realism and instrumentalism

8/3/2019 Realism and instrumentalism

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Michael R. Gardner

Realism and Instrumentalism inPre-Newtonian Astronomy

1. IntroductionThere is supposed to be a problem in the philosophy of science called

"realism versus ins t rumenta l i sm." In the version with which I am con-cerned, this suppo sed problem is wh ether scientific theories in general areput forward as true, or whether they are put forward as untrue butnonetheless convenient devices for the prediction (and retrodiction) ofobservable phenomena.

I have argued elsew here (1979) that this prob lem is m isconceived.Whether a theory is put forward as t rue or merely as a device depend s onvarious aspects of the theory's structure and content , and on the nature ofthe evidence for it. I i l lustrated this thesis with a discussion of thenineteenth-century debates about the atomic theory. I argued that theatomic theory was initially regarded by most of the scientific c o m m u n i t y asa set of false s ta tements useful for the deduction and systematization of thevarious laws regarding chemical com bination, therm al phen om ena, etc . ;and that a gradu al trans ition occurred in which the atomic theory came tobe regarded as a literally t rue picture of matter . I claimed, moreover, thatthe historical evidence shows that this transition occurred because ofincreases in the the ory 's proven predict iv e pow er; because of newdete rminat ions of hi ther to indeterm ina te m agni tudes through the use ofm e a s u r e m e n t results and well-tested hypotheses; and because of changesin some scientists ' beliefs about w hat concepts m ay appear in fundamenta lexplanations. I posed it as a problem in that paper whether the same orsimilar factors might be operative in other cases in the history of science;and I sugg ested that it m ig ht be possible, on the basis of an exam ination ofseveral cases in which the issue of realistic vs. inst rum en tal acceptance of aThis materia l is based upon work supp or ted by the Nat ional Science Fo undation und er GrantsN o. SO C 77-07691 and SOC 78-26194. I am grateful fo r c o m m e n t s on an earlier draft byIan Hacking , Geoffrey H e l l m a n , Roger Rosenkrantz , Robert Rynasiewicz and FerdinandSchoeman.

201


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202 Michael R. Gardnertheory has been debated, to put forward a (norm ative) theory of when it isreasonable to accept a theory as literally tru e and when as only a convenientdevice.For simplicity I shall usua lly speak of the acceptance-status of a theory asa whole. But sometimes it will be helpful to discuss individual hyp otheseswithin a theory, when some are to be taken literally and others asconceptual devices.

In th e present paper I wo uld like to discuss a closely analogo us casethetransition, du ring the Copernican revolution, in the prevailing view of theprop er purpos e and correlative mo de of acceptance of a theory of theplanetary motions. I shall briefly discuss the evidencewell known tohistoriansthat from approximately th e t ime of Ptolemy until Copernicus,most astronomers held that the purpose of planetary theory is to permit th ecalculations of the angles at which th e planets appear from the earth atgiven t imes, and not to describe the planets' true orbits in physical space.For a few decades after Copernicus's death, except among a handful ofastronomers, his own theory was accepted (if at all) as only the most recentand most accurate in a long series of untrue prediction-devices. Buteventually the Copernican theory came to be accepted as the literal truth ,or at least close to it. T hat this tr ansitio n occurred is well kno w n; why itoccurred has not been satisfactorily explained , as I shall try to show. I shallthen try to fill in this gap in the historical and philosophical literatu re. Inthe concluding section I shall also discuss the relevance of this case totheses, other than the one just defined, which go by the name "realism."

2. The Instrumentalist Tradition in AstronomyThe tradition of regarding theories of planetary mo tion as m ere devices

to determine apparent planetary angles is usually said to have originatedwith Plato; but it also has roots in the science of one of the first civilizationson earth, that of the B abylon ians. Their reasons for bein g interested in theforecasting of celestial phenomena were largely practical in nature. Suchevents were am ong those used as om ens in the c onduct of gov ernm ent.Pred ictions o f eclipses, for exa mp le, were thus needed to determine thewisdom of planning a major undertaking on a given future date. Inaddition, since the new month was defined as beginning with the newmoon, one could know when given dates would arrive only throughpredictions of new moons. The Babylonians therefore appear to havedeveloped purely arithmetical procedures for the prediction of apparent


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R EALISM A N D I N S T R U M E N T A L I S M 20 3

angles of celestial bodies. Their main technique was the addition andsubtraction of quantities, beginning with some initial value and movingback and forth between fixed limits at a constant rate. Through suchtechniqu es they could forecast such quantities as lunar and solar velocity,the longitudes of solar-lunar conjunctions, the times of new moons, etc.Although numerous tablets have survived showing techniques for thecomputation of such quantities, and others showing the results of thecomputations, we have no evidence that these techniques were based onany underly ing theory of the geometrical structure of the universe(Neugebauer 1952, Chapter 5). Moreover, the arithmetical character of theregu larities in the v ariatio ns of the qu antitie s also sug ges ts tha t thecomputations are based on purely arithmetical rather than geometricalcon siderations. Of course it is possible that the fore casting techniq ues werebased u pon s tatem ents about and/or pictures of the g eom etry of theuniverse that were not committed to clay or that do not survive. But itappears that in Bab ylonian mathem atical astronomyprobably developedbetween about 500 and 300 BC we have an extreme instance of instru-mentalism: not even a theory to be interpreted as a prediction-devicerather than as purportedly true, but only a set of prediction-techniques inthe literal sense.

