" alternative beliefs and then always choosing the number of the day of the month!(23)
This is not a deep insight. Kitcher's model of cognitive progress adds very little to what Duhem noted at the turn of this century.
"[If we wish] to increase the rapidity of scientific progress by trying
consciously to make good sense within [scientists] more lucid and more
vigilant. . . nothing contributes more to entangle good sense and to disturb
its insight than passions and interests. . . . it is not enough to be a
good mathematician and skillful experimenter; one must also be an impartial
and faithful judge."(24)
The only difference between Duhem and Kitcher is that Duhem does not make a big deal out of this obvious goal.
Furthermore, it should be clear that to distinguish between good cognitive design and bad cognitive design (good and bad sociological and psychological support structures) one still needs to tell an epistemological story of reliable criteria that will enable one to separate the two. Without such a rational reconstructive approach, one is prone to take too seriously sociological analyses of the causally linking of belief with interests such as the following:
1. Why did Rheticus become a Copernican so early when all other Wittenberg astronomers did not? Answer: When Rheticus was a teenager his father was convicted of sorcery and beheaded. In Copernicus, Rheticus found a kind and strong father he had always wanted, but one who was also a little rebellious as his father had been. Furthermore, in the Copernican system, Rheticus found the unity that his father lacked after his beheading! Rheticus was in "search for wholeness, strength, and harmony," and was "unconsciously (trying to) repair the damage earlier wrought on his father." Also, Copernicus "had a head and heart which were connected to the same body."(25)
2. Why did Tycho not accept the Copernican system when he appreciated
the unity and parameter determination linkages as much as that of Kepler?
Answer: Tycho's personality was very different from that of Kepler. Unlike
Kepler's constant religious introspection, Tycho was a man of this world,
heavily attached to la dolce vita. He drank heavily and loved to
party. (He died when his bladder burst from the consumption of numerous
libations during a long speech by a nobleman.) As such, in an era of heavy
religiosity, and as a Lutheran, he carried around with him considerable
guilt and concern about his fate in the next life. Thus, although he acknowledged
the astronomical superiority of the Copernican system, he could not shake
the fact that its physics conflicted with the Bible. So, not wanting to
risk any conflict with the Bible, he developed his famous compromise.(26)
Human beings are indeed messy creatures. We cannot avoid the fact that such speculative causal factors may be involved in belief commitment. There are no doubt some interesting psychological reasons for why some people flock to the U.S Airforce's top secret Area 51 in New Mexico claiming to be aliens from another planet. They say they have come to be picked up to go home. However, not only would our time be better spent analyzing evidence for actual visitation by extraterrestrials, but it is doubtful that we need spend much time on analyzing whether the noncognitive source of this belief is good or bad in terms of promoting progress. Even if we did, our assessment would be based on epistemic criteria. Similarly, our time will be better spent understanding the epistemic significance of Rheticus's important insight that if the Copernican system is true, Mars should show a greater parallax at opposition than the sun,(27) or how Tycho's vacillation on and eventual acceptance of geoheliocentrism were related to the gradual weakening and strengthening of hypertextual adjudicatory trails.(28)
For that matter, a better sociological explanation for Tychonic pursuit of geoheliocentrism would cite his concern for patronage. Because he needed to be very careful politically, he did not have the freedom of vision that Kepler did. He vacillated on many issues -- whether Mars showed a parallax greater than the sun at opposition, whether the crystalline spheres should be dropped -- because he had much to lose financially if he was wrong. In short, Tycho was absorbed by constant machinations to maintain the attention of financial backers and was easily distracted. By contrast, Kepler's relative poverty, eccentricity, and steadfast vision of being the first to find the mathematical clockwork with which God made the universe -- to literally read the mind of God -- allowed him to be less distracted by political winds.
In Kitcher's terminology, both Tycho and Kepler had propensities. Both wanted to be right, but for different reasons. Kepler desired a Platonic glory, Tycho a this-world glory and substantial financial commendations.(29) But our time will be better spent analyzing what kinds of adjudicatory trails activated these propensities. Ironically, considering how much reassurance Kuhn's work has given the sociologists, we should follow his advice here: "To understand why science develops as it does, one need not unravel the details of biography and personality that lead each individual to a particular choice, though that topic has vast fascinations."(30)
Contra Kitcher, we need neither compromise with the sociologists nor spend much time separating good from bad noncognitive processes. As Kitcher admits, even so-called bad noncognitive factors may aid progress. A modern Kepler who has a passionate religious interest in being the first to arrive at the God equation, a super unified field theory that can explain not only the origin of the big bang out of a quantum fuzz and the crystallization of the forces of nature immediately after the big bang, may have just as much chance at success as the most dispassionate secularist. What matters is for us to become more rational over time, to learn from the past, to see what normative factors did eventually overwhelm or activate "the damnedest and weirdest of wrong reasons." Perhaps, if there is any lesson to be derived from a sociological analysis of Tycho's life, it is that the modern scientist should reflect on how much the incessant pursuit of our contemporary version of patronage, i.e. grants -- the forms, the networking, the establishing of reputation -- may distract one from fruitful pursuits, seeing new approaches to problems, and/or the merit of maverick positions.(31)
Thus, the "meliorative epistemological project" is still primarily logical, albeit ampliative and historical. This said, the concepts defended in this thesis do not deny that research into cognitive psychology and sociology may provide some empirical data relevant to epistemological issues, but the traditional epistemological project, stripped of foundationalism, is still primary. This thesis attempts to handle the complexity and messiness that one finds in the historical record without capitulating to the sociologist and by using the notion of complex hypertextual adjudicatory trails while simultaneously recognizing the contextual nature of scientific problems.(32)
