Chapter 4: Lakatos, Parameter Determination,

and the

End of Infallibilism




Before developing my argument in greater detail regarding the role of parameter determination during the Copernican episode, we need to clearly distinguish it from positions that have made too much of parameter determination. Soon after Kuhn's Structure of Scientific Revolutions many philosophers of science labored with increased urgency to separate the rational-normative features of scientific change from the historically contingent, cultural, and socio-psychological features involved in any human endeavor. Implied in this task was a simultaneous acknowledgement of the important role historically contingent factors play in scientific change, and the importance of viewing such factors in a proper epistemological perspective to avoid the seductive trap of relativism.

Imre Lakatos summarized this challenge well in his paraphrase of Kant's famous remark, "Philosophy of science without history of science is empty; history of science without philosophy of science is blind."(1) According to Lakatos, we ought to be able distinguish between the internal, rational-normative explanatory factors of scientific change and the external, socio-psychological supplementary factors necessary for a complete understanding of history. For Lakatos, this distinction serves two important functions. It provides the historian with a proper focus -- external history is just "confused rambling" until internal history is clarified(2) -- and it provides a means for evaluating competing theories of scientific methodology, because a rational reconstruction of scientific change based upon a proposed theory of scientific methodology should reveal the greatest possible content in internal history and should not relegate important moments of scientific change solely to external history. In other words, assuming that science is ultimately a rational process, internal history is primary to external history. According to Lakatos, for all its insights regarding the importance of history, the problem with Kuhn's philosophy of science is that it relegates too much to external history; scientific change becomes a matter of "mob psychology."(3)

In an analysis of the Copernican episode, for instance, it may have been necessary for Copernicus and Kepler to be pythagoreans and neoplatonists, but it surely was not sufficient. There must have been "good reasons" in some sense for allegiance to heliostasis before the external cultural factors could act on a scientist of this time. To use Kantian language, the external factors may have played a crucial role as the "occasioning cause" of the Copernican inversion, and help us understand why the change took place when it did, but the internal factors were epistemologically prior in the sense of making any change at all possible.

In this chapter we will see that a critical ingredient of Lakatos's own theory of internal history -- the role of novel facts in the theory of scientific research programmes -- fails by his own method of appraisal; the rational reconstructive use of novel facts is degenerative by relegating too much of the Copernican episode to external history.(4) We will also see that in spite of his explicit commitment to Popperian fallibilism, his philosophy of science involves a latent commitment to an implicit, unnecessary, vestigial infallibilism and this slip causes Lakatos to grant an extravagant epistemological role to parameter determination.

Using the distinction between internal and external history in two important papers(5) written towards the end of his distinguished career, Lakatos was able to explicate and bring to completion the major themes of his philosophy of science. (1) Against his close friend, Feyerabend, and other relativists, Lakatos argued that ultimately science is a rational process; that there are normative-rational constraints involved in scientific change, and thus, anything does not go.(6) (2) In addition to problems with Kuhn's work, a meta-methodological historiographical level of appraisal reveals that major theories of normative scientific methodology (strict inductivism, probabilistic inductivism, falsificationism, and simplicism or conventionalism) are inferior to Lakatos's own theory of the methodology of scientific research programmes, in the sense that the former relegate too much to external history and shipwreck onto the shifting sands of relativism by their own standards.(7)

To substantiate these claims, Lakatos argues that an historical test of theories of normative scientific methodology requires a meta-methodological standard of appraisal, and Lakatos is quick to argue that a simple meta-methodological falsificationism will not get us very far. Just as all scientific theories are born refuted, the rich and complex interplay between external and internal history always will result in refutations for any theory of scientific methodology.(8) Lakatos thus introduces a purported new meta-methodological approach, one modelled on his own methodology of scientific research programmes. Accordingly, appraisal of competing normative scientific methodologies will be the result of whether or not the competing methodologies are progressive or degenerative, whether or not they reveal novel normative historical internal insights -- or simply collapse into relativism by relegating too much of scientific change to mere psycho-social, or cultural Weltanschauung shifts.

A year before Lakatos's untimely death, he presented a paper at the Quincentenary Symposium on Copernicus of the British Society for the History of Science.(9)

This paper, which was the result of a joint effort with Elie Zahar, is doubly important because, in addition to providing a detailed historical test of Lakatos's methodology, it contains an "important amendment"(10) (provided by Zahar) to the methodology of scientific research programmes, i. e., that empirical progress is shown by a research programme's ability to account for atemporal novel facts as well as temporal ones. Although Lakatos does not say so, this amendment can be viewed as a modification of the protective belt that surrounds the hard-core of Lakatos's meta-methodology, the hard-core postulate that ultimately science is a rational process. This amendment is necessary, because of the "unwelcome conclusion" that according to Lakatos's previous conception of "temporally novel facts," the Copernican programme cannot be seen as empirically progressive until 1616 (1610?), with the observation of the phases of Venus.(11)

Prior to the Venus observations there were no spectacular confirmations for heliostasis. This is a major problem for Lakatos because although his theory does not demand falsifications -- all theories are born refuted, and supporters of a research programme are constantly adjusting the protective belt (auxiliaries) of a theory -- it does demand conceptual and empirical progress. Concerning the latter, a progressive research tradition must not only make some novel predictions but some must also be observed.

Hence, without some amendment regarding empirical progress, commitments to the Copernican system prior to 1610 can be explained only by external factors. In other words, without some amendment there would be no clear, rational internal factors that key scientists prior to Galileo could recognize, no decisive foundation upon which external factors could act.(12)

Using the research of Gingerich, Kuhn, Neugebauer, Price, and Westman(13), Lakatos is able to make an excellent case against inductivism, falsificationism, and simplicism as degenerative in the sense of relegating too much of the Copernican episode to external history.

The Copernican system was not a simple inductive generalization from either new or old observations, because both the Copernican and Ptolemaic systems were factually inadequate quantitatively in terms of predicting planetary positions.(14) Hence, from an inductivist standpoint the Copernican and Ptolemaic systems were locked in an internal standoff and one is left with only external factors to understand why scientists accepted or pursued one or the other. Also, one cannot make a case for falsificationism -- that Ptolemy's system was irrefutable, and hence not scientific, and Copernicus's refutable, and hence scientific -- nor, if one grants that the Ptolemaic system was refutable, that a crucial deciding observation emerged that falsified this system at an early stage of appraisal of the two systems. The charge of irrefutability is based on the "adding epicycles myth." Astronomers of the time were not adding epicycles to epicycles to the Ptolemaic system to keep it from being falsified by the observational data. A recomputation by Gingerich shows that the Alfonsine Tables were based upon the strict Ptolemaic system of single epicycles. Furthermore, Copernicus added epicyclets to epicycles to adjust his system to known observational problems. To counter the charge that the Ptolemaic system was falsified, neither the Prutenic Tables, the observations of the phases of Venus, nor stellar parallax will help a falsificationist. The Alfonsine Tables were equal to or more accurate than the Prutenic Tables often enough to prohibit establishing a clear case of superiority of the latter. An appeal to the phases of Venus ignores Tycho's geoheliocentric solution, and the observation of stellar parallax occurred much too late to provide a normative reason for being a Copernican.(15) Hence, from a falsificationist perspective the Copernican and Ptolemaic systems were locked in an internal standoff and one is left with only external factors to understand why scientists accepted or pursued one or the other. Finally, the exposure of the "80/34 myth" discredits an appeal to the much invoked simplicism. To pay for removing the equant, Copernicus must use numerous epicyclets to bring the general heliostatic scheme in line with Ptolemaic predictions, and by the time of the Copernican system's evolution from the Commentariolus to the De revolutionibus, it is difficult to tell exactly how many circles the Copernican system had.(16) Hence, Lakatos argues, simplicity becomes a matter of taste, and external historical factors must be appealed to solely to account for why key scientists committed to the Copernican system.

According to Lakatos, the methodology of scientific research programmes succumbs to the same degenerative fate unless his previous conceptions of novel facts and empirical progressiveness are amended. By this point in the development of his normative theory of scientific change, Lakatos had become aware of two problems. First, given the old conception of empirical progressiveness, we are at a loss to point to any decisive, "immediate," normative-internal reasons why any scientist in the middle or late 16th- century would consider committing to the Copernican theory. Second, in criticizing falsificationism, Lakatos had argued that crucial falsifying observational events are never temporally dramatic, but always the result of hindsight.(17) So if temporal falsifications are a myth, why should temporal confirmations be any less so? Hence, Zahar's amendment.