As I have said, another major source of the in strum entalist tradition inastronomy is Plato. I do not m ean that he w as a source of the instr um en tal-ists' conception of the aims of astronomical theorizing , but rather of theirstrictures upon the permissible means for achieving those ends. Vlastos(1975, pp. 51-52) has assembled from various P latonic works an argumentthat run s as follows: celestial bodies are gods and are m oved by their souls;these souls are perfectly rational; only uniform circular motions befitrationality; hence all celestial m otions are uniform (in speed) and circular.To docum ent this, we m ust note that in Laws Plato (in Hamil ton and Cairns1963) asserted that th e sun's "soul guides the sun on his course," that thisstatem ent is "no less applicable to al l . . . celestial bodies," and that the soulsin question possess "absolute goodness"i.e., divinity (898 C-E). Platorequ ired in the ar gu m en t the tacit assu m ptio n that goodness entailsrationality. H e could then conclude that since bodies "moving regularlyand uniformly in one compass about one center, and in one sense" must"surely have th e closest affinity and resemblance that may be to therevolution of intelligence," celestial mo tions m us t be uniform and circular(898 A-B). Plato was also in a position to argue for the rationality of a


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204 Michael R. Gardnercelestial soul on the grounds that it , unlike our souls, is not associated witha hu m an body, which causes "confusion, and when ever it played any part,would not allow the soul to acquire truth and wisdom." (Phaedo 66A, inBluck 1955)

Tw o clarifications are n eed ed. A lthou gh Plato was not explicit on thepoint, he seems to have assumed that all these circular motions areconcentric with the earth. This is presumably why at Timaeus 36D (inCornford 1957) he says that the circles of the sun, moon, and five (visible)planets are "unequal"so that they can form a nest centered about theearth, as Cornford suggests, (p. 79) Second, we are not to assu m e that these"circular" motions trace out simple circles. Rath er, the complex observedpaths are compounded out of a plurali ty of motions, each of which isuniform and circular. (Timaeus 36 C-D)

A story of uncertain reliability (Vlastos 1975, pp. 110-111) has it thatPlato, perh aps aware of the em pirical inadequ acies of his own the ory ,proposed to astron om ers the problem : "What uniform and orderly motionsmust be h ypoth esized to save the phe nom enal m otions of the stars?"(Simplicius, quoted in Vlastos 1975) The first astronomer to make a seriousattempt to answer this question in a precise way was Plato's studentEudoxus . He postu lated tha t each of the seven "wand ering" celestialbodies was moved by a system of three or four earth-centered, nested,rotating spheres. E ach inne r sphere had its poles attached at some angle orother to the nex t larger sphere. The celestial body itself was located on theequator of the inn erm ost sphere of the system. By adjustments of theangles of the poles and the (uniform) speeds of rotation, Eudoxus was ableto obtain a fairly accurate representation of the motion in longitude(including retrogression) of three planets and the limits (bu t not the times)of the planets' motion in latitude. (Dreyer 1953, pp. 87-103)

In the extan t sources on the E udo xian theory (A ristotle and Simplicius),no mention occurs of any theories regarding the physical properties ofthese spherestheir material, thickness, or mutua l distancesnor on thecauses producing their mo tions. A nd even though the o uterm ost sphere foreach celestial body m ove s with the same period (one day), E ud ox usappears to have provided no physical connections among the varioussystems. (Dryer 1953, 90-91) The (adm ittedly inconclusive) evidencethere fore sugge sts that E ud ox us regarded the spheres no t as actualphysical objects in the heavens, but as geometrical construc tions suitablefor computing observed positions. If this is correct, Eudoxus, the founder


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R E A L I S M A N D I N S T R U M E N T A L I S M 2 0 5

of qua nt i ta t ive ly prec ise geomet r ical as t ron om y, w as also an impor t an tearly instance of some aspects of the ins t rum enta l i s t trad i tion wi th inthat field. B y th is I do not mean tha t E udo xu s denied tha t his theory ist ru e, or even that he w as sceptical of i ts tru th , but only that he appears tohave l imited the aim of as t ronomy to a geometr ical representat ion (notinc lud ing a causal exp lanat ion) of the observed p hen om ena . From thisposition it is only one step to the ins trum en talist view that there cannotbe a causal explanation of the orbits postulated by a given ast ronomicaltheory, and that the theory's descriptions of the orbits are thereforenot true.

Whether Eudoxus held this view about the status of the spheres or not, itis quite clear that A ristotle held the opposite view. In Metaphysics XII , 8,he remarked that in addition to the seven spheres added to the Eudoxiansystem by C allipus for the sake of greater obse rvational accuracy, addi-tional spheres m u s t be intercalated below the spheres of each planet, inorder to counteract the motions peculiar to it and thereby cause only itsdaily motion to be t ransmit ted to the nex t planet below. "For only thus," hesaid, "can all the forces at work produce the observed motion of theplanets." (in M c K e o n 1941, 1073b-1074a) Clearly, then, Aristotle thoughtof the spheres as real physical objects in the heavens , and supposed thatsome of their motions are due to forces transmitted physically from thesphere of stars all the way to the moon.

A t Physics II, 2 Aristotle expressed his realistic view of as t ronomy in adifferent way. H e raised the quest ion,

Is as t ronomy different from physics or a depar tment of it? It seemsabsurd that the physicist should be supposed to know the nature of sunor m o o n , but not to know any of their essential attributes, particularlyas the writers on physics obviously do discuss their shape also andwh e th e r the earth and the world are spherical or not .N ow the mathemat ician, though he too t reats of these things,nev erthe less does not treat of them as the l imits of a physical body, nordoes he consider the attributes indicated as the attributes of suchbodies. That is why we separated them; for in thought they areseparable from m o t i o n . . . .Similar eviden ce is supp lied by the m ore physical of the branchesof mathemat ics , such as optics, harmo nics, and astronomy. These arein a way the converse of geo m etry. W hile ge om etry investigatesphysical l ines, but not qua physical , optics [and, presu m ably, astron-o m y ] invest igates mathemat ical l ines, but qua physical , not quamathemat ical .


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206 Michael R. GardnerAlthough the m essage of this passage is som ew hat amb iguou s, its m ain

point can be discerned. A ristotle tho ug ht that, generally, m athem aticiansdeal with geom etrical objects, such as shapes, as non phy sical entities, andthus they are presumably unconcerned wi th such ques t ions as theconstitution of objects and the forces upon them . A lthough astronom y is abranch of m athem atics, it is one of the mo re ph ysical branches; thu s theforegoing generalization does not apply to astronomers, who must treatspheres, circles, etc. as physical objects. They cannot, then, as anastronomical instru m en talist wou ld say they should, limit their concerns tothe question of whether various geometrical constructions permit correctdeterminations of planetary angles.