However, before proceeding any further, it is important to appreciate the refined historical analyses that have revealed the complexity of the Copernican episode in all its grand detail. First, by way of contrast, popular treatments in introductory science textbooks, substantially influenced by Legend, often portray Kepler, Galileo, and Tycho as heroic empiricists, not only vanquishing resistance to the truth of our noncentral location in a vast universe, but ushering in the very methodology of modern science, as if such a methodology was sitting in some dusty drawer of rationality waiting to be plucked by brilliant minds, thus implying, of course, that all that had gone before was mysticism and ignorance. From these models of good scientific practice students are taught that we should treat with derision any attempt to prove a priori any feature of the world, such as the alleged medieval attempt to prove that the number of planets must be six.(33) Kepler is then seen as honorably giving up his cherished five-perfect-solids hypothesis when he realized that he could not make it agree with observations. Galileo is seen as attempting to get resistent dogmatic supporters of the Church to look through the telescope, as if every school boy at the time should have known that this instrument was a reliable empirical tool. Moreover, Galileo's Assayer is quoted over and over again, as a manifesto of a new science of observation and mathematical analysis in preference to philosophical speculation and dogmatic authority. And Tycho is seen as working collaboratively with Kepler, cheerfully supplying the astronomical data that will prove the Church wrong.(34)
Yet, Kepler never gave up on his five-perfect-solids conviction and argued, like Rheticus, an early promoter of Copernicanism, that there could be only five planets besides the earth, even after the discovery of his three laws of motion. Furthermore, Kepler supported, as did Copernicus, heliostasis in part because as a neoplatonist he thought that the sun was the "material domicile" of God, and his tense relationship with Tycho, theoretical and personal, is well known by any first-year historian of science.(35) Kepler also opposed Bruno's promotion of an infinite universe, later adopted by Newton, and thought that the stars were part of a packed, relatively narrow, celestial vault composed of ice. He was also fully convinced that God was on his side in the race to be the first to truly understand the architecture of the universe, for why else, he thought, would he arrive in Prague at the very time that Logomontanus, Tycho's assistant, was working on Mars, the relatively greater eccentricity of which was the key to the discovery of elliptical orbits.(36)
Speaking of Bruno, the revolutionary nature of his work is clearly attenuated by the fact that he does not appear to have read carefully or understood Copernicus's De revolutionibus. His personal copy lacks any annotations. In his La Crena he pictures Mercury and Venus being on the same epicycle, which in turn revolves on the same deferent for the Earth and moon, the latter also revolving on a single epicycle, and in his De immenso, Bruno claims that the Earth, moon, and planets must be approximately the same size and have the same revolution around the sun, just like animals of the same species. According to Ernan McMullin,
"It is hardly necessary to say that these constructions were at odds not only with the Copernican system but with the accumulated observational evidence on which mathematical astronomy had rested for more than two millennia. It was obviously not on observational evidence that Bruno was relying."(37)
Then there is the complexity of Galileo. We have already acknowledged Feyerabend's attention to the convoluted nature of the acceptance of the telescope. (Actually Feyerabend is only "borrowing" this analysis from the work of Vasco Ronchi.(38)) Galileo paid little if any attention to Kepler's work and supported the notion of uniform circular motion as dogmatically as any supporter of Ptolemy. He was convinced that his mistaken theory of tides proved heliostasis correct, and perhaps worst of all, balked at the thought of a vast universe to incorporate the Tychonic proposal of large elliptical orbits of comets, in the process changing his mind on the nature of comets in such a way as to seriously weaken arguments against Aristotelian cosmology.(39) Also seldom mentioned by supporters of a simplistic Legend is that Galileo's great philosophy of science treatise, The Assayer, is full of ad hominem polemic against taking as authoritative the Tychonic observational and mathematical analysis of comets ("Tycho's monkey-planets")!(40) And speaking of Tycho, also rated X for historical virgins is any mention that the great observationalist Tycho could not bring himself to believe in heliostasis in part because he was convinced that God would not "waste" the vast amount of empty space implied between Saturn and the stars.(41)
Aside from these historical embarrassments for the supporters of a simple
scientism, consider the confusing situation an impartial observer, say
during the first decade of the 17th-century, would find attempting to apply
a purely linear-logical fit between evidence and theory for deciding between
geostasis and heliostasis. For a defender of Ptolemaic-geostasis there
were the following problems.
1. There were many failures to save the most basic observational phenomena.
Most of these were well documented by Regiomontanus as early as the second half of the fifteenth century.(42) It was no secret that by the 16th century serious calendar reform was needed due to the growing embarrassment of when important religious dates fell. Some of the Ptolemaic predictive errors were very large. In 1504 a Ptolemaic prediction for a conjunction of planets was off by 10 days, and in 1563 another predicted conjunction was off by a month. Gingerich believes there is strong evidence that Copernicus observed the 1504 failure. For the 1563 conjunction, the Copernican prediction was off by only a day or two.(43) There were also errors in predicting the time and duration of lunar eclipses, and there was a total failure to predict annular eclipses.
2. The appearances of the magnitudes and sizes of Venus and the moon were anomalous.
Although Ptolemy's solar and lunar models, when combined, allow for
the calculation of solar eclipses for any particular geographical location
for the first time in the history of astronomy, a major problem occurred
when the model of the moon is combined with that for Venus. Based on Ptolemy's
lunar model, the moon should appear twice as large at its closest approach
to Earth. The model for Venus predicted that it should appear 7 times brighter
on its closest approach to earth, and when linked with the lunar model
it should appear at times 40% the size of the moon. Part of the problem
is that Ptolemy was trying to account for what has come to be called evection,
a periodic change in the range of the speeds of the moon. To account for
what thus appears to be a regular variation in the eccentricity of the
moon's orbit, Ptolemy used a device later used many Arab astronomers and
in a substantial way by Copernicus. Sometimes known as an epicyclet, the
center of the lunar deferent is placed on its own small internal circle.
As this circle turns it cranks the deferent nearer and farther from the
Earth. There were similar diameter and magnitude appearance problems for
3. The prediction of a pattern of transits for Venus and Mercury of the sun were not observed.
4. A substantial parallax can be observed for the moon but not for Mercury.
Since Ptolemy has Mercury being the next celestial object, being positioned between the moon and Venus and with its orbit nested immediately on top of the moon's, parallax for this planet should be observed at perigee. But no such parallax was observed. According to Ptolemy in his Planetary Hypotheses, "If (planetary) distances are correctly given, Mercury, Venus, and Mars (should) display some parallax. . . The parallax of Mercury at perigee is equal to that of the Moon at apogee."(45) Although previously, he says that "no phenomenon allows us to fix their (the planets) parallax with certainty."(46) Presumably, and this is the way Goldstein interprets this remark, Ptolemy is referring to the inability of naked-eye observations to measure parallax for any of the planets. This is clearly true of Mercury, given its closeness to the sun and the relatively small amount of time it is visible after sunset.