Essentially Zahar's amendment allows for the consistent completion of the Lakatosian programme by showing that the Copernican system had "immediate support" if we recognize that 'novel' is not limited to 'new' phenomena; that previously known but problematic or unintelligible (apparently non-linked) facts of celestial motion gave dramatic support to the new theory, because they can be seen as distinctively intelligible by heliostasis in the sense of being directly explained and linked by that new theory, and they played no role in the construction of that theory. In other words, if there are well-known but apparently disjointed observations, and a new theory is able to link these observations with a single explanation, whereas a previous theory explains them separately, the new theory has immediate support.

Zahar and Lakatos then list previously known factors that they claim were not instrumental in the development of heliostasis, but nevertheless were handled by the new theory in a dramatic, straightforward manner. The most important of these relative to the historical context are: (1) retrograde motion, increased brightness of each planet during retrogression, and frequency of retrogressions for each planet, and (2) the fact that the calculated periods of the planets strictly increase with their calculated distances from the sun. According to Lakatos and Zahar both are distinctly intelligible under even the most rudimentary version of heliostasis. Thus, even though there may have been a nondecisive mixture of subjective and objective motivating factors for Copernicus's development of a heliostatic system, such as the important roles played by neoplatonism and pythagoreanism in Copernicus's dissatisfaction with the use of the equant and the factual inadequacy of the Ptolemaic system, once developed there were immediate, rationally compelling reasons to accept Copernicanism. Furthermore, this cannot be revealed via inductivism, falsificationism, or simplicism, but only by the normative internal spectacles of Lakatosian philosophy of science -- heliostasis can be seen as progressive and geostasis as degenerating for a long time.(18)

In a strikingly revealing passage Lakatos gives an "historical thought-experiment" to corroborate this interpretation. Of paramount importance for my purpose, it is worth quoting in full.

"Let us imagine that in 1520 -- or before -- all we knew about the heavens was that the Sun and the planets move periodically relative to the earth; but our records, because of, say the cloudy Polish skies, were so scanty that stations and retrogressions have never been experimentally ascertained. Because of his Sunworship and his belief in the Platonic heuristic, astronomer X proposes the basic Copernican model. Astronomer Y who adheres to the Platonic heuristic but also to Aristotelian dynamics puts forward the corresponding geocentric model: the Sun and the planets move uniformly on circles centered around the Earth. If so, then X's theory would have been dramatically confirmed by observations carried out later on the coast of the Mediterranean. The same observations would have refuted Y's hypothesis and compelled Y to resort to a series of ad hoc maneuvers (assuming that Y was not so disheartened as to abandon his programme instantly).

Zahar's account thus explains Copernicus's achievement as constituting genuine progress compared with Ptolemy. The Copernican Revolution became a great scientific revolution not because it changed the European Weltanschauung, not -- as Paul Feyerabend would have it -- because it became also a revolutionary change in man's vision of his place in the Universe, but simply because it was scientifically superior. It also shows that there were good objective reasons for Kepler and Galileo to adopt the heliostatic assumption, for already Copernicus's (and indeed, Aristarchus's) rough model had excess predictive power over its Ptolemaic rival."(19)
 

Lakatos would have done well to finish this rhetorical flourish with a quote from Kepler: "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 causes."(20) In other words, key parameters of the Ptolemaic system must be "read off" from observation; there is a parameter flexibility to the system such that if certain features of celestial movement had not already been observed, they would not have been predicted. The flexibility allows ad hoc adjustments after the observations. By contrast, the Copernican system locks us into the most important observations of celestial motion; even if they had not already been observed, they would have been predicted. Thus, there is a rational sense of confidence that it is unlikely that the Copernican system would predict these phenomena by chance unless it was getting something fundamentally correct, whereas the adaptability of the Ptolemaic system engenders the suspicion that its resuscitation is more the result of the ingenuity of its proponents in patching an inaccurate model.

At first glance this historical caricature may seem like Lakatos inadvertently slipped into his old conception of novel facts. Note that this example uses a temporally new observation. However, because Lakatos and Zahar are now using "novel, even though well known" to refer to facts or observations that could have been predicted prior to any observation, we will see that it is more fruitful to develop the train of thought in Lakatos's historical thought experiment, rather than engage in an acrimonious analysis of consistency and/or further definitional emendation.(21) In this way we will see that the most telling aspect of this historical caricature is that if it is supplemented with details of the actual historical context, there were equally "good reasons" for early followers of Copernicus not to accept realistic heliostasis, that novel facts in the Lakatosian sense existed in the latter half of the 16th-century(22) that would equally support acceptance of geostasis, or Tychonic geoheliocentrism.

It is important to grant that Lakatos and Zahar have chosen items that were important in the commitment of some scientists of the time. The so-called "fixed symmetry" -- elegant determination of the aspects of retrograde motion (size and frequency) and the fixed ordering of planetary orbits that both were a direct consequence of heliostasis -- had a profound effect on Copernicus, Rheticus, and Maestlin, and one can indeed follow a direct internal and external historical trail on this basis from Copernicus to Kepler.(23)

Problematic, however, in terms of what Lakatos and Zahar want to show, is that one can also follow a direct internal and external historical trail from Melanchthon, Reinhold, Peucer, Praetorius, Ursus, and Wittich to Tycho and the development of geoheliocentrism, complete with the ability to incorporate novel facts in the new and old Lakatosian senses. As the work of Westman and Gingerich has made clear, what is most striking about the reception of the orbital interconnectivity and "symmetria" of the Copernican system is the "silence" by which it was greeted initially by virtually a whole generation of astronomers concerned primarily with the pragmatic, methodological aspects of planetary motion, and the struggle of the best minds of the time to reconcile a host of discordant features which affected not only the acceptance of heliostasis but the continued pursuit of geostasis.(24)

Hence, one could be unimpressed for cosmological or methodological reasons, or both. From the standpoint of modern astrophysics, parameter determination is one of the most important constraints on theory evaluation. Witness the dissatisfaction with the Standard Model of quantum field theory and its application to the origin of the universe. It can solve many problems, not the least of which is the temporal sequencing of the origin of the laws of nature microseconds after the big bang. However, 18 numerical parameters are not fixed and must be taken from experiment. Thus, we find many physicists pursuing the "God equation" and esoteric theories such as string theory that will lock in the parameters all at once while explaining all the things the Standard Model does. According to Steven Weinberg, a contributor to the unification of the electromagnetic and weak nuclear forces, "The intellectual investment now being made in string theory without the slightest encouragement from experiment is unprecedented in the history of science."(25) An analogous situation would have arisen if the majority of Ptolemaic astronomers had "jumped ship" and begun to work on heliostasis immediately after the publication of De revolutionibus without the slightest encouragement from any new observation supporting Copernicus.

Either the majority of the astronomers of the Copernican episode were irrational, or there was an obvious difference that Lakatos ignores in the weighing of this constraint, a difference in the constraint's efficacy between our time and this historical episode. Parameter determination as a constraint on theory choice is not going to be impressive unless it is backed by a clear cosmological commitment and is part of a gradual strengthening of a hypertextual adjudicatory trail of inference. As we have seen, a Ptolemaic astronomer had a cosmological basis for a certain amount of "individualization" of planetary motion within a geostatic system.(26)

In short, parameter determination was hardly a fixed, universally agreed upon constraint for theory appraisal. Lakatos not only grants an extravagant epistemological status to parameter determination, but also modernizes it, presenting it as if it were a timeless, fixed constraint recognized and agreed upon by all generations of scientists.