The most influential astronomer before Copernicus was, of course,Ptolemy ( f l . 127-150 A D ) ; and it is therefore of considerable interestwhether he regarded his theory as providing a true cosmological pic ture oras only a set of prediction-devices. This question, however, admits of nosimple answer. To some extent, Ptolemy worked within traditions estab-lished by P lato and by A ristotle. E cho ing (bu t not explicitly citing) Plato'spostulate about uniform circular m otion s in the div ine and celestial realm ,he wrote in the Almagest, IX, 2:

Now that we are abo ut to dem on strate in the case of the five planets, asin the case of the sun and the moon, that all of their phenomenalirregularities result from regular and circular motionsfor such befitthe nature of divine beings, while disorder and anomaly are alien totheir natureit is proper that we should regard this achievement as agreat feat and as the fulfillment of the philosophically groundedmathematical theory [of the heav ens]. (Trans. Vlastos 1975, p. 65)

Again, he wrote, "we believe it is the necessary purpose and aim of themathem atician to show forth all the appearances of the heavens as productsof regular and circular motions." (Almagest, III, 1)

Ptolemy followed A ristotle's division of the sciences, but diverg edsomewhat when it came to placing astronomy within it :

For indeed Aristotle quite properly divides also the theoretical intothree immediate genera: the physical, the mathematical, and theth eo lo gi ca l . . . . the kind of science w hich traces throug h the m aterialand ever mo ving quality, and has to do with the white, the hot, th esweet, the soft, and such things, would be called physical; and such anessence [ousia], since it is only generally what it is, is to be found incorruptible things and below the lunar sphere. A nd the kind of sciencewhich shows up quality with respect to forms and local motions,


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seeking figure, n u m be r , and magnitude, and also place, time, andsimilar things, would be defined as mathematical. (Almagest, I, 1)He then remarked that he himself had decided to pursue mathematics(specifically, astron om y), because it is the only science that attains "certainand tru stw orth y know ledge ." Physics does not do so because its subject(sublunar matter) is "unstable an d obscure." (Almagest, I, 1) Ptolemy,then, separated astronomy from physics more sharply than A ristotle did:he held that it is a branch of mathematics and did not say that it is one of the"more physical" branches. Such a claim, indeed, wo uld make no sense inview of Ptolemy's claim that physics deals with th e sublu nar, corruptiblerealm.

Since Ptolemy denied that astronom y is a branch of physics, or even oneof th e m ore physical branches of mathematics, he did not put forward anytheory analogous to Aristotle's of a cosmos unified through the transmissionof physical forces productive of the planetary motions. Rather, he treatedeach planet's motion as a separate problem, and held that th e motions arenot explained in terms of physical forces at all, but in te rms of the individualplanet's essence: "The heavenly bodies suffer no influence from without;they have no relation to each other; the particular motions of eachparticular planet follow from the essence of that planet and are like the willand understanding in m e n . " (Planetary Hypotheses, Bk . II; trans. Hanson1973, p. 132)

But were these "motions" mere geometric co nstructions, or were theyphysical orbits? A key point is that Ptolemy did not claim in the Almagest toknow how to determine the distances of the planets from th e earth or evento be entirely certain about their order: "Since there is no other way ofgetting at this because of the absence of any sensible parallax in these stars[planets], from which appearance alone linear distances are gotten," hesaid he had no choice but to rely on the order of "the earlier mathemati-cians." (IX, 1) Although the angles given by Ptolemy's con structions in theAlmagest are to be taken as purportedly corresponding to phy sical reality,the suppo sed physical distances were left unspe cified. B ut this leaves openthe possibility that Ptolemy thought his constructions gave the physicalorbits up to a scale factori.e. , that they gave the orbit 's shape. Dreyerargues that Ptolemy's theory of the moon, if interpreted in this way,implies that the mo on's distance and there fore apparent diam eter vary by afactor of 2; and Ptolemy (like nearly everyone) m us t have been aware thatno such variation in diameter is observed. (1953, p. 196) A gainst this it must


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208 Michael R. Gardnerbe said that in the Almagest Ptolemy claimed that the moon's distance,un like those of the five planets, can be determ ined from observational datavia his model and that it varies from about 33 to 64 earth radii. (V, 13) Hegave no indication that these numbers were not to be taken literally,despite what he obviously kne w they imp lied about apparen t diam eter. H ealso took the numbers seriously enough to use them (and data on theapparent diameters of the sun, moon, and the earth's shadow) to obtain afigure for absolu te distance to the sun1210 earth radii. (Almagest, V, 15)

A stronger piece of evidence fo r Dreyer's view is Ptolemy's admission inPlanetary Hypotheses: "I do not profess to be able thus to account for all themotions at the same time; but I shall show that each by itself is wellexplained by its proper hypothesis." (Trans. Dreyer 1953, p. 201) Thisquotation certainly suggests that Ptolemy did not think the totality of hisgeometric constructions was a consistent whole, and thus that he could nothave thought that it (that is, all of it) represented physical reality.

Again, discussing the hypothesis that a given planet moves on anepicycle and the hypothesis that it moves on a deferent eccentric to theearth, he claimed: "A nd it m u s t be understood that all the appearances canbe cared for interchangeably according to either hypothesis, when th esame ratios are involved in each. In other words, the hypotheses arein te rchangeable . . . . (Almagest, III, 3) This relation of "interchangeability"is apparently logical equivalence of actual asserted content; fo r whenconfronted with th e identi ty of the two hypotheses' consequences for theappearancesi.e . , planetary angles at all timesPtolemy did not throwup his hands and say he could not decide between them (as would havebeen rat ional had he thought them nonequ iva len t ) . H e straightwaydeclared (in the case of the su n) that he w ou ld "stick to the hypo thes is ofeccentricity w hich is simpler and completely effected by one and not twomovement s . " (Almagest, III, 4) In sum , his argument s in these passagesappear to make sense only on the assump tion that the genuine assertedcontent of the orbital constructions is exhausted by what they say aboutobserved angles.