Furthermore, as Ptolemy himself notes, his purely geometric model does not allow one to ascertain whether Venus or Mercury is closer to the Earth.(47) Thus, opening up his astronomical model to the charge of ad hoc flexibility discussed next.
5. By the end of the 16th century Tycho's parallax measurements showed that comet orbits would have to cut through the orbits of Saturn, Jupiter, and Mars. This and other problems drew increasing attention to a long standing tension between Ptolemy's purely astronomical models and Aristotelian auxiliaries as a system.
Because Ptolemaic geostasis, as a complete system able to ascertain planetary distances, depends crucially upon referential commitment to solid celestial spheres, this was a major defect judged against a criterion of systematicity -- a criterion, if not new, at least emerging as more important due to the clamoring of the supporters of Copernicanism. Furthermore, the Aristotelian cosmological auxiliary support for Ptolemy was further weakened by the observation of several novae by 1604. Finally, as the criteria of systematicity and parameter determination became increasingly important, Ptolemaic planetary models became vulnerable to the charge that they were ad hoc and created to handle individual planetary problems and could not work well as part of a system.
We have already seen how Ptolemy can get an adequate fix for solar eclipses with his solar and lunar models, but that the lunar model will not only not match other observations well but conflict with the model for Venus. Consider another important example. Using the mechanisms of deferent, epicycle, eccentric, and equant point, Ptolemy is able to fashion an adequate model for its time for Saturn. He could account for the major anomalies of retrograde motion and frequency of such motions, and couple these fairly well for its time with observations of longitudinal positioning. Furthermore, he is able in his Planetary Hypotheses, to use the deferent and epicycle devices, coupled with the nesting sphere hypothesis, to fashion a system that predicts planetary distances.(48) However, when the positioning of the equant point, created as an individual fix to square with planetary positional concerns and the pythagorean maximum of uniform circular motion, is placed within the nested spheres system, it must fall within the nested sphere of Mars!(49)
Ptolemy can be found arguing in his Planetary Hypotheses for a cosmological justification for treating each planet's motion as a separate problem.
"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."(50)
This is often overlooked by Copernican apologists when arguing that it is obvious that heliostasis was the better system. However, Ptolemy and his supporters could give no explanation for how Saturn's equant point could function as part of a system of any kind, of how the celestial machinery expressing the essence of one planet could not interfere or would work with that of another planet.
6. In this light, a major conceptual problem that bothered just about everyone was the equant point used by Ptolemy to save uniform motion.
Because a planet in the Ptolemaic system will have uniform motion relative to the equant point, but not to the earth or the center of the planet's deferent, this device not only appeared to be inconsistent with pythagorean-aesthetic requirements, but would not work well with referential commitment to solid celestial nesting spheres. Hence, the equant point was seen not only as a conceptual embarrassment but was open to the charge that it was another individual ad hoc patch that did not work well as part of a system.(51)
7. Although much was made that the Copernican system was committed to the "absurd" physical notion that the heavy earth spun on its axis at a great speed and revolved around the sun at an even greater speed, in the Ptolemaic system the velocity of fixed stars would have to revolve around the earth in excess of 20 million miles per hour to account for their diurnal motion.
Although the plausibility of this belief was supported by Aristotelian cosmology and its commitment to the celestial nature of the stars, any weakening of this cosmology imposed by the observation of novae and comets made acceptance of this great speed problematic.
8. Finally, Ptolemy as well as the later Alfonsine Tables give an incorrect prediction for the precession of the equinoxes.
This was thought to be very serious by Regiomontanus.(52) Instead of 1 degree per 70 years, Ptolemy used 1 degree per century. As it became apparent that the stars were drifting more rapidly than Ptolemy's figure predicted, an auxiliary patch called trepidation was concocted by geostatic supporters. To be able to maintain that Ptolemy was not in error at his time, it was proposed around A. D. 1000 that precession was variable. In the centuries that followed Ptolemy, precession was said to be gradually occurring at a faster rate. By the time of Regiomontanus, however, this patch was hard to accept.
As early as 1464, in noting many of these discrepancies between observation and prediction, Regiomontanus complains that most astronomers were like "credulous women" for accepting Ptolemaic predictions from tables without noting their inconsistency with observations. According to Regiomontanus, a major undertaking was necessary "to restore the heavens. . . . (and) remove the rust from the heavenly spheres."(53)
But did obvious need of reform require a radical new cosmology? Did
the Copernican system fair any better? For a defender of Copernican-heliostasis
there were the following problems.
1. There were also many failures to save the most basic observational phenomena. In fact, in spite of Copernicus's stated goal of achieving an accuracy of planetary positioning within 10' of arc, Copernicus was only trying to match most of Ptolemy's predictions.(54)
Although much is sometimes made of the superior predictive accuracy of the Copernican system,(55) the actual situation was far from decisive. Here is Owen Gingerich's description of what Tycho experienced:
Tycho frequently compared his own observations to the predictions from the Alfonsine and Copernican tables, usually to the advantage of Copernicus. A particular favorable comparison occurred at the time of the great conjunction of Jupiter and Saturn in 1583, although by August 20, 1584, Tycho's comparison for Jupiter showed the two schemes equally in error, and by 21 December, 1586, the Alfonsine calculation was decidedly better, especially in latitude. Frequently, the Copernican latitudes proved inferior, even when the longitude excelled -- for example, for Saturn on January 24, 1595. Tycho compared lunar positions in December 1594, and toward the end of the month the Alfonsine-based Leovitius ephemeris was superior. The most conspicuous Copernican errors found by Tycho occurred during the August opposition of Mars in 1593, exceeding 5 (degrees).(56)
Tycho's experience is important because it must be remembered that prior to his more accurate measurements, astronomers could not ascertain whether Copernican predictions were better than Ptolemy's. Furthermore, "ease of calculation" has often been confused with "superior predictive ability." By the late 16th century more and more calculating almanacs were based on Copernican tables. Johannes Praetorius, a contributor to the Wittenberg tradition, summarized the situation well in 1592.