To see that the Lakatosian interpretation of novel facts does not work, let us supplement his Gedanken drama by adding an historically plausible astronomical character. Suppose that in the middle of our story is a Tycho-like figure, who in spite of Lakatosian cloudy skies is making the most accurate observations of planetary positions since humankind began to survey the heavens systematically. He knows that his observations show that the rough models of geostasis and heliostasis are only qualitatively accurate; that precise measurements show that both systems are inaccurate quantitatively.(27) He knows that these inaccuracies are roughly equivalent over the course of a year, but that on any given date one system would come closer to predicting an actual planetary position than the other. He also knows that geostasis is consistent with the best physics of the day (Aristotelian dynamics), but seems to violate a major accepted pythagorean mathematical postulate, i.e., the planets do not seem to move uniformly about their perfect circles in relation to the earth. He knows that the advocates of heliostasis are attempting to get much mileage from this apparent defect of geostasis and knows that this was a key motivating factor for the creation of heliostasis in the first place.(28) Furthermore, he knows that heliostasis can account for the fact that planets appear brighter at various times during the course of a year, and that in doing so it makes a strange prediction -- that planets will show retrogressions, the number of which depend on the distance of each planet from the sun. On the other hand, he knows that geostasis predicts that a careful observation of the stars in a six month period will show no stellar parallax, and that heliostasis makes the strange prediction (given the then widely accepted estimate on the size of the universe) that there will be stellar parallax. Finally, he knows that because of their epistemological realism, the followers of heliostasis are very impressed with the orbital interconnective "symmetria" that follows from their theory, but that because of the accepted "modest ignorance" or instrumentalism in astronomical matters, many in the respected scientific community are not only initially unimpressed by this, but bothered more by the many inconsistencies of heliostasis with the best physics of the day, not the least of which is not a single, but a triple motion of the "lazy, sluggish" earth.

Now, suppose our Tycho-like figure gets word of the dramatic confirmation from the coast of the Mediterranean of retrogression, but suppose at the same time during the last six months he has been carefully applying his observational skills looking for stellar parallax, and finds none. Suppose that during this time he has also observed a supernova and a comet, and that after some time is able to determine that the latter shows no retrogression, that neither can be sublunar phenomena because they show no parallax, and that the comet must somehow penetrate the solid celestial spheres that both the followers of heliostasis (Maestlin-like figures) and geostasis (Praetorius-like figures) accept.(29) Suppose now that as all these observations are announced (more accurate measurements of planetary position, retrogression, but no stellar parallax, a comet with no retrogression, etc.), both camps begin to tinker with their systems.(30) The followers of heliostasis add epicycles, eccentrics, epicyclets, and indulge in numerous parameter adjustments to bring their system more in line (it is still shockingly inaccurate, especially for Mars(31)) with the new observations of our Tycho-like figure. They also explain that the apparent lack of stellar parallax can be understood by an appeal to a larger universe and they win support for this (ad hoc, post hoc) move from radical (Bruno-like) theologians who are arguing for a decentralized, non-hierarchial cosmos and a greater conception of God's creative ability. On the other hand, the followers of geostasis also add epicycles, eccentrics, and equants bringing their system more in line with the new observations, and explaining (ad hoc, post hoc) planetary retrogression and variations of brightness.

Put this way, Lakatos cannot successfully argue that the heliostatic moves were a continuation of the positive heuristic of heliostasis due to the dramatic progressiveness of the retrograde motion prediction, and that the geostatic moves were ad hoc, post hoc examples of degeneration. From the perspective of the middle and late 16th-century the "could-have-been-predicted-prior-to-any-observation" game could have been played by both sides. The geostatic moves can also be seen as a continuation of a positive heuristic due to the dramatic confirmation of the no-stellar-parallax prediction.(32) Lakatos cannot argue that "in the long run" we see that this was only a momentary success for geostasis (just as the momentary success of a planetary prediction), for then the claim of immediate success in the sense of decisive, internal, normative appraisal factors falls apart because excess predictive value in the middle and late 16th-century was a matter of context, interpretation, and contingency.(33) But it gets worse.

Our Tycho-like figure is very impressed, as are other influential astronomers, with the lack of the equant in the heliostatic system. He knows, however, that others are impressed primarily due to their instrumentalism, that the equantless heliostatic system is intriguing as a "hypothesis," as constituting a new set of calculation devices used to save the phenomena,(34) and that many of these astronomers are busy following the "reasonable" strategy of seeing to what extent these devices can be incorporated into geostasis. Also, because of his own realistic tendencies, our Tycho-like figure, (1) knows that his observation of the comet is problematic for both systems, and especially for any system that maintains celestial spheres, (2) knows that although the modified heliostatic system preserves the pythagorean requirement of uniform circular motion, it does so at the expense of proposing the realistic absurdity of objectless centers of motion,(35) and (3) he is very disturbed by the "big universe" claim of the heliostatic apologists. The latter makes no rational sense; what would all this new "wasted space" be for? Finally, he knows better than anyone else that the factual accuracy situation has not changed: During any given month one system would be more accurate than the other with a slight, but nondecisive overall edge to heliostasis.(36)

Perhaps our Tycho-like figure knows too much! Eventually he sees a good reason to develop a new system, a geoheliocentric system(37) that will not only be conceptually progressive in reconciling and maintaining the reasonable elements in both systems (the equantless elegance of heliostasis, and the well established, traditional Aristotelian physics), but empirically progressive as well, predicting the same novel facts as heliostasis -- retrogression,(38) planetary brightness during retrogressions, systematic linkages in planetary distances, and a full phase for the planet Venus -- in addition to being consistent with the novel fact (Zahar's amended version) of no stellar parallax. It will also be the first system that will have a physical body, the earth, at the exact center of the celestial sphere.(39) Thus, Tycho's new system can be seen as a continuation of the heuristic power of geostasis and Lakatosian apologists are wrong about geostasis having a weak heuristic at this time.(40)

Based on the history of late 16th-century astronomy, it is clear that Lakatos and Zahar have conveniently ignored Tycho(41) and certain aspects of the planetary motion debate that were of importance to the best astronomers of the time. According to Owen Gingerich,

"Today we view Tycho's scheme as a giant step backward, but we are nonetheless disconcerted by the fact that it was proposed by the most innovative astronomical observer since antiquity. . . . [and that] We can well imagine that Tycho believed he was taking a great step forward toward understanding the physical reality of the universe..."(42)

And, according to Westman, when seen in the full light of the empirical and conceptual problems facing the best astronomers of the time, "Here was no mere philosophical conjecture, but a world system with potentially serious predictive value."(43) Clearly, Tycho made rationally constrained moves in attempting to reconcile conceptual and empirical difficulties.(44) Like Kepler, and unlike the Wittenberg astronomers who were very influential in the latter half of the 16th century, he began to see the importance of parameter determination as a constraint in astronomy, and of moving beyond mere "hypothesis" and "moderate ignorance" to unification of physics and astronomy. With hindsight we see that he made the wrong choice in terms of which physics to preserve. Prompted by the realization that the comet of 1577 would have crashed through crystalline spheres, Tycho was faced with the apparent choice of preserving the harmonious orbital interconnectivity of heliostasis (its "more exquisite order") and the stability of the sluggish, heavy earth. As we have seen there was "progressive" support in the Lakatosian sense for Tycho's choice: Aristotelian dynamics as well as no stellar parallax. In Lakatosian language, were there decisive reasons for Kepler's neoplatonism to act and counter this progressive support for geoheliocentrism? Would not a comparative analysis of Tycho's 1588 De mundi aetherei recentiorbus phaenomenis reveal better or equally good appeals to internal reasons as Kepler's 1596 Mysterium cosmographicum? No doubt yes, and hence such a comparative analysis would show more degeneration for the Lakatosian theory of scientific appraisal from a meta-methodological perspective.(45)

Previously Lakatos would have argued that "immediate support" here does not mean immediately decisive or obvious to all concerned, but only that some good reasons were there to act on a scientist who was receptive to them. As he had argued previously, scientific change involves long protracted battles. There are no immediate quick kills, and it is difficult, if not impossible to give "advice" as to exactly when a degenerating research programme should be given up. But at this point in the development of his work, he does not seem to have his heart in this any longer after it has become apparent via several critical assaults on his philosophy of science(46) that talk of progressive and degenerative research programmes is subject to the same historical contextualism and contingency, hindsight and timing arguments that Lakatos had levelled against Popperian falsificationism. If degeneration is such a slippery concept that it is impossible to pin down a time when there is decisive degeneration versus decisive progressiveness, then of what help is it in identifying the internal history which then avoids the necessity of appealing too much to external history? Something new is needed, a new Archimedean demarcational point to perceive the clear internal, decisive rationality for Copernican superiority.