On the other han d, his use of the lun ar mod el to determ ine d istancesmakes sense only on a realist interpretation. Moreover, his planetarymodels are based part ly on the assumption that maximum brightness(minimum distance) coincides with retrogression because both occur onthe inner part of the epicycle (Pedersen 1974, p. 283); and this reasoningalso presupposes that the model gives true orbits. We can only conclude


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that Ptolemy's attitude w as ambivalent , or at least that the evidenceregarding it is ambiguous .

Whatever we say about P tolemy's atti tude towards the planetary orbits,it would clearly be an exaggeration to say that his theory had no assertedcon tent at all beyond wh at it im plies about observed angles. For Ptolem yexplicitly subscribed, of cou rse, to a cosm ology that placed the earth at restin the center of an inco m parably larger stellar sphe re; and he arg ued forthis conception on the basis of physical considerationssup posed effectsthe earth's motion would have on bodies on or near the earth. (Almagest, I,2 and 7)

Moreover , some of his a rgumen ts are based on physical considerationsregarding the nature of the ether (Almagest, I, 3) and heavenly bodies(XIII, 2)their hom ogen eity , e tern i ty , constancy, i r resist ibi l i ty , e tc .(Lloyd 1978, p. 216) Thus th e theory has considerable (li terally-in tende d)cosmological and physical as well as observational content.

By the t ime he wrote Planetary Hypotheses, Ptolemy had changed hisview about th e possibility of de te rmin ing the distances of the five planetsdespite their lack of visible parallax. He explained his procedure as follows:"We began our in qu iry into the arra nge m ent of the spheres [ i .e . , sphericalshells] with the determina t ion , for each planet, of the ratio of its leastdistance to its greatest distance. W e then decided to set the sphere of eachplanet between the furt hes t distance of the sphere closer to the earth, andth e closest distance of the sphere fur ther (from th e earth)." (Goldstein1967, pp. 7-8) I shall call the assumption decided upon here the "nesting-shell hypothesis": no space between shells. Us ing the ratios mentionedhere and his values for the lu na r distancesbo th supplied by the theory ofthe Almagesttogether with this new hyp othesis, Ptolemy com puted leastand greatest distances for all the plan ets. A nd what was the eviden ce for thenesting-shell hyp othe sis? Ptolem y said only that "it is not conceivable thatthere be in nature a v a c u u m , or any meaningless and useless thing," andthat his hypo thesis (after some ad hoc fiddling with parameters) me ets theweak constraint that it agree with his inde pen den tly m easured value forsolar distance. He was apparently not entirely convinced by the argumenthimself; for he continued: "But if there is space or em ptin ess betwee n the(spheres), then it is clear that the distances ca nno t be sm aller, at any rate,than those mentioned."

To conclude on Ptolemy, then: in his post-Almagest writings, Ptolemyadded a fur the r quanti ty that was to be taken seriously and not just as an


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210 Michael R. Gardnerangle-predictornamely, earth-to-planet distance. But he could com putethe values of this quanti ty from observational data (on lun ar eclipses) on lythrough the use of a hypothesis for which he had almo st no observationalevidence.

In the period between Ptolemy and Copernicus, when Ptolemy'sapproach dom inated astro no m y, i t is possible to dist in gu ish severalpositions concerning the sense (if any) in which Ptolemaic astronomyshould be accepted. One is the v iew sugg ested by some of Ptolem y s ownremarksthat the circles associated with the planets determine onlyobserved angles and not orbits in physical space. A prom inen t exam ple of aperson who h eld such a view qu ite ex plicitly is Proc lus, a fifth-centurycommentator . He indicated that he was alive to the distinction between theinstrumental is t and realist interpretation of Ptolemaic astronomers byasking, "what shall we say of the eccentrics and the epicycles of wh ich the ycontinually talk? A re these only inven tions or have they a real existence inthe spheres to which they are fixed?" He concluded his discussion byconceding that some Ptolemaic system was acceptable at least with th eformer interpretation: "these hypotheses are the most simple and mostfitting ones for the d ivine bodies. T hey were inve nted in order to discoverthe mo de of the p lanetary m otion s which in reality are as they appear to us,and in order to make the measure inherent in these motions apprehend-able." (P roc lus 1909, VII 50 (236, 10); trans. Sambursky 1962, pp. 147-149)E arlier, ho wever, Proclus had given a variety of arg um en ts to show that noepicyclic-eccentric theory could be accepted as genuinely t rue . Forexample, he argued that such a theory, literally interp reted, is "ridiculous"because it is inc on siste nt with the p rincip les of physics he acceptedspeci-fically, those of Aristotle: "These assu m ption s mak e void the generaldoctrine of physics, that every simple motion proceeds either around th ecenter of the universe or away from or towards it." (P roc lus 1903, 248c [III146, 17]; tran s. Sam bu rsk y 1962, pp. 147-149) He argu ed further: "B ut ifthe circles really ex ist, the astronomers destroy their connection with thespheres to which the circles belong . For they attribute separate motions tothe circles and to the spheres and, m oreover, m otions that , as regards thecircles, are not at all equal but in the opposite direction." The point here isthat th e oppositeness of the deferent and epicyclic m otions (for sun andmoon) is physically implausible in view of their spatial interrelations(Proclus 1909, VII 50 (236, 10); trans. Sambursky 1962, pp. 147-149)In ad dition, Proclus gave two ar gu m ents of an epistemological character