"Now, just as everyone approves the calculations of Copernicus [Reinhold's Prutenic Tables], so everyone clearly abhors his hypotheses on account of the multiple motions of the earth . . . we follow Ptolemy, in part, and Copernicus, in part. That is, if one retains the suppositions of Ptolemy, one achieves the same goal that Copernicus attained with his new constructions."(57)
According to Gingerich, the Ptolemaic Alfonsine Tables were very difficult to work with,(58) and
"After De revolutionibus was published, Erasmus Reinhold
reworked the planetary tables into a far handier form. His
Tables superseded the Alfonsine Tables remarkably
quickly. This is actually very curious because, in the absence of systematic
observations, nobody really knew how good or bad any of the tables were.
In fact, it was not until Tycho Brahe that a regular series of observations
established the inadequacies of all the tables."(59)
2. Similar to that of the Ptolemaic system there were significant inconsistencies between observation and prediction regarding the diameter and brightness of Mars and Venus. For Copernicus the apparent diameter of Mars and Venus should vary by factors of 8 and 6 respectively. But Mars appears to change size only by a factor of 2 and that of Venus is negligible.
Osiander in his famous nonsolicited preface to De revolutionibus cites these discrepancies as conclusive proof that both the Copernican and Ptolemaic systems were not true. Some supporters, however, would cite the Mars variation as a positive confirming instance of the Copernican system. But Galileo can be found arguing in the Assayer that until his telescopic observations, "the movements of Mars and Venus stood always in the way (of accepting either the Tychonic or Copernican systems.)"(60)
3. Copernicus predicts a full range of phases for Mercury and Venus which could not be observed.
It is doubtful, however, whether or not the players in the Copernican episode were fully aware early in the debate that this was an apparent refutation of Copernicus, or even if phases were observed, as they eventually were by Galileo, that this would be a dramatic confirmation of heliostasis. It must be kept in mind that it was not a closed issue whether the planets reflect light from the sun or are self-generators of the light observed. Or, even if they do reflect light from the sun whether they do so directly or somewhat indirectly, being transparent, such that "the light of the sun becomes incorporated with these stars and gets soaked up in all their parts, which does not happen for the moon." (Albert of Saxony, 1360)(61)
Thus, even if phases were not observed in planets, this was sometimes interpreted to mean that planets do not reflect light from the sun. If phases were observed, even a full phase for Venus, Aristotelian and Ptolemaic cosmology could be saved by the reemission theory.(62) Even if the angle between the planet, Earth, and sun is such that only a portion of the planet is "soaking" in the light from the sun, as it should always be in the Ptolemaic system, the planet itself could reemit the light such that a full phase appears!
Again we see the importance of auxiliaries, and how often not all the necessary auxiliaries are in place for a crisp confirmation or falsification of a particular theory. We view the Venus episode from the modern standpoint of connected auxiliaries that produce a crisp falsification for Ptolemaic geostasis, and forget that astronomers in the 16th and early 17th centuries did not necessarily share the same auxiliaries. Required were a further weakening of Aristotelian cosmology, greater support for the belief that the moon and the planets are physical places that reflect light, and an understanding of the negative ramifications of the reemission theory (If this theory is true, why didn't Venus show a full phase at all times?), before the adjudicatory trail for Ptolemaic astronomy saving the Venus full phase observation by Galileo could be significantly weakened.
4. It was assumed that parallax for the sun could be established. In the Copernican system, Mars and Venus should show parallax, but there are no naked-eye observations of this. Ptolemy predicts a substantially smaller parallax for Mars.
In the Copernican system Venus is closer to the Earth than Mercury; whereas in Ptolemy's system Mercury is closer. A clear potential observational difference in terms of parallax except for the fact that the observing time for Venus and Mercury is small and parallax measurements of these planets is not within naked-eye resolution. However, Tycho knew that since Ptolemy always has the orbit of Mars beyond the sun, whereas Copernicus has Mars approach the Earth at less than the sun's distance at opposition, the extent of parallax for Mars was a pivotal potential observation that would separate a geostatic system from a heliostatic or geoheliocentric system. As a defender of the geostatic system, he was convinced that no parallax for Mars could be determined within the naked-eye resolution. Later as he became interested in preserving Copernican linkages by promoting a geoheliocentric system, he convinced himself that he did observe parallax for Mars!(63) It is not possible to observe parallax for Mars without a telescope.
Tycho also argued that the relative closeness of Mars is confirmed by the swift speed of its retrograde motion. But a Ptolemaic astronomer has no trouble saving and explaining (to some extent) this appearance. The speed of Mar's epicycle is adjusted a posteriori to match the relatively faster retrograde motion.(64)
5. Careful observations by Tycho showed no stellar parallax. Hence, a Copernican must not only assume that the stars are very far away but also of humongous size (800 times size of sun). In the Copernican system, the entire solar system becomes virtually a mere point.(65) Why should the sun be such a minute center of such a vast system?
In De revolutionibus Copernicus can cite no persuasive independent evidence for this startling claim. He thinks that the immense distance to the stars is "proved" by the fact that they do not show retrogressions like the planets. At the beginning of his book, after citing how well heliostasis explains the linkages of retrogressions and their frequencies for the planets, Copernicus says, "Yet none of these phenomena appears in the fixed stars. This proves their immense height, which makes the annual parallax vanish from before our eyes." Copernicus is guilty here of some rather obvious sleight-of-hand that fooled very few. Although Copernicus can cite this as a consistency condition of his system, to claim much more is circular reasoning, because "no observed retrogressions" is just another way of saying that the stars don't show parallax. The closest Copernicus comes to citing an independent reason for believing in the immense distance between Saturn and the stars is that the stars "twinkle"!(66)
Related to the stellar distance problem is that Copernicus appeared to still endorse the Ptolemaic notion of solid spheres. If so, there are huge unexplained gaps between the spheres, that in the old system needed to be in contact to explain their coordinated motion, not to mention the problem of an even greater gap between Saturn and the fixed stars. According to Barker, Copernicus's objection to the equant is better understood in terms of referential commitment to uniformly rotating solid spheres.(67) Recall that commitment to solid celestial spheres appears to be radically inconsistent with a Ptolemaic equant point for Saturn. But followers of Copernicus can not have it both ways. They can not object to the equant point because it is inconsistent with commitment to celestial spheres, and then ignore how a heliostatic system is also inconsistent with such commitment.