So sensitive is Lakatos at this point to the charge of relativism that he is compelled to argue for immediate and decisive progressiveness of heliostatic allegiance based on the parameter determination features of heliostasis. His examples are of the middle and late 16th-century rather than the early and middle 17th, and he has appealed to a constraint that was not yet well accepted. Here, like the positivists and logical empiricists before him, he has succumbed to the trap of implicit infallibilism, that an adequate analysis of scientific methodology must reveal those universal, internal fixed principles that when applied properly give us rationally compelling and decisive reasons to follow one path rather than all others.(47)

Lakatos is aware (of the "unwelcome conclusion") that all he has done previously is to show that there were good reasons to pursue heliostasis, not that there were not equally good reasons to continue to pursue geostasis, which means, he thinks, that one must appeal to external history as the decisive factor to account for why scientists would commit to one or the other. For Lakatos, commitments based on external reasons are not out of the question (we often in fact need these to supplement internal analyses), but a sound rational reconstruction should show the internal good reasons that allowed the external to be relevant, that were rationally instrumental in activating the external reasons. But need the internal reasons be rationally decisive constraints? Now it appears that he thinks so; otherwise his position produces by his own demarcation criteria an unwanted relativism. If Lakatos is not arguing that the internal reasons that he and Zahar have identified were "decisive," that any rational scientist of the time "ought" to have switched to Copernicus, then what is all the talk about "superseding" based on internal reasons?(48) If he is arguing this, then, as we have seen, he is wrong about there being rationally decisive internal reasons in favor of heliostasis in the late 16th-century. In either case his position is reduced to the position of the moderate relativist(49): There were good reasons to develop heliostasis, but there were equally good reasons to continue to explore some version of geostasis, and that for external reasons the right men at the right time picked heliostasis and produced the refinements (elliptical orbits, a new theory of motion) that made heliostasis the preferred choice in the 17th century.

Typically, infallibilist responses to relativism involve two mistakes: (1) the assumed need of having rationally compelling and decisive commandments -- some clear "sign" -- for early theory choice in the sense that one is better to develop than all others; (2) which in turn is a symptom of a larger mistake, an "infallibilism fallacy," the assumed need that some final resting point of certainty along an adjudicatory trail is needed to answer the relativists. Since Lakatos has made much of the fact that relativism emerges primarily when one's standards of appraisal are too utopian, my infallibilist charge should be a rather surprising claim. According to Lakatos,

"...utopian scientific standards either create false, hypocritical accounts of scientific perfection, or add fuel to the view that scientific theories are no more than mere beliefs bolstered by some vested interests. This explains the 'revolutionary' aura which surrounds some of the absurd ideas of contemporary sociology of knowledge: some of its practitioners claim to have unmasked the bogus rationality of science, while, at best, they exploit the weakness of outdated theories of scientific rationality."(50)

However, as I have argued, Lakatos blinks when his fallibilism is challenged by relativism. Now a clear sign is needed or we are "relativists in disguise."

By the late 16th-century, parameter determination was emerging as an important consideration for theory evaluation, but it was neither universally accepted nor did it in isolation clearly select heliostasis over geostasis. Lakatos, in his search for a universal, fixed scientific methodology, has imposed a modern standard of theory appraisal on a previous time, ignoring the transitional, formative nature of that time and the as yet unclear role of parameter determination.

To prepare for a proper understanding of parameter determination in the Copernican episode, and its role as a gradually strengthening node along an adjudicatory trail, we can conclude this chapter by sketching a consistent fallibilist position and show in the process that Lakatos's implicit infallibilism slip is symptomatic of much of post-Kuhnian philosophy of science. As I have argued, if we are to take fallibilism seriously we must acknowledge that science is a somewhat messy, meandering, contingent process, but that in doing so, the fallibilism and open-endedness this implies is not an endorsement of irrationalism and/or relativism.

A simple way of providing such a sketch is to see how some post-Kuhnian philosophers of science attack avowed fallibilist positions. Larry Laudan has provided a fruitful model of fallibilistic scientific deliberation with his reticulational model of scientific change.(51) Using this model we can view science as a process where scientists either do (during their best moments) or ought to follow adjudicatory trails among empirical results and theories, methodologies, and aims or cognitive values in resolving disagreements. Empirical disagreements (theories or facts) are resolved by applying agreed upon methodologies; methodological disagreements involve appeals to agreed upon aims and cognitive values; disagreements in cognitive values are resolved ultimately by appeals to factors that are also empirical and methodological. All justificatory appeals are instrumental, relational, ultimately empirical (at either a primary or meta-level), and hence fallible. No node on the network has an intrinsic status. According to Laudan, as we probe nature for its secrets we presuppose and impose in the process at any given time a network of theoretical, methodological, and axiological stances. In the process we may not only find weaknesses in our theories and auxiliaries, but learn about our methodologies and aims (neither are transtemporally fixed) as well; discoveries may be produced that expose weaknesses in the nodes of our networks, in either our methodologies or aims or both.(52) In this way scientific change is piecemeal, comparative, and rational. All three levels need not be questioned at the same time. This process will allow for a relative best selection from a number of alternatives most of the time, but is of course still subject to "underdetermination" in terms of some ultimate best solution. It is imperfect and nonutopian epistemologically. However, as fallibilists we do not attempt to separate the reasonable from the conceivable -- a Platonic quixotic goal -- but only the most reasonable and thus most reliable given the alternatives.

Laudan's position has been attacked(53) by alleging that his position cannot escape either a vicious circularity(54) or infinite regress, or an implicit foundationalism. In short, either the adjudicatory trails scientists are alleged to follow in Laudan's scheme are "aimless," and hence endless, or there must be some implicit, overriding meta-meta-criterion of "self-justificatory" judgment to determine the rationality of any given trail and/or the rational, indubitable terminus of any given trail.

Typically, only a formal argument is offered in these criticisms -- there is hardly ever any scientific flesh added, any actual analysis of real scientific cases. A good example is Doppelt.(55) The only examples he uses are those of the people (Shapere and Laudan) he criticizes. In both cases his argument reduces to something like this: Both S and L have shown an actual historical case where scientists had some good reasons -- because of their acceptance of new theories T1, T2, T3 -- to change allegiance to methodologies from M1 to M2. But, according to Doppelt, logically this does not prove that there were not also some good reasons to maintain acceptance of M1. As a bare, formal, logical fact this is true. But Doppelt ignores, or is ignorant of, all the good reasons the scientists of the time had for accepting T1, T2, and T3, and the rational force that these reasons produced in favor of M2.

So, stripped of its constricted logic what does this criticism amount to? Given any particular item of disagreement, scientific discussions are potentially endless, but are as a matter of historical fact not endless because a scientific community will eventually reach agreement about a particular node along an adjudicatory trail. Consensus is reached, but seen in the light of the historical context it is not "mere" consensus as relativists often make it out to be. Science is an open-ended process. This process is potentially endless, but clearly not aimless, because directed adjudicatory trails are followed; decisions are based on reasons that are in turn based on other reasons, that stopping points of consensus are reached along adjudicatory trails (facts, theories, methodologies, aims.)(56) Key stopping points are fallible -- we take a risk and might be wrong in thinking that any given stopping point is a good reason, a good place to stop, and some day, based on new developments, we might need to reevaluate this decision.

Doppelt, for instance, makes much of the fact that when a choice is made we may or do lose something.(57) But first of all what we may lose may not be weighted very highly in the light of the scientific developments of the time. Tycho was disturbed at first by the prospect of giving up crystalline spheres, but as we have seen, the comet of 1577 in conjunction with other considerations changed his mind. Doppelt puts no independent scientific flesh on his a priori arguments, and hence is misled by the trivial logical fact that in every decision that involves great risk a different trail is followed than one that could have been followed. Second, how much infallibilism is implicitly assumed by this notion of loss, becomes clear when Doppelt tinkers briefly with the notion of "epistemic possibility."(58) After bringing up the issue, Doppelt admits that "Clearly the rationality of a choice to accept a new theory, standard, etc. is not thrown into question by other 'possible choices' of aims, theories, standards, etc. unknown at the time." This would be like saying that Copernicus and his initial followers were irrational because they did not consider the possibility of elliptical orbits. But this unrealistic requirement is precisely what is also behind Doppelt's allegedly more moderate requirement that the rationality of a choice is called into question because an "existing rival," may have possible epistemic advantages and may, if followed, lead to actual gains. This is similar to saying that the rationality of a decision is thrown into question, because although a person followed a valid trail of reasoning, there existed or may exist a different valid path with a different conclusion. Doppelt's a priori analysis reduces to the trivial fact that it is possible to have two valid chains of reasoning with contradictory conclusions. In following one rather than another we may be disappointed when we find that our conclusion does not work when tested against the world, but it does not follow either from our being wrong or the possibility of our being wrong that we acted irrationally.