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R E A L I S M A N D I N S T R U M E N T A L I S M 2 1 1purport ing to show that we have insufficient evidence to justify acceptanceof any Ptolem aic theo ry on a realistic interpretation. O ne of these is that theheavens are necessari ly beyond the reach of merely human minds : "Butwhen any of these [heavenly] things is the subje ct of investigation, we, whodwell, as the saying goes, at the lowest level of the universe , must besatisfied with 'the approximate.' " (Proclus 1903, I, pp. 352-353; trans.Duhem 1969, pp. 20-21) This argument appeals to the specific character ofast ronom y's dom ain; he bolstered his conclusion with a second epistemolo-gical ar gu m en t that is, in princip le, applicable to othe r scienc es as we ll. It isthat there could be, and in fact are, alternative sy ste m s of orbits (epicycle,eccentric, and homocentr ic) equal ly compat ib le wi th the observed data;hence which of these sets com prises the true physical orbits is unknowab le :"That this is the way thing s stand is plainly show n by the discov eries m adeabout these heavenly thingsfrom different hypotheses w e draw the sameconclusions relat ive to the same objects. . . hypotheses [about] . . . epi-cycles. . .eccentrics. . .counterturningspheres." (Proclus 1903,1, pp. 352-353; trans. Duhem 1969, pp. 20-21)

A com plication in Pro clus's position is that where as he conceded that thePtolemaic theory is useful for predictions, even though it is not physicallyt rue, he did not th ink one can in the long run be satisfied with astronom icaltheories that are only conceptual devices and fail to provide causes: "For ifthey are only contr ived , they have u nw it t ingly gone over from physicalbodies to mathematical concepts and given the causes of physical move-men t s from things that do not ex ist in na tur e." (Trans. Lloyd 1978, p. 205.M y in terpretat ion follows Lloyd, in d i sag reemen t wi th Duh em. )Essentia l ly the same three arguments against realist ic acceptance ofepicycles and eccentricstheir violat ions of physical pr inciples, theimpossibility of human as t ronomica l knowledge, and the existence ofal ternat ive observat ional ly equivalen t theoriesare found in m any wri tersin the period between Pto l emy and C op ern icus . (See D uhe m 1969,pass im.) W e should also take note of one fur ther type of argum ent aga ins taccepting an epicyclic theory on a realist ic interpretat ion: i t is that thetheory thus understood has consequences that have been observed to befalse. Along these l ines, Pontano, a widely read ast ronomer in the earlysixteenth c en tury , argued that if the epicycles were real physical orbits,they would have been fo rmed (like the planets) from "solidification" of thespheres carrying them, and thus would be visibleas, of course, they arenot . (Quoted in Duhem 1969, pp. 54-55)


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212 Michael R. GardnerA m o n g those w ho conceded that the evidence showed Ptolemy's theory

agrees with the observed celestial motionsand was thus acceptable injust that sensewe can dist inguish a subgroup who made it clear that theynonetheless thought that since the theory could not be accepted on arealistic interpretation, it should be replaced with one that could. Somewriters also maintained that such an astronomical revolution would alsoopen the way to the sort of logical reconciliation between astronomy andphysics attempted by Aristotle: real physical orbits, unlike Ptolemaicepicycles, must obey the laws of physics. A n example of such a writer is thegreat Islamic philosopher Averroes (1126-1198):

The astronom er m ust, therefore, construct an astronomical systemsuch that the celestial m otion s are yielded by it and tha t no thin g that isfrom the standpoint of physics imp ossible is impl ied . . . .Ptolemy wasunable to see astronomy on its t rue foundations. . . .The epicycle andthe eccentric are impossible. W e m ust therefore, apply ourselves to anew investigation concerning that gen uine astro nom y whose founda-tions are principles of p h y s i c s . . . . Actually, in our t ime ast ronom y isnonexistent; what we have is something that fits calculation but doesnot agree with what is . (Quoted in Duhem 1969, p. 31)

Another cognitive attitude towards the Ptolemaic theory, held by a fewpre-C opern ican thin ke rs, is that it should be accepted not only as an angle-determiner, but also as literally true. O ne possible argument for such aview is that if the theory (taken literally) were false, it wou ld certainly havesome false observational consequences. The thirteenth-century scholasticBernardus de Virduno (1961, p. 70) gave such an arg um en t: "And u p to ourtime these predictions have proved exact; which could not have happenedif this principle [Ptolemy's theory] had been false; for in every department,a small error in the beginning becomes a big one in the end." (Trans.Du he m 1969, p. 37) A second reason why so m eo ne who accepts aPtolem aic type of theory as at least a conv en ien t device may also accept it ast rue is that he, unlike Proclus, accepts a physical theory with which th eastronomical theory in question is consistent. For example, Adrastus ofAphrodisius and Theon of Smyrna, near-contemporaries of Ptolemy,interpreted an epicycle as the equator of a sphere located between tw ospherical surfaces concentric with the earth. The smaller sphere movesaround the earth between the two surfaces to produce the deferent mo tion,while it rotates on its axis to produce the epicyclic motion. (Duhem 1969,pp. 13-15) These three spheres are evidently to be understood as realphysical objects, since Theon argued that their existence is demanded by