6. In the Copernican system the moon's motion is not around the center of the universe. Why the exception? Even in a heliostatic system, all the other astronomical bodies revolve around the center of the universe. Furthermore, although Copernicus's lunar theory is an improvement in terms of avoiding the dramatic variation in apparent size predicted by Ptolemy, Copernicus's multiple epicyclic motion for the moon results in not having the same side of the moon always facing the earth.
7. A supporter of the Copernican system had to face a huge physical problem. Whatever kinematic benefits might accrue to a heliostatic system were surely offset by the dynamical problem of a triple motion for the Earth.
In De revolutionibus Copernicus is able to offer only a very weak auxiliary patch -- actually only an extension of the uniform circular motion dogma. According to Copernicus, large amounts of substance, whether terrestrial or celestial, tend to form perfectly round circular wholes and such objects naturally rotate. Furthermore, although problems with Aristotelian dynamics were highlighted by competition from impetus theory, it was not clear how the latter would help a Copernican and the former, to use Feyerabendian language, was far from a "dead dog."
8. In contrast to the sketch of a heliostatic system presented in the Commentariolus, the full heliostatic system presented in De revolutionibus is quite complex.
The myth that Copernicus used far fewer circles than Ptolemy originates with Copernicus's summation in his Commentariolus to the effect that a heliostatic system needed only approximately 30 circles whereas Ptolemy used about 80. It is known that Copernicus wrote his Commentariolus before 1514.(68) Ironically, Copernicus did not get his hands on the full edition of Ptolemy's Almagest until 1515. According to Gingerich, "Through this work he must have become more fully aware of the tremendous task facing any astronomer with the courage to construct a complete celestial mechanism."(69) Thus, in order to be a serious contender -- to at least match Ptolemaic planetary positioning -- and to eliminate the equant point, Copernicus must use numerous epicyclets. To this day there is not agreement on just how many circles Copernicus used. According to Gingerich, "Even Copernicus would have had difficulty in establishing an unambiguous final count."(70) See Figure 2.
9. Finally, we can add to this list the fact that many Tycho-like, geoheliocentric systems competed with the Copernican system by the first decade of the 17th century, and every astronomer was familiar with the merits of a third approach.(71)
Adding to the confusion and possible choices, some of these systems, such as Tycho's own, were fully geoheliocentric with all the planets other than the Earth revolving around the sun, and some, such as that of Andreas Cesalpinis in his Peripatetic Questions, were partially geoheliocentric with only Mercury and Venus revolving around the sun. (Tycho had also experimented with this arrangement as early as 1578.(72)) Some of these systems had Mars enclosing the orbit of the sun (Ursus), and some had the orbit of Mars intersecting the orbit of the sun (Tycho). Some retained solid celestial spheres and some did not. There were also different schemes in terms of the distances to the superior planets, and hence heaven. Some used elliptical orbits; some eccentrics, and some were multiple epicyclic using the same interior epicyclet device used by Copernicus. Some had the Earth rotating and some did not. Finally, John Craig even suggested that a third point be added, closer to the Earth than the sun, for the true center of planetary motion.(73)
Just as Copernicus's work revived that of Aristarchus, these systems resurrected the approach of Heraclides Ponticus, Adrantus of Aphrodisias, and Theon of Smyrna.(74) Some of these systems accommodated comets, preserved many of the parameter linkages that were appealing in a Copernican system, and made similar empirical predictions. But with a stationary and centralized Earth, they were consistent with lack of observed stellar parallax and did not require a new terrestrial dynamics.(75)
As we will see in more detail in chapter 5, Howard Margolis has argued that in fact by the first decade of the 17th century, support for a pure Ptolemaic system had almost completely faded from the scene, and that the comparativist situation was between heliostasis and geoheliocentrism.(76) He argues that even in Galileo's Dialogue, "Galileo's identification of the Tychonic arrangement (not the Ptolemaic) as the surviving non-Copernican alternative is unambiguous and emphatic, but discrete. . ."(77) Margolis builds an interesting case that Galileo had been ordered by the Pope not to attack the Tychonic system, which the Church then supported, but Galileo nevertheless did so indirectly forcing the Pope to realize that he had been deceived by Galileo. As part of the evidence for this thesis, Margolis notes the number of pages devoted in the Dialogue to issues that would only concern a debate between supporters of heliostasis and geoheliocentrism (Galileo's trick), and the fact that Inquisition reports never complain that Galileo fallaciously weakens the geostatic case by leaving the Tychonic system out of the debate. Given that Galileo has often been criticized by historians and philosophers of science for so blatantly creating a false dilemma in his Dialogue, but given that the historical actors did not so criticize him for this when they surely would have been aware of it, Margolis's new interpretation does explain some long-standing puzzles about the Galileo affair.
According to Margolis, Galileo indirectly sets up an opposition between geoheliocentrism and heliostasis where geoheliocentrism is the weakest, but does not mention the geoheliocentric alternative when it would be the strongest competitor to heliostasis, such as the observation of a full set of phases for Venus. Instead, Galileo indirectly draws just enough attention to the geoheliocentric alternative to make the informed reader wonder how this cumbersome system would work, then drops it in such a way as to leave the reader realizing that no one could possibly develop a dynamics for it in contrast to an emerging dynamics for Copernicanism. In effect, Galileo is saying to the Pope, "Ok, you won't let me mention Tycho's system, so I won't even in cases where you would want me to!"
In some ways the Copernican episode was more like a grand soap opera than the neat laboratory setting of a rat psychologist. There was a rich labyrinth of possibilities and a meandering parade of characters with diverse interests defending many positions. Indeed, no viable rational reconstruction can ignore the messiness and contingency that history reveals. But complexity does not automatically endorse "anything goes." Given this complex background, I would now like to develop my thesis further by contrasting it to three well-known interpretations of the Copernican episode. It is my contention that these three influential interpretations are either wrong on significant details or incomplete in such a way as to set the current stage for the epistemological malaise found in socio-cognitive relativism.