What the critics of Laudan's position are clearly assuming is that unless we find some absolute, assured resting point, some indubitable rational terminus, reason ends up chasing its own tail and the slide to relativism and irrationalism is inevitable. Western philosophy, both empiricist and rationalist traditions, has suffered much from this "Platonic fallacy." Whitehead may be right that all Western philosophy is but a footnote to Plato, but in this sense it is no longer something to brag about and it is time to begin writing some new chapters. What I believe is needed is a new metaphor for rationality: the open-ended, yet constrained following of hypertextual adjudicatory trails of reasoning with fallible, empirically-linked decisions made along the way, without sky-hook clear signs that we are on the right trail.(59)

The justification of science as a rational process is not much different from the answer one must often give to perceptive first year logic students. Why be logical they ask? If our premises are often in doubt, and hence valid deductive arguments can have false conclusions, and whether our premises are in doubt or not, invalid deductive arguments can have true conclusions, why prefer valid reasoning? The answer, of course, is that in the long run valid reasoning forces us to test our ideas against the world, whereas invalid reasoning offers an attempted safe haven from confrontation with the world by offering excuses for not testing our beliefs. The justification of the rational framework offered by the adjudicatory trails followed by science is similar: It is a process that forces interaction with the world; a process that allows the world to "kick back" empirically and endlessly.(60)

In post-Kuhnian philosophy of science it is fashionable not to generalize too much from the Copernican episode. It involves only one kind of science and a rather special, "clean" mathematical one at that. However, much can be learned by observing the meandering trails followed by late 16th-century astronomers, and as we have seen, the tension in Lakatos's response to this episode, between his avowed fallibilism and the alleged immediate clear sign offered by novel facts and parameter determination.

As Laudan has also pointed out, almost all discussions of scientific appraisal assume a uni-contextual modality.(61) They assume that for an individual scientist or a scientific community to be rational in using a particular theory there must not only be some clear transtemporal and trans-cultural criteria that are being applied, but the theory in question must be "done" so to speak; it must have already been completely successful in fulfilling those criteria. As we have seen, philosophers like Feyerabend can then use a little history and make short work of theories of scientific appraisal based on this assumption. In other words, it can easily be shown that scientists have often pursued theories that have not yet lived up to proposed criteria and ought not to be accepted yet based on those criteria.

However, by distinguishing a context of rational pursuit from that of acceptance one can show, as I intend to do in the next chapter, that although scientists had good reasons not to accept heliostasis during the Copernican episode, it would have been irrational not to pursue it. Heliostasis created an "immediate stir"(62) in terms of the way it solved the core problem situation of astronomy, and contra Kuhn's leap of "faith" on the part of those converted to a new perspective,(63) or Feyerabend's pursue-anything- because-the-situation-was-such-a-mess, we find astronomers of many different persuasions studying the heliostatic model and acknowledging its parameter determination features in terms of the core problem situation of astronomy. Whereas Kuhn finds only faith and aesthetics, Lakatos, by assuming that acceptance is the only valid cognitive modality and in response to the criticism of Feyerabend and others, is now looking for some clear sign for why Copernicus superseded Ptolemy.

Clearly, rational constraining trails were followed by the key players. But it was a time of transition and emerging constraints, and because new trails were not completely worked out, there was no clear choice. It was a time of new empirical developments (comets, novae, and more accurate observations), and an emerging appreciation of parameter determination and the possibility of unifying physics and astronomy. Not until several decades into the 17th century were the trails sufficiently worked out and key developments present (Kepler's development of elliptical paths for the planets and his Rudolphine Tables; Galileo's explication of a new dynamics and observations of the moons of Jupiter, mountains on the moon, and spots on the sun) that a rational threshold or crescendo was reached, and the stage set for heliostasis being accepted as a preferred choice from the alternatives.(64)

In other words, when seen in the light of the meandering and transitional developments of the late 16th-century, we can understand the powerful (psychological and rational) persuasive nature of the work of Kepler and Galileo in the first decades of the 17th century. Tycho, as we will see, was already impressed with the parameter determination features of heliostasis. If he were still alive, would he have continued to promote his version of geostasis, say in 1627, once he had used Kepler's astronomy and the Rudolphine Tables to predict a position for Mars, assimilated Galileo's dynamics and the implications for a moving Earth, or used a telescope himself to see the evidence that the moon and the sun were physical places and to make more accurate measurements of parallax?(65) Would the man who was willing to give Copernicus a "fair hearing" not be powerfully affected by these developments and consequently troubled by the censoring of heliostasis by the Church? Or, would he, as the relativists maintain is always equally rational, continue to seek auxiliary patches for geostasis, "maintaining obstinately at any cost" and bearing any "price of continual repairs and many tangled-up stays, the worm-eaten columns of a building tottering in every part. . ?"(66) Would he have continued to seek alternate explanations or interpretations for Galileo's observations of the moons of Jupiter, mountains on the moon, and spots on the sun? Would he have continued to support an underlying commitment to Aristotelian dynamics in the light of these observations, when he also realized that a full articulation of his own geoheliocentric system would need to have the Earth rotate to even begin to approach the simplicity of Kepler's elliptical orbits and produce a competitor to the Rudolphine Tables?(67) Or, would he not have recognized that there were now too many fingers in the geostatic dike?

We can close this chapter with a short test of the position I have outlined by comparing it with the responses of relativism on the one hand and Lakatos on the other to the Church's action of 1616. In doing so, let's translate the Church's position and consequent action of censoring heliostasis into what would be its modern equivalent, i.e., the complete withdrawal of institutional support and research funding due to alleged poor scientific rationale. Relativism is clearly committed to the view that the Church's position was as good as that of Galileo's; because "anything goes," the reasons for the Church's position were just as good (or just as bad). And since truth is simply a question of power, we can not say that it was wrong in any sense for the Church to act on its position, to attempt to implement its position by molding reality according to its views. The amended Lakatos, in spite of his previous epistemological leniency in such matters, is now committed to saying that the Church's position was irrational because an application of timeless, universal principles of scientific appraisal show that the Ptolemaic-Aristotelian cosmology was degenerating for centuries, that it was no longer possible for rational people to deny its poor public record, and that decisive internal support had existed for Copernicanism for decades. Hence, for Lakatos research money should have been withdrawn from the Ptolemaic-Aristotelian program.(68)

The position I have sketched is committed to saying the Church's position was irrational, not necessarily because by this time all the discordant developments of late 16th-century and early 17th-century were completely assimilated by all the key players, but because by this time a well-worked out adjudicatory discussion had been taking place for several decades, and at precisely the time the discussion was reaching an adjudicatory threshold, the Church decided to withdraw funding and institutional support for further development of what was clearly by this time a viable and robust scientific alternative. In short, the Church decided to cut off discussion of precisely the type that would allow the world to "kick back" further. Given the rate of progress achieved by heliostasis, it was a mistake not to continue to pursue it. Nowhere is this put better than in Galileo's letter of 1615 to the Grand Duchess Christina. According to Galileo,

". . . to ban Copernicus now that his doctrine is daily reinforced by many new observations and by the learned applying themselves to the reading of his book, after this opinion has been allowed and tolerated for those many years during which it was less followed and less confirmed, would seem in my judgment to be a contravention of truth, and an attempt to hide and suppress her the more as she revealed herself the more clearly and plainly."(69)

Contrary to relativism, some decisions are just not well supported. Contrary to Lakatos there is no universal analysis that can be applied to the discussions of the middle and late 16th-century that shows the inevitable progressiveness of heliostasis. Tycho-like figures abound in science. They make solid contributions. They give competing ideas fair hearings. They follow adjudicatory trails and impose axiological, methodological, and theoretical stances in the process. And because of this, not in spite of this, they pay close attention to what the world is telling them. The world, however, does not reveal all its secrets at once, and so scientists must make decisions and take a risk on where to stop and place their bets. Many times they are wrong, and they become a minor footnote in history.