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physical considerations, specifically, the physical impossibility of theplanets' being carried by merely mathematical circles: "the movement ofthe stars should not be ex plained by literally tyin g them to circles each ofwhich mo ves arou nd its ow n particula r center and carries the attached starwith it. After all, how could such bodies be tied to incorporeal circles?"(quoted in Duhem 1969, pp. 13-15) Since epicyclic motions violate th eAristotelian physical principle that all superlun ar mot ions are circular andconcentric with the earth, we can see that Theon rejected Aristotelianphysics and appare ntly as sum ed that the celestial spheres roll and rotate inthe same man ner as terrestrial ones. This, then, is at least part of the reasonwhy Theon would have been unmoved by the Aristotelian physicala rgument s on the basis of which Proclus adopted an ins trumental is tinterpretation of epicycles.L et us sum up our results on the main types of cognitive attitude adoptedtowards the Ptolemaic theory in the period between Ptolemy and Coperni-cus, and the main reasons given in support of these attitudes . O ne possibleattitude, of course, is that the theory should be rejected as even a device fo rthe dete rm ina tion of observed angles. But because of the lack of a superioralternative, Ptolemy's accuracy was generally conceded before Coperni-cus. Another position is that the theory is acceptable as such a device butshould not be accepted on a literal interpretation. Those w ho took this viewgenerally did so on such g rou nds as that the theory (literally interpreted ) isinconsistent with the physics they accepted, deals with a realm whose tru enatu re is inaccessible to hu m an m ind s, fits the observations no better thansome alternative theories, or has false observationa l consequences. Per-sons who thought the theory was a convenient device but was untruesometimes did, and sometimes did not, think it therefore needed to bereplaced by a convenient device that was also a true theory. Finally, somepersons thought some Ptolemaic type of theory gave a correct descriptionof the actual physical orbits. Possible supporting grounds were that falsetheories always have false observational consequences, and that epicyclicorbits are compatible with th e laws of a t rue (non-Aristotelian) physicaltheory.

3. HarmonyIn the period between Copernicus and Kepler, a gradual transition

occurred in the dominant view among astronomers of the purpose andcontent of planetary theory. Eventually certain Copernican theories came


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214 Michael R. Gardnerto be accepted as true descriptions of the actual orbits of the planets inphysical space. Before attem pting to dete rm ine the reasoning involved inthis transition in acceptance-status, I shall explain and criticize w hat I taketo be the most im portant existing attempts to explain the rationale for theacceptance of Copernicus's theory. M o s t of these do not distinguishbetween ins tru m en tal and realistic acceptance and so do not attempt todiscern separate grounds fo r each. Still they pro vide a useful starting pointin dealing with my more "refined" question.

There is a prima facie difficulty in accounting fo r such appeal as theCopernican systemat the t ime of its initial pub lication by Rheticus andCop ernicushad to the scientific com m unity, or even to Copernicus andRheticus themselves . Briefly, the difficulty is that th e most obvious factorsin appraisalsimplicity and observational accuracygive no decisiveverdict in Copernicus's favor. True, Copernicus did say of his theory andcertain of its im plication s, "I th in k it is m uc h easier to concede this than todistract the understanding with an almost infinite multiplicity of spheres,as those who have kept th e Earth in the middle of the U niverse have beencompelled to do." (1976, Book I, chapter 10) As Gingerich (1973a) hasshown by recomput ing the tables used by the leading Ptolemaic astrono-mers of Copernicus's t ime, the familiar story that the y were forced to useever-increasing numbers of epicycles on epicycles is a myth. In fact, theyused only a single epicycle per planet. Since Copernicus's theory oflongitudes used two and sometimes three circles per planet (Kuhn 1957,pp. 169-170), his total number of circlesthe m ost obvious but not the onlymeasure of simplicityis roughly comparable to Ptolemy's. Gingerich'scomputations of the best Ptolemaic predictions of Copernicus's t ime,together with the earliest C opernican predictions and with com putations ofactual positions based on m od ern tables, also enabled him to conclude thatthe latest Ptolemaic and earliest Copernican predictions did not differmuch in accuracy (1973a, pp. 87-89). Ind eed , C ope rnicu s him self con-ceded that except in regard to the leng th of the ye ar, his Ptolem aicopponents "seem to a great extent to have extracted. . . the apparentmotions, with numerical agreement . . . ." (1976, prefatory letter)

Because of the difficulties in using accuracy and simplicity to account fo rthe app eal of the C opern ican sys tem to its early sup po rter s, a tradition hasgrown up am ong highly respectable historian s that the appeal was primar-ily aesthetic, or at least nonevidentiary. Some of Copernicus's remarkscertainly lend themselves to such an interpretation. For example, he


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wrote: "We find, then, in this arrang em ent the marvellous sym m etry of theuniverse, and a sure linking together in harmony of the motion and size ofthe spheres, such as could be perceived in no other way." (1976, Book I,chapter 10) K oyre interprets this passage as reflecting Copernicus'salleged reliance upon "pure intellectual intuition"as opposed, presum-ably, to superior evidence. (1973, pp. 53-54) Similarly, Kuhnwho says(1970, p. vi) Koyre was a principal influence on himremarks that in hismain arguments for his theory, including the foregoing quotation, Coper-nicus appealed to the "aesthetic sense and to that alone." (1957, p. 180)Gingerich falls in with this line when he rem arks that Co pernicus's defen seof his theory in Book I, chapter 10, is "based entirely on aesthetics."(1973a, p. 97)

This interp retatio n of the Copernican revolution may well have been oneof the things that produced th e irrationalist tend encies in Kuhn's generaltheory of scientific revolutionsi.e. , his comparisons of such revolutionsto conversion experiences, leaps of faith, and gestalt-switches. Certainlythe Copernican case is one he frequently cites in such con texts. (1970, pp.112, 151, 158)

4. Positive Heuristics and Novel PredictionsClearly the most effective way to counter such a view is to show that

Copernicus's aesthetic language really refers to his theory's evidentiarysupp ort, the p articular term s havin g perhaps been chosen m erely for ascientifically inessential poetic effect. One attempt to show just this iscontained in a paper by Lakatos and Zahar (1975). They try to show thatacceptance of Copernicus's theory was rational in the light of Lakatos's"methodology of scientific research programs," as modified by Zahar(1973). According to this view, the history of science should be discussed,not it terms of individual theories, but in terms of "research programs,"each of wh ich is a sequence of theories possessin g a com m on "hard core"offundamental assumptions and a "positive heuristic" guiding the construc-tion of varian t theories. One research program will supersede ano ther if thenew program is, and the old one is not, "theoretically" and "empiricallyprogressive." These ter m s mean that each new theory in the series exceedsits predecessor in conten t and also predicts som e "novel" fact not predictedby its predece ssor, and that such predictions are from time to timeconfirmed. (Lakatos 1970, pp. 118, 132-134) It is implicit in this claim thatthe only observational ph eno m ena that have any bearing on the assessment