Notes for Chapter 2:
1. In the Introduction to Duhem, 1969, p. xxv. Jaki's statement is worth quoting in full.
History is the great equalizer. Sooner or later it cuts all things and all men down to their true size. Science looms up as a savior only for those whose familiarity with it is restricted to what Duhem so aptly call 'the gossip of the moment.' Those who are brave enough to look past the popular but ephemeral truths of the day will find in history a most instructive teacher. The history of physical science can indeed forcefully show the student that myths are present in science no less than in other areas that owe so much to science for the reduction of their myths. Recognition of this may be a humbling experience in a scientific age such as ours; yet it is indispensable if science is to become man's servant rather than his tyrant.
2. Koyré, 1973, p. 17.
3. Ibid., p. 10.
4. Koestler, 1959, p. 15.
5. Santillana and Drake, 1959.
6. Ibid., pp. 255, 257, 259-260.
7. Ibid., p. 255, n. 2. An extreme characterization when one considers Galileo's adherence to circular motion and his flipflop on comets. See below.
8. Graubard, 1976, pp. 31-32.
9. Dreyfus and Dreyfus, 1986, p. 91.
10. Otherwise, according to Dreyfus and Dreyfus, the traditional approach of seeing appraisal, understanding, or learning as a neutral rule-based activity leads to "not only a regress of rules for applying rules but an exponential explosion of them. . ." Ibid., p. 80. As we will see (Chapter 5), parameter determination became a theoretical constraint for both geostasis and heliostasis by the late 16th century. Although it can be seen as emerging from heliostasis, it gradually became linked with the pursuit of patching geostasis.
11. As such my portrayal of scientific assessment will have much in common with Lakatos's notions of progressive and degenerating research programs. However, as we will see in chapter 4, because Lakatos does not completely extricate himself from infallibilism and deductive assessment, he becomes too sensitive to criticisms based on the alleged need for crisp cut-off points for acceptance and rejection of scientific theories. In answering critics, he finds something in the Copernican episode that he does not need.
12. Feyerabend, 1987, p. 188.
13. Darwin finishes his epic On the Origin of Species with a stunning rhetorical flourish:
"There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved." (1900, pp. 669-700)
14. Kitcher, 1993.
15. Ibid., pp. 184, 200, 201, n. 27.
16. Ibid., p. 201, n. 27, p. 197.
17. Ibid., p. 185.
18. Ibid., p. 186.
19. Ibid., p. 209.
20. Ibid., p. 391.
21. Ibid., p. 162.
22. Ibid., p. 196.
23. Ibid., p. 185.
24. Duhem, 1954, p. 218.
25. Westman, 1975a, pp. 187-189. Not one of Westman's finer moments.
26. As far as I know, no sociologist has advanced this thesis. But given time and encouragement, encouragement that Kitcher is unintentionally providing, we are likely to see such nonsense published eventually.
27. Narratio Prima, in Rosen, 1971, p. 137. Rheticus thinks that Mars can be observed to have a closer approach to the Earth than the sun. Tycho vacillates on this issue, eventually claiming that he has measured parallax for Mars. Both men have an interest in this particular result -- it supports heliostasis and geoheliocentrism over geostasis. Relativist fodder? No. Kepler too has an interest is this particular result, but admits that parallax for Mars cannot be determined with naked-eye instrumentation. Gingerich and Westman, 1988, p. 70-71; Gingerich, 1993, p. 149.
28. Developed below, chapter 5.
29. Kepler, of course, was not totally uninterested in patronage and a "job." The claim here amounts to a matter of degree. Kepler wanted to survive; Tycho wanted castles.
30. Kuhn, 1970, Postscript, p. 200.
31. And perhaps we should be wary of drinking too much during long speeches.
32. There are, however, other points of agreement with Kitcher's work and my thesis once terminological differences are made clear. His use of "admissible cost functions," "rival admissible cost functions," (pp. 250-51) and "escape trees," and "Duhemian predicaments" (p. 256) are very similar to my "hypertextual adjudicatory trails and auxiliary nodes," and related language. Kitcher also emphasizes the gradual nature of acceptance, "position crumbling," and crystallization of debate focus (pp. 204-205) which are similar to my strengthening of a hypertextual trail. These points of agreement will be explored in more detail in chapter 5.
33. Over the years I have sat in on three different Introductions to Astronomy, at the University of Washington, University of Hawaii, and Honolulu Community College. Almost on que, usually during the second lecture, all three instructors, all excellent lecturers otherwise, would trot out this claim as an obvious example of poor methodology and ignorance, apparently totally unaware that it was Copernican supporters, Rheticus and Kepler, that often made this a priori argument for six planets. In the case of the University of Washington professor, Rheticus's Narratio Prima was quoted (Rheticus comparing the number of bodily orifices to the number of planets!), but students were left with the impression that this was the asinine thinking of a medieval cleric.
34. See for instance, Carl Sagan's treatment of Kepler in his Cosmos, chapter 3. Although Sagan does record the discordant personal relationship between Kepler and Tycho, Kepler is shown rejecting his five perfect solids hypothesis because the facts did not support it. In introductory astronomy books one finds statements such as: "Their (Galileo, Kepler, and Tycho) lives culminated in conclusive proof that the Copernican system could work. . ." (Seeds, 1986, p. 71); "Tycho proved that the stars and planets were many times farther away than the moon. . . (Hartmann, 1985, p. 114); and "Kepler derived (his three laws) from Tycho's extensive observations, not from any fundamental assumptions or theory" (Seeds, p. 76-77). In Kaufmann (1993, p. 38) we still find,
"Copernicus's astronomical studies detailed the advantages of the straightforward Sun-centered cosmology over the cumbersome Earth-centered theory. This work instilled a revolutionary concept that pervades modern science. Simplicity is the hallmark of correctness. Thus, nowadays, when a theory becomes unduly elaborate and complicated, scientists begin to suspect that the theory is probably wrong."
In this same vein it is worth noting that as late as 1969 the Encyclopedia Britannica promoted the myth (p. 645) that the Ptolemaic system needed a monstrous amount of patching (40 epicycles per planet!) to save the phenomena. Hartmann (p. 112) repeats the Alfonso myth of tacked-on epicycles and then cites Occam's razor as the origin for the basic scientific principle that "the best is simplest." Hartmann also gives students the impression in discussing Galileo (p. 116) that "intelligent people could see the plain truth through the telescope."