Science is a process that attempts to walk a complex, difficult epistemological path between the extremes of a reassuring, but unrealistic, Platonic absolutism and a seductive, easy relativism. Both are reactions to the insecurity that we must live with to maintain a consistent fallibilism. But as Socrates admonished us centuries ago, we will be "better, braver, and less idle" when we take this epistemological path.

Notes for Chapter 4:

1. Lakatos, 1978, p. 102.

2. Ibid., p.121.

3. Lakatos and Musgrave, 1970, p. 178.

4. I will be resisting the temptation to indulge in "a prioristic" definition bashing of Lakatos's conception of novel facts. I will take Lakatos's definition (what has come to be called the heuristic conception following the work of Worrall and Zahar) at face value and show that it does not do what he thinks it will, i.e., show decisive internal-rational factors for early theory choice in the case of the Copernican episode. For a summary of various definitions and amendments, see Nancy Murphy, 1989. Murphy suggests that a novel fact for a new theory be one that "was first documented after that theory was proposed." But planetary retrogressions and increased brightness would be ruled out as novel for realistic heliostasis under this amendment. See discussion below. For other discussions of the definitional question see Gardner, 1982, Campbell and Vinci, 1983, and Nunan, 1984. For an excellent defense of the heuristic conception see Worrall, 1978.

5. Lakatos, 1978. Reprinted as chapter 2, "History of Science and its Rational Reconstruction," and chapter 4, "Why did Copernicus's Research Programme Supersede Ptolemy's?" Chapter 2 was originally published in 1971, Boston Studies in the Philosophy of Science, 8, pp. 91-135; chapter 4 was written in 1972, presented at the Quincentenary Symposium on Copernicus, and also published in The Copernican Achievement, Robert S. Westman, (ed.) (Berkeley: Univ. of Calif. Press, 1975b). My references will be to Lakatos, 1978.

6. Because external history must supplement internal history, normative appraisal alone will not explain or justify commitment, acceptance or rejection (Ibid., pp. 168-169, 190). Although Lakatos seems to vacillate on this point (..."we may in the end have to admit that Copernicus's and Kepler's and Galileo's adoption of the heliocentric theory...is not rationally explicable...", p.178, (but) "Copernicus recognized the heuristic degeneration of the Platonic programme at the hands of Ptolemy...", p.181, emphasis added), surely Lakatos wants to argue that being rational human beings, key scientists, as a matter of fact, will often choose for good reasons the most progressive research programme to work on. If objective appraisal features are involved in scientific change, they must be recognized. What good would they be, if no one ever recognized them? However, in deference to Feyerabend, Lakatos says this does not mean that the philosopher of science can give advice, that scientists "ought" to always choose what appears to be the most progressive research programme (p.117). This entanglement between psychological factors behind commitment and adoption on the one hand, and the recognition of rational factors on the other is no doubt one reason for his "agonizing reappraisal" of a key feature of his philosophy of science. See below and note 12.

7. Although the main focus of this chapter is a criticism of a key element in the machinery needed to establish 2, it is worth pausing to reflect on the indirect method Lakatos used to argue 1. In admitting that it is difficult to argue against relativism directly (Ibid., p. 178.), Lakatos says in effect that we must assume the ultimate rationality of science, which in turn then reveals the heuristic fruitfulness of this assumption. Although shockingly Augustinian in one sense -- we don't believe because we see, we see because we believe -- this approach is consistent with the "hard-core" feature of Lakatos's theory of scientific research programmes. In this case, the rationality of science is made a hard-core element of a meta-programme which in turn is not judged on the basis of simple confirmations or disconfirmations, but on whether an analysis of scientific change shows this programme to be progressive or degenerative. Although a complete analysis of this response to relativism is beyond the scope of this thesis, it is also worth noting Laudan's point in this context that many philosophers of science purporting to go beyond the closet or implicit infallibilism of logical empiricism, end up advocating either torturous theories of normative methodology or some version of relativism, because they unconsciously or unwittingly acquiesce to the logical empiricist's axiological axiom that in matters of cognitive value there is little or no possibility of rational disputation and adjudication. See Laudan, 1984, pp. 47-50. In agreement with Laudan, in the terminology of this thesis, cognitive values are nodes on a hypertextual adjudicatory trail with their own network of connections to methods, theories, and evidence.

8. Lakatos, 1978, pp. 131-132.

9. See note 5.

10. Lakatos, 1978, p. 184.

11. Lakatos refers to the observation of a full set of phases of Venus taking place in 1616 and mentions Galileo at the same time. (Ibid., p. 184) He seems to be confused on dates here. Galileo's observations of Venus were conducted throughout 1610 and completed on New Year's day, 1611. The Church's first action against realistic heliostasis took place in 1616. If Lakatos knows of, or is referring to, a special corroboration of Galileo's observations, he does not say, and I am unaware of any special corroboration by another astronomer taking place in 1616.

12. According to Toulmin in his commentary on Lakatos's paper (in Westman, 1975b, pp. 384-391) this amendment represents an "agonizing reappraisal."

13. The references Lakatos cites are: Gingerich,1975a; Kuhn, 1957; Neugebauer, 1968; Price, 1959; Westman, 1972.

14. Lakatos cites Gingerich (1975a). As we have already seen, what is less well known is that the so-called factual equivalence of the two systems was in actual practice an average, that at any given time during the course of a year one model might be making better predictions of planetary positions than the other.

15. Curiously, Lakatos says that although the observation of a full phase for Venus in 1616 (1610?) cannot help Popper because of its late occurrence and an adequate geoheliocentric solution (Lakatos, 1978, p. 171, N2), it can help the Lakatosian theory because its prediction was novel in the sense described below, and because "Copernicans predicted the phases of Venus, while Tychonians only explained them by post hoc adjustments." (Ibid., p.115, N1) However, Lakatos gives no evidence for the latter claim, it conflicts with authoritative astronomical conclusions on the predictive value of the Tychonic system (see note 41 below), and it is puzzling to say the least how the Tychonic solution to the full phase of Venus works against Popper because it is adequate, but works in favor of Lakatos because it is ad hoc.

As we will see in the next chapter, a better way of handling geoheliocentrism is too ask whether as an auxiliary patch to geostasis, as an adjusted hypertextual adjudicatory trail in the light of apparent falsifications, it showed promise or whether it exposed many weak nodes in the set of theories, auxiliaries, etc. that constituted the general geostatic defense. I will argue the latter, and that

1. Its production was driven by an admission that parameter determination was an important feature that astronomical models should have. One of the main arguments being made by supporters of heliostasis.

2. Many of the details for geoheliocentrism were not worked out. There were no predictive tables, for instance.

3. What little details were worked out forced supporters to make the Earth rotate! This was a dangerous admission to the supporters of heliostasis and further weakened Aristotelian dynamics, one of the important nodes in the geostatic set.

16. Gingerich, 1975a, p. 87.

17. Lakatos, 1978, pp. 69, 92.

18. This long-term degeneration is, of course, the result of hindsight. The Ptolemaic system cannot be seen as degenerating unless there is another research programme whose progressiveness reveals the degeneration of geostasis. Although Lakatos does not say so in this article, his charge that geostasis can be seen as degenerating by the middle of the 16th century, and that this degeneration begins with Eudoxian tinkering with homocentric spheres to account for retrogression, does not imply that pre-sixteenth century adherents to the Ptolemaic system where acting irrationally.

19. Ibid., pp. 187-188. Lakatosian apologists could argue that the first paragraph in this citation is just a slip of the pen, that Lakatos gets carried away here and that he does not need this thought experiment to make his point. My argument is that it is no accident that it occurs where it does. It consistently carries out features of Lakatos's argument and reveals a major defect in the his amendment that is more difficult to see otherwise.