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216 Michael R. Gardnerof a research program are those that are "novel." A ccordingly Lakatosclaimed that a program's success or failure in accounting fo r non-novel factshas little or no bearing on its assessment. (1970, pp. 120-121, 137)In their joint paper on C ope rnic us, L akatos and Z ahar (1975) use Zahar's(1973) cr iterio n of novelty: a fact is novel with respect to a given hypothesisif "it did not belong to the problem-situation which governed th e con-struction of the h ypo thesis." E lsewhe re (1982) I have argued that adifferent criterion is preferable, but I shall discuss only Lakatos's andZahar's attempt to use this one, and other L akatosian prin ciple s, to give arational rather than aesthetic interpretation of the C opernican revolution.They assert that Ptolemy and Copernicus each worked on a researchprogram and that each of these programs "branched off from the Pythago-rean-Platonic program." Evidently, then, we have three programs todiscuss. N ow the positive heuristic of the last-men tioned program , theysay, was that celestial phenomena are to be saved with the minimumn u m be r of earth-centered motions of uniform linear speed. Ptolemy,however, did not follow this principle, they continue, but only a weakerversion of it, which allowed (epicyclic and eccentric) motions to havecenters other than the earth, and motions to be uniform in angular speedabout a point (the "equant") other than their centers.

It is well known that Copernicus objected to this feature of Ptolemaicast ronomy. (1976, prefatory letter) The objection might be taken asaesthetic in character, and/or as symptomatic of Co pernicus's intellectualconservatism. (Kuhn 1957, pp. 70, 147) But Lakatos and Zahar think theycan show that the objection is reasonable in light of their methodology,which req uires that the positive heuristic of a program provide an "outlineof how to build" sets of auxiliary assum ptions throug h some "unifying idea"which gives the program "continuity." N ew theories that violate thisrequirement are said to be "ad hoc3." (Lakatos 1970, pp. 175-176) Inparticu lar, Ptolem y's use of the eq uan t, be cause it violates the Platonicheuris t ic , is said to be ad hoc3, or to be an example of "heuristicdegeneration." (L akatos and Z ahar 1975, Sec tion 4)

W hat I do not understand is why , from the standp oint of the L akatos-Zahar m ethod ology , it is suppo sed to be an objection to one program that itdeviates from the positive heuristic of an earlier program. I take it that itwou ld not be at all plausible to sayand Lakatos and Z ahar do not seem tobe sayingthat Ptolem y was wo rking on the Platonic research program ,since (despite his use o f circular motion s that are uniform in some sense) his


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assumptions and m ethods were so different from Plato's. If they do want tosay this, they owe us a criterion of identity for research programs thatmakes the claim true. A s matters stand, their criticism of Ptolemy has asmuch cogency as a criticism of Einstein for deviating from the Newtonianheuristic by u sing laws of mo tion analogous but not identical to N ewton's.

They also assert that Copernicus had two further criticisms of thePtolemaic program: (1) that it was un-Platonic in giving two motions to thestellar sphe re, and (2) that it failed to predict any novel facts. But they fail togive any references to support the attribution to Copernicus of (1 ) and (2),which do not appear in his (1976, prefatory letter) principal su m m ar y of hiscriticisms of Ptolemy et al., or elsewhere in his writings, as far as I know.

In at tempting to discern what reasons favored the Copernican programupo n pu blication of On th e Revolutions, Lakatos and Zahar first claim thatCopernicus "happened to improve on the fit between theory and observa-t ion ." (p. 374) W hy they make this claim is puzzling, since relativenumbers of anomalies are supposed, as we have seen, to be irrelevant toth e rational assessment of a research program. In any case, they thenproceed to list a group of facts which they claim to be predictions of theCopernican program that were previously known but novel in Zahar'ssense: (a) the "planets have stations and retrogressions"; (b) "the periods ofthe superior planets, as seen from the Earth are not constant"; (c) eachplanet's motion relative to the earth is complex, an d has the sun 's mo tionrelative to the earth as one com pon ent; (d) the elongation of the inferiorplanets from the sun is bounded; (e) "the (calculated) period s of the planetsstrictly increase with th eir (calculable) distances from the Su n. " (Section 5)

But there are grave difficulties in construing these consequences ofCopernicus 's assumpt ionsas novel in the sense of not being in the problem-situation, the facts he was t rying to account fo r. Ce rtainly (a), (b), and (d)were long-known facts, which any as t ronomer of Copernicus s t ime wouldhave expected any planetary theory to account for. Thus Copernicuscertainly was t rying to account for them. Perhaps Lakatos and Zaharnonetheless th ink that Copern icus designed his theory to account for otherfacts and then discovered to his pleasan t surprise that it also accounted for(a), (b), and (d). But they present not a single argu me nt to show that this wasthe case. Instead they make an entirely irrelevant point: that (a) and (b)follow easily from Copernicus's assumptions. On the other hand, (c) ismerely a result of a coordinate-transformation of Copernicus s theory, not apiece of (independently obtainable) evidence for the theory. Point (e)


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218 Michael R. Gardnerpresents a different problem. Since, as Lakatos and Zahar are aware, thecalculations it refers to are done by means of the Copernican theory, it isimpossible to claim that the correlation (e) describes is a long-knownobservational result that supp orts Copernicus's theory. Since Cop ernicus'stheory provided the first and, at the time, the only reasonably satisfactoryway to determine the planetary distances, there was certainly no questionof a prior or sub seq uen t indep end ent determ ination of the distances,whose agreem ent w ith Cop ernicus's results could supp ort his theory. If hisdetermination of the planetary distances was a crucial consideration in itsfavor (and we shall see later that it was), Lakatos and Zahar have not shownwhyor much (if anything) else about the Copernican Revolution.