35. Well almost. In his apology for Galileo's role in the controversy of the comets of 1618, Drake refers to Tycho as Kepler's "revered predecessor," by way of explaining in part how Kepler came to comment on the comet controversy. (Drake, 1960, p. xxi.) In this same work Drake claims that Galileo's advocation of the modern "scientific method as a road to truth" was the novel element that was responsible for the revolution that took place in the 17th-century, and that "only in Galileo's day, and largely through his efforts, that a clear parting of physics and metaphysics was eventually reached." (pp. viii-ix.)
36. Astronomia Nova, 1610b, pp. 324-325.
37. McMullin, 1987, p. 59.
38. Ronchi, 1957. According to Ronchi, Galileo's advocacy of the telescope as a reliable instrument was initially the "new faith" of one man against all of "conventional science" that was "hostile and distrustful." According to Ronchi, "The entire academic world reacted violently (to Galileo's Sidereal Message), with one voice accusing Galileo of extolling as real discoveries figures seen only with the telescope, a notoriously misleading and untrustworthy contraption." (p. 46.)
39. Koestler claims that Galileo's flipflop on comets from the Tychonic position he appeared to endorse in his Letters on Sunspots was due primarily to ego -- Grassi failed to mention Galileo's contributions in his Jesuit manifesto On the Three Comets of the Year 1618. (Koestler, pp. 466-471.) More consistent with my thesis is the explanation, also noted by Koestler to his credit (p. 467), of Galileo's entrenched resistance to elliptical orbits. For Galileo's resistance to the idea of a vast universe to incorporate such orbits, see his Discourse on the Comets, in Drake, 1960, p. 27. For Drake's apology for Galileo on resisting elliptical orbits, see note 7, p. 363. For Grassi's reply to Galileo on the possible nature of the orbits, see his The Astronomical and Philosophical Balance in Drake, 1960. Grassi's reply is particularly interesting because he admonishes Galileo for not realizing how such orbits could be seen as consistent with his own position. According to Grassi, "What if it be not even elliptical but entirely irregular -- since especially in Galileo's system it would be able to move freely without any hindrance?" (p. 75)
In Tycho's discussion of comets, De Mundi Aetherei Recentioribus Phaenomenis (On the Most Recent Phenomena of the Aetherial World), he refers to the possibility of the orbits "not be(ing) at all points exquisitely circular, but somewhat oblong, in the manner of the figure commonly called ovoid. . ." Boas and Hall, 1956, p. 263.
40. According to Drake, the "difficulty of rationally accounting" for Galileo's outburst against the "reasonably sensible discourse" of Grassi on the celestial nature of comets can be solved by believing that Galileo was prohibited from directly advocating Copernicanism but not from the new methodology by which he had arrived at heliostasis. So, he was using the controversy of the comets of 1618 as a pretext to advocate his new method, which in turn would win converts to Copernicanism. Massively problematic for this apologia is that Galileo was attacking the anti-Aristotelian, empirically derived position of Tycho! (See Drake, 1960, xiii-xv) In this case, the psychological explanation of Koestler is preferable: Galileo's wrath is best seen as a pure outburst of ego kindled by frustration -- he was not able to get his theory of tides published and because of the ban on promoting a realistic heliostasis his work was in danger of being forgotten or co-opted by the Jesuits in defense of a geoheliocentric system. (Koestler, 1959, pp. 468-471)
Concerning the number of times The Assayer is quoted to illustrate the birth of modern scientific methodology and an anti-metaphysical positivism, small wonder that quotations such as the following are never to be found in introductory science texts. According to Galileo,
"You cannot help it . . . that it was granted to me alone to discover all the new phenomena in the sky and nothing to anybody else. This is the truth which neither malice nor envy can suppress." (Quoted from Koestler, p. 468)
Given Drake's apology for Galileo, small wonder that this passage does not occur in Drake's translation!
41. Given the traditional view that there were no voids between the celestial spheres, Tycho's reaction is, of course, understandable. My point, however, is that his "wasted space" argument is never mentioned in popular texts that emphasize Tycho's observational contributions. Typically, students are left with the impression that Tycho, Kepler, and Galileo all worked collaboratively and empirically to bring about the downfall of dogmatic geostasis.
42. Swerdlow, 1990.
43. Gingerich, 1973b, p. 90.
44. Note that for the relativist who advocates that we can always patch our networks when they fail to mesh with experience, one could argue that Venus, Mars, and the moon gradually shrink in size as they approach the Earth, thus accounting for the magnitude problem. However, no defender of geostasis suggested or advocated this auxiliary patch for obvious reasons: anything does not go.
45. Goldstein, 1967, p. 9.
46. Ibid., p. 6.
47. Ptolemy's reason for picking Mercury as closer to Earth than Venus, he says, has to do with Mercury's motion. Invoking Aristotelian cosmology, Ptolemy says in his Planetary Hypotheses, "The spheres nearest to the air move with many kinds of motions and resemble the nature of the element adjacent to them. The sphere nearest to universal motion is the sphere of the fixed stars which moves with a simple motion. . ." (Goldstein, 1967, p. 7) Hence, since Mercury's orbit is more erratic than that of Venus, it must be closer to the sublunary realm.
48. Margolis, 1987 & 1993; Van Helden, 1985. Margolis says that Ptolemy fashioned an "elegant system," but he nowhere discusses the Saturn equant problem.
49. Gingerich, 1993, p. 27. For diagrams of the basic Ptolemaic system, see Figure 3.
50. Gardner, 1983, p. 207. Gardner's emphasis.
51. Barker, 1990.
52. Swerdlow, 1990, p. 171. Also see Gingerich, 1993, pp. 22, 27, and Pannekoek, 1965.
53. Swerdlow, 1990, pp. 170, 174.
54. Gingerich, 1975b, pp. 103-104. Gingerich demonstrates this by comparing computerized actual locations of planetary positions that would have easily been observable for Copernicus with what both Copernicus and Ptolemy predict. For instance, a prediction for Mars on February 22, 1523 is off by more than two degrees. According to Gingerich, it is obvious that Copernicus adjusted his initial parameters to match what were thought to be authoritative observations, "rather than to reform the accuracy of astronomical predictions."
According to Gingerich, "it is in fact shocking that Copernicus, with the accumulated experience of fourteen more centuries, did not come up with a substantial advance in predictive technique over the well-honed mechanisms of Ptolemy." Gingerich, 1975a, p. 90.