20. Quoted from Gingerich, 1993, p. 327.

21. See above note 4.

22. We will also resist the temptation to be picky here and assume that Lakatos knows full well that Galileo and Kepler were not intellectually active in the 1520s, and is here discussing the developments that led up to their commitment and consequent work in the latter half of the 16th and early 17th centuries.

23. Is this "fixed symmetry" an internal or external factor for Lakatos? In arguing for his own position it is a powerful internal factor; in arguing against simplicism and Kuhn, "geometric harmony" is rejected as an inadequate internal reason because perceiving it is a matter of taste. In the 20th century it might be possible to argue that the quantitatively fixed positions of planetary orbits and the aesthetic appreciation of this are distinguishable in terms of different "types" of reasons (the former, internal, and the latter, external), but they clearly were not distinguishable for 16th century heliostatic realists. Parameter determination, as I will argue in the next chapter, was still inextricably linked to pythagorean elegance and a picture of God as the great mathematician who would do nothing superfluous.

24. Gingerich, 1973a, 1973b; Westman, 1975a, 1975b, 1975c; and Gingerich and Westman, 1988.

25. Weinberg, 1994, p. 46. Emphasis added.

26. See Chapter 2 and point 5 on Ptolemaic problems. For future reference, however, consider that one can push the cosmological treatment of each planet individually only so far and still maintain some sort of system. If the individual features of one planet clearly interfere with those of another, it is difficult to see how any cosmological fix would be forthcoming to explain this. Recall (also from Chapter 2, point 5) that in Ptolemy's system, Saturn's equant point falls within the nested sphere of Mars.

27. Remember that Lakatos uses only the "rough models" of both theories. Presumably if we are to be fair, this means not only nonepicyclic, noneccentric, and equantless geostasis, but also nonepicyclic, noneccentric, and nonepicyclet heliostasis. Hence, my story will also be inaccurate in terms of real historical sequencing -- it ignores the timing of the Appollonius' and Hipparchus' epicyclic-deferent modification of Eudoxus and its role in the full Ptolemaic system. Given Lakatos's caricature we are to see this as a clear example of long term degeneration, but Lakatos can't have it both ways; he can not use an inaccurate historical sequence that favors heliostatic dramatic facts and then claim that changes to geostasis to respond to these facts is ad hoc, post hoc. The same game can show heliostasis in need of ad hoc, post hoc moves. See the development below.

28. Here my historical caricature suffers from the same defect of that of Lakatos; the rough heliostatic model would also violate the uniform motion postulate. (It is intriguing to speculate that this may be one of the reasons that Aristarchus's system was rejected immediately.) This shows that if we stayed true to the rough model illustration that Lakatos wants to use, heliostasis would be shown to degenerate on the very same basis which supposedly motivated its creation in the first place and require an ad hoc fix of multiple epicyclets and eccentrics just as geostasis would of epicycles, eccentrics, and equants.

29. This "ridiculous penetration of the orbs" will later help our Tycho-like figure reconcile his critical misgivings about his own system where the orbit of Mars is made to intersect that of the sun.

30. It is intriguing to speculate to what extent the mode of communication available played in the commitments of the time. Although Gingerich (1975c), and Eisenstein (1968, 1969) have written on the crucial role printing had on objective discussion, one can still hypothesize that a significant "delay factor" existed in acknowledging the full force of the evidence. Would the Church have made the decision to censor heliostasis if FAX and electronic mail were available? Today, Lakatos is wrong on another account. There are apparent quick kills. Electronic mail and FAX transmissions played a major role in the North American and Western European quick kill of cold fusion. For some of the involvement of electronic mail and FAX transmissions in the cold fusion debate see how Pon's and Fleishman used FAX (Cookson 1989, p. 20.), and Douglas R.O. Morrison's discussion of his cold fusion electronic mail newsletter (from CERN laboratory), and his analysis of a "regionalization" of findings -- North America and Western Europe reported predominantly negative results, but Eastern Europe, Italy, Asia, and most of South American reported positive results ("Cold Fusion Sessions at the American Physical Society Baltimore Meeting," PR NEWSWIRE, May 9, 1989.).

31. To see how Copernicus himself adjusted the parameters of his system to match "inaccurate" Mars data, see Owen Gingerich, 1975b, pp. 103-4. According to Gingerich, the comparison of recomputations and the planetary data used by Copernicus shows that Copernicus was not "testing" his theory with new observations that were becoming available, but rather using ad hoc parameter adjustments to make sure his theory matched accepted data. According to Gingerich, "...the entire exercise was carried out primarily to show that the heliocentric cosmology was compatible with reasonable planetary predictions rather than to reform the accuracy of astronomical predictions." To see how Tycho vacillates ("deluded himself") on another Mars problem (parallax), see Gingerich and Westman (1988), pp. 70-72.

32. The lack of stellar parallax follows naturally from geostasis, just as the features Lakatos and Zahar appeal to in supporting Copernicanism. For instance, the use of parallax for geostasis would be no different than using the bonded elongation of the inferior planets for Copernicanism. To see how this would be consistent with the heuristic account of novel facts, see Worrall's defense and elaboration of Zahar and Lakatos (Worrall, 1978, especially note 23). According to Worrall, the relevant question would not be whether any defender of geostasis was thinking about the lack of stellar parallax during the theory's formative phase, but whether this measurement was fixed by the theory or had to be first "read off" from observation. It is also important in this context to remember that there was renewed interest in the relevance of stellar parallax during this time, after geostasis had been fully developed and challenged by heliostasis. And geostasis handles Tycho's more accurate measurements in a straightforward dramatic way, whereas heliostasis has to bring in radical theologians and a new conception of God.

33. According to Gingerich and Westman (1988), we can also throw into this epistemological stew personal conflict and claims of priority. And when we do so, claims of "inevitable" scientific developments are suspect. Hence, we should be wary of historiographical analyses that show that scientific change is "historically and logically sequential."

34. According to Gingerich, 1973a, p. 520, "The matter is very nicely put around 1555 in a letter from Gemma Frisius that was published in several editions of Stadius's Ephemerides . . . . Gemma allowed that the Copernican system gave a better understanding of planetary distances as well as certain features of retrograde motion. He added, however, that those who objected to the ephemerides because of the underlying hypothesis understood neither causes nor the use of hypotheses." (emphasis added) Gingerich then quotes sections of the letter that reveal the importance of the standard instrumentalist interpretation.

35. Geostasis, of course, also does this. But most of the advocates of this view are not arguing for a realistic interpretation of eccentrics and epicycles. Remember that one of the primary selling points of heliostasis is supposed to be its realism, particularly its ability to fix the spacing between the planets so that specification of the orbits are no longer arbitrary. This blatant conceptual inconsistency is one of the many reasons it was difficult to take seriously a realistic interpretation of Copernicus's full version of heliostasis.

36. But according to Kuhn, 1957, "...the length of the year determined from the Prutenic Tables was actually slightly less accurate than that determined from the older tables." (Vintage Books ed., p.188.) Hence, one could weigh as important either daily predictions, overall monthly accuracy, or overall calendar construction and get a different result as to which system was better.

37. He is also pushed by the fact that issues of patronage and reputation are at stake, that pressures for cosmological reform are building, and others, if he doesn't act fast, may get credit for introducing a new system. See Gingerich and Westman, 1988.

38. Retrograde motion is "'naturally' explained" in Tycho's geoheliocentric system. Gingerich, 1973b, p. 101.

39. As noted in the introduction, neither Ptolemy nor Copernicus had the earth or sun respectively at the exact center of their systems. Hence, my repeated reference to geostasis and heliostasis, rather than geocentrism and heliocentrism.

40. See Worrall, 1978, p. 60.

41. As noted above (note 15), Lakatos claims that Popper conveniently ignores the importance of Tycho prior to ignoring him himself (see p. 171, N2). Kuhn does not; see 1957 (Vintage Books ed.), p. 224. Nunan (1984, p. 285) also does not, but by looking at the matter through Bayesian spectacles, he fails to see the significance of parallax as a novel fact for geostasis. Although beyond the scope of this thesis, I would argue that Nunan's definition and use of novel facts are even more utopian (see development below) than that of Lakatos and Zahar.