55. Erasmus Reinhold seems to be the original source of this claim. Although a Wittenberg astronomer and anti-realist in terms of referential commitment to astronomical devices used to save the phenomena, in Reinhold's introduction to his 1551 Prutenic Tables, he claims that the Copernican-based tables will show that "the science of celestial motions was almost in ruins" but that Copernicus "has restored it." (Quoted from Duhem, 1969, pp. 72-73)
56. Gingerich, 1975a, note D, pp. 92-93, emphasis added.
57. Quoted from Westman, 1975b, p. 293. Emphasis added.
58. Gingerich, 1990.
59. Gingerich, 1993, pp. 171-172.
60. Drake, 1960, p. 184. Kepler also discusses this in his Appendix to the Hyperaspistes, Drake, 1960, pp. 344-345. Also see, Barker, 1990, p. 322.
61. Quoted from Ariew, 1987, p. 85.
62. Ibid., pp. 85-86.
63. Gingerich and Westman, 1988, pp. 70-71.
Tycho, of course, also recognized that a measurement of stellar parallax could separate the two systems empirically. For future reference (chapters 4 & 5), note that from one point of view the issue of empirical equivalence (EE) is decided right here -- the Copernican and Ptolemaic systems were not empirically equivalent. Kepler is emphatic about the role of Mars in this regard in his Apologia Tychonis contra Ursum, 1601 (Jardine, 1984, p. 141).
However, a defender of EE would argue that we should not be so hasty. At the time it was not possible to measure parallax for Mars, so a defender of Copernicus could argue for an auxiliary patch and that this discrepancy was not a falsification of heliostasis. On the other hand, when parallax for Mars at opposition was eventually observed with the invention of the telescope (a half a minute of arc, well below naked-eye resolution), a defender of geostasis could argue for some creative auxiliary patch. Perhaps, to take a deliberately bizarre example, the epicycle of Mars swells up only when the planet is being observed by the telescope! This shows that the real issue is not whether theories can be made empirically equivalent, but whether our attempts at auxiliary patching are rational, whether there is evidence for an auxiliary patch and whether the patch has positive or negative ramifications throughout one's adjudicatory trail, whether such patches are consistent with what else is well established or is intolerably inconsistent with it.
Relativists, using EE as a major premise for their positions, usually reply that my example in unfair. That the issue is whether it is always possible to find an adequate auxiliary patch, one that is consistent with what else is well established and saves the theory in question. With this response their position unravels. We cannot assume that it is always possible to find an adequate auxiliary patch, and with this response they have capitulated to my major thesis, that we can distinguish ampliatively between rational and irrational auxiliary patches. See the discussion of Doppelt below, chapter 4.
64. Also for future consideration (chapter 5), Tycho sees this as a corroboration of Mar's distance at opposition because by this time he is very impressed with Copernican linkages. The Ptolemaic system has its own planetary linkages. For instance, a Ptolemaic astronomer cannot adjust the rate of epicycle revolution independent of the sun's revolution about the earth. However, there is more freedom to adjust planetary parameters individually a posteriori, whereas frequency and size of retrograde motions are much more determined all at once by a heliostatic or geoheliocentric system. As is well known, some philosophers of science have interpreted this all-at-once fixing of key parameters to be decisive evidence in favor of heliostasis. See chapter 4 on Lakatos. My argument will be that this is historical chauvinism. Although we find the key players in the Copernican episode gradually more and more impressed with heliostatic linkages, contextually we do not see consensus in the late 16th, and even early 17th, century that such linkages should constitute a decisive constraint on theory choice. Without clear evidence to the contrary, it is possible for one to argue that each planet should be treated individually to some extent. After all, even today we don't suppose that the planets must all contain the same elements, be the same density and size, etc. What is needed, and did eventually occur, is the weakening of auxiliary support for an approach that would allow one to continue to argue rationally that it is permissible to treat the planets separately in terms of adjusting parameters to match core observational problems. See point 5 above on Ptolemaic problems for Ptolemy's Aristotelian defense for treating planets individually.
65. Dreyer, 1953, pp. 360-61.
66. De Rev. Book I, cap. X, p. 29 (Quoted from Koyré, p. 54).
67. Barker, 1990.
68. At this time it was known to be part of the personal library of Matthew of Miechow, a Cracow University professor. Gingerich, 1993, p. 163.
69. Ibid., p. 164.
70. Gingerich, 1975a, p. 87; also see Koestler, 1959, pp. 572-3, and Palter, 1970.
71. Gingerich and Westman, 1988; Schofield, 1981.
72. Gingerich, 1993, p. 179.
73. Schofield, 1981, pp. 110, 139-141, 148, 176, 189.
74. Duhem, 1969, p. 83.
75. This needs qualification, as we will see in detail later. A complete Tycho-like system was never fully articulated. However, being a geostatic transform of the Copernican system, it has customarily been assumed that astronomical tables based on this system would be close to the predictions of Copernicus. Furthermore, a geoheliocentric system will position Venus in such a way that it will show full phases like that predicted in the Copernican system. The latter is not controversial. However, the following should be noted against the former. Given that a rough geometric model is not the same as a system that must be used to get down to the business of creating astronomical tables, and given that the rough Copernican system can be seen as a heliostatic transform of the Ptolemaic system (Price, 1959; Margolis, 1993), yet as fully articulated systems their predictions do not always agree, it could not be assumed that a fully articulated system would be empirically equivalent to the Copernican alternative.
Concerning the issue of terrestrial dynamics, there is no need for a non-Aristotelian one provided that the Earth does not rotate. In some versions of the geoheliocentric alternative, the Earth is made to rotate to cut down on the complexity of the system. For instance, William Gilbert advocated a Tychonic system with a rotating Earth, and Longomontanus, Tycho's disciple, developed such a system after Tycho's death. (Schofield, 1981, p. 180).
76. Margolis, 1987, 1991, 1993, particularly 1991. Boas and Hall, 1956, seem to agree in their introduction to Tycho's presentation of his geoheliocentric system, a digression actually in his De Mundi Aetherei Recentioribus Phaenomenis. They refer to Tycho's system as "a replacement for the obsolescent Ptolemaic one," and the Ptolemaic doctrine as "long uncomfortably shaky." (pp. 253, 254)
77. 1991, p. 266.