Lakatos also claims that "Copernicus predicted the phases of Venus, while Tychonians only explained them by post hoc adjustments." p. 115, N1. But Tychonic geoheliocentrism was developed several decades before Galileo's observations (hence there is no "reading off" from observation for parameter adjustment) and Lakatos gives no evidence for his conclusion. There is no evidence that Tycho used the Copernican prediction to construct his theory, and it is not necessary in terms of parameter adjustment for the development of geoheliocentrism. It also runs counter to what other authoritative sources have claimed. According to Gingerich, "Until Galileo's telescopic observations of the phases of Venus in 1610, no observational evidence could be brought against the Ptolemaic system. Even Galileo's observations could not distinguish between the geoheliocentric system of Tycho Brahe...and the purely heliocentric system of Copernicus." (1986, p. 81). Also see Gingerich, 1982, p. 137.

42. Gingerich, 1973b, pp. 87, 101. Emphasis added. Westman (1975b, pp. 329, 332) also refers to Tycho's "modern, critical attitude" in reference both to his appreciation of the scientific merits of heliostasis and his own geoheliocentrism, in contrast to Maestlin's stance as a "slavish admirer" and "faithful disciple" of heliostatic particulars.

43. Westman, 1975b, p. 326.

44. According to Westman, "Tycho offers a fair hearing (emphasis added) to the physical arguments of Copernicus. His annotations show him exploring and paraphrasing the inner logic of Copernicus' theses without formulating any rejoinders. There seems little question, however, that he was never quite persuaded by these arguments." (Ibid., p. 317.)

45. A complete analysis of Maestlin's work and comparison with Tycho's would also reveal Lakatosian degeneration. Although a pivotal figure in an assumed internal trail leading to Kepler, the former clearly ignored many of the internal considerations that Tycho took seriously. See Ibid., pp. 329-339.

46. See Feyerabend and Kuhn, 1970.

47. This in spite of Lakatos's observation in reply to Feyerabend that "If it were irrational to work on a theory whose superiority was not yet established then almost all of the history of science would indeed be rationally inexplicable." Lakatos, 1978, p. 178.

48. Followers of Lakatos may argue that I have misconstrued Lakatos's point; that all he is arguing is that a rational reconstruction shows a "fruitfulness" or progressiveness "edge" to heliostasis, that although the situation was not absolutely clear, one could not deny in the late 16th century the "poor public record" of geostasis (Ibid., p. 117). But we have seen that there was no such edge in the late 16th century in favor of heliostasis, and a distinction between "decisive fruitfulness" and "rationally compelling and decisive" good reasons is no distinction at all. Lakatos's analysis degenerates into moderate relativism (see below). Further evidence of Lakatosian confusion is seen in that Lakatos wants a cake-and-eat-too situation: the Copernican proposal was immediately progressive on the basis of a rational reconstruction of the late 16th century, but it was also immediately degenerative, and this is why Kepler eventually produced elliptical orbits. (p. 188.)

49. Doppelt, 1986, 1988.

50. Lakatos, 1978, p. 135, n2.

51. Laudan, 1984.

52. According to Owen Gingerich (In Westman and Gingerich, 1975b, p. 244) in science we have "not merely an extension of man's knowledge of the universe, but an evolution of his entire mode of assimilating his discoveries." (emphasis added)

53. What follows is a simplified, but I would argue not oversimplified, composite of the arguments of Gerald Doppelt (1986, 1988), Harvey Siegel (1983, 1985, 1989), and John Worral (1988).

54. Laudan does not deny some circularity, but calls it a "central, but nonvicious, circularity." (1984, p. 39 n13.)

55. Doppelt, 1988.

56. Even if agreement is not sometimes reached, the debates will still have a rational framework. See Laudan, 1984, p. 86.

57. 1986, 1988.

58. 1988, p.28.

59. In this regard, Laudan's own appeal to a "shared canon" to evaluate the aims of science is suspect. See Laudan, 1990a, and Leplin's criticism (1990) of Laudan's "strange conservatism."

60. A quick comment on the epistemological hubris implied by relativism is in order here, behind the notion that it is just a question of power, that any trail of ideas will work with the world as well as any other. Although it may be true, it is clearly egocentric to assume that human concepts can be so powerful as to veil nature completely. Metaphysically it may be true that the world is itself ambiguous or flexible enough to allow for any trail of ideas. Then the main issue is whether our meandering is constrained at all by nature, that nature is so flexible as to allow for any trail whatsoever, whether "anything goes." But is this not also then an empirical matter? If there are indeed "complementary" trails possible, it will be nature that tells us so.

It is at this point that a Doppeltian-like philosopher of science will step in and say, "Ah-ha! You have identified an absolute: Prefer theories that force interaction with the world." My response is that at this point we see how silly this "relativist challenge at a new level" game gets. Of course 'science' must have a definition. At issue is not whether an identifiable activity of systematically forcing intimacy with nature is an absolute; at issue is whether this activity is better than meditation, palm reading, astrology, and so on, in terms of accomplishing the goal of finding reliable beliefs with which to interface with the natural world. It may not be, but a combination of reason and experience will tell us so.

61. Laudan, 1977, pp. 108-114.

62. This phrase is Laudan's, Ibid., p. 113.

63. 1962, p. 157

64. As we have seen, Feyerabend also assumes an implicit infallibilism in arguing his infamous version of Copernican-revolution-relativism. In addition to assuming that scientific rationality is in trouble because the arguments of Copernicans "were not regarded (his emphasis) as decisive (my emphasis). Nor were (his emphasis) they that decisive (my emphasis) as shown in AM." (Feyerabend, 1978, p.45), typically he fails to distinguish between the developments of the middle and late 16th century and the early to middle 17th century, and the examples he uses jump around between these two epistemologically distinguishable periods of time. In short, like most relativists he commits an epistemological slippery slope in arguing that because early theory pursuit is not the result of overwhelming rationally compelling reasons, so must later acceptance be just a leap of faith.

65. Not of the stars, the primitive level of telescopic observation would have been no help in determining stellar parallax yet. But more accurate measurements of parallax of closer astronomical bodies, and the further weakening of Aristotelian celestial theory (the moon, the sun, and planets as physical places rather than etherial bodies) would surely have affected a man who gave Copernicus a "fair hearing."

66. The language here is borrowed from Duhem, 1954, p. 217. Duhem is not endorsing the rationality of this move, other than to acknowledge that it is "good sense" rather than logic that allows us to see that our buildings are tottering. According to Duhem,

"The day arrives when good sense comes out so clearly in favor of one of the two sides that the other side gives up the struggle even though pure logic would not forbid its continuation." Ibid., p. 218.

Duhem's insights were clearly a contribution to fallibilistic epistemology. The problem with Duhem, as discussed earlier, is that this good sense remains unarticulated; we are given no ampliative theory.

67. The claim implied in my rhetorical question is highly controversial and at his point totally unsupported. In the next chapter, I will show that geoheliocentrism was never fully articulated in terms of producing tables and ephemerides. This was not due only to Tycho's death in 1601, for this model had many supporters and versions (Gingerich and Westman, 1988; Schofield, 1981). However, supporters of this model experimented with rotating the Earth to lesson their system's reliance on a cumbersome dynamics -- a dangerous admission to the supporters of heliostasis and another severe blow to the Aristotelian auxiliary. Even Kuhn admits that,

"Ultimately (Kepler's) version of Copernicus' proposal would almost certainly have converted all astronomers to Copernicanism, particularly after 1627 when Kepler issued the Rudolphine Tables, derived from his new theory and clearly superior to all astronomical tables in use before." Kuhn, 1957, p. 219.

The Rudolphine Tables generated an overall accuracy of planetary positioning 30 times better than any predecessor. It also was the basis for a prediction and Gassendi's successful observation of a transit of Mercury across the face of the Sun on November 7, 1631. According to Gingerich, referring to Kepler's "cleansing and mechanization" of the Copernican system, "For the professionals, this improvement was a forceful testimony to the efficacy of the Copernican system," and "the evidence for the new system was overwhelming." Gingerich, 1993, pp. 329, 342.

68. According to Lakatos, one "may rationally stick to a degenerating program," but "scientific journals should refuse to publish" the papers defending such a program and research foundations should refuse monetary support. (Lakatos, 1978, p. 117.)

69. Emphasis added. Galileo, 1615, from Drake (1957), p. 196.