5. Simplicity and ProbabilityI now turn to Roger Rosenkrantz's (1977) attempt to give a Bayesian

account of the rationality of pref erring C opernicus's to P tolemy's theorywithin a few decades after the fo rmer was published.

Rosenkrantz is a Bayesian in the sense that h e th ink s that the probabili-ties of hypotheses form the basis for compar ing them , and that probabilityP(H) of hypothesis H changes to P(H/x) when evidence x is obtained, wherethis conditional probability is com puted usin g Bayes's theorem. He is not aBayesian, how ever, in the strong er sense that he thin ks prior prob abilitiesare subjective. Instead he maintains that the objectively correct distribu-tion is to be computed by assum ing that entropy is maxim ized subject togiven constraints. If we have a partition of hypotheses H {, then th e supporteach receives from observation x is defined as the likelihood P(x/H t). ByBayes's rule the po sterior p rob ability is

A s a Bayesian, Rosenkrantz must hold that all supposed virtues oftheoriesin particular, simplicityare such only to the extent that theymanifest them selves somehow in high probabilit ies. His theory of simplic-ity begins from the observation that we make a theory more complex if weadd one or more adjustable parameters. For example,

is less complex than

Moreover , if we take a special case of a theoryby which Rosenkrantz


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seems to mean that we set som e of its free parameters equal to particularvaluesthen we obtain a simpler theory, as when we set c 0 in ourexamples. To make sense of such intuit ion s, Ro senk rantz introduces theconcept of sample coverage of theory T fo r experiment X, defined as "thechance probability that the outcom e of the ex perim ent will fit the theo ry, acriterion of fit being presupposed." (1977, pp. 93-94) A criterion of fit willbe of the form "x e R ," where P (x e KIT) > a, so that outcom es outside acertain hig h-likelihood region are said not to fit T. (1976, p. 169) "A 'chance'probability distribution is one conditional on a suitable null hypothesis ofchance (e.g., an assumpt ion of independence, randomness, or the like),constrained perhaps by background information." In the straightforwardcase in which th e chance distribution is uniform, the sample coverage isjust the proportion of experim ental outcomes which fit the theory. In anycase, simplicity (relative to the experiment, cri terion of fi t , and nullhypothesis) is measured by smal lness of sample coverage (1977, p. 94). Itfollows from this that (1) is simpler than (2 ) relative (e.g.) to an experimentyielding three points (x,y), to a reasonable criterio n of f i t , and to a uniformchance distribution. To deduce this (though R osen kran tz does not say so),we need to make the n u m b e r of outcomes finite by assuming that .t and yhave finite ranges divided into cells correspond ing to the precision ofm eas ur em en t. Then the p ropo rtion of triples of these cells that fall close tosome qu adra tic curve w ill obv iously be larger than the p ropo rtion that fallnear th e subset of such curves that are straight lines.

To see the bearing of this on the evaluation of theories, consider (for easeof exposition) a theory H with adjustable parameter 6 and spec ial cases H,(i = 1, 2 , . . . , n) corresponding to the n possible values of 6. SinceH OHi V . . . . Y Hn,

N ow let H be the //, that maximizes P(x /Ht)i.e., th e best-fitting (best-supported) special case of H. Since P(x/H) is a weighted average ofP(x/H/\H) and quan ti ties that are no greater, we can infer that "H is neverbetter supported . . . than it s bes t-fitting special case," and will be less well-supported if any of its special cases fit worse than H, as happens inpractice. The same conclusion holds if 0 varies con t inuou sly, but the summust be replaced by / P(x/Q/\H) dp (0/H). W e can therefore infer that the


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220 Michael R. Gardnermaxim "simplicity is desirable ceteris paribus" has its basis in the greatersupport which x affords H than H, H being a special case and hences impler . (1977, p. 97)Dissatisfied as we were with the accounts of K u h n and of Lakatos andZahar, R osen kran tz now attem pts to use his theory to show the rationalityof the Copernican revolution. H e represents the Copernican, Tychonic,and Ptolemaic systems for an inferior planet in Figures 1-3 respectively.

Figures 1-3. Reproduced by permission of publisher from Rosenkrantz1977.Since in the Almagest Ptolemy specified no values for the planetarydistances, Rosenkrantz assumes that the distance EC to the epicycliccenter C for planet P is a free param eter, constrained only in that C m u s t lieon the line from the earth to the sun S . Since he wants to ma intain that allspecial cases of the Ptolemaic system fit the angular v ariations of P equallywell, however, he evidently has in mind that the epicyclic radius extendsproportionally as C move s towards S . Fig ure 2 is a special case of Fig ure 3,and "can be t ransformed into an equivalent heliostatic picture by thesimple device of fixing S and sending E into orbit around S (Figure 1)."Thus Copernicus's theory is a special case of Ptolem y's. Con sidering onlyobse rvation s of plan etary angles, all the special cases are equ ally wellsupported. Hence the Ptolemaic system (with free param eter) has exactly


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R E A L I S M A N D I N S T R U M E N T A L I S M 221the same support as any of its special cases, including Figure 1. But if weconsider Galileo's famous telescopic observation that V en us has a full set ofphases, the only special cases of Figure 3 that fit at all well are those thathave P m o v i n g in a circle centered (at least approximately) at S , as in Figure2 or the "equiva len t" Figure 1. (See K u h n 1957, Figu re 4 4.) ThusCopernicus 's system is much better supported than Ptolemy's, whosesupp ort is obtained by averaging that of C opernicus's theory w ith m anymuch smal ler numbers . (1977, pp. 136-138) Note that this Bayesian viewdenies that there is any importance in the fact that the n ature of V enu s'sphases followed from a theory proposed before they were observed. Cf. thecom m on opp osite op inion of L akatos and Z ahar 1975, p. 374 and K uh n1957, p. 224.

There are a number of simplifications in Rosenkrantz 's version of thehistory. As he is aware (1977, pp. 156-159), all three ast ronom ical systemswere mo re complex than F igures 1-3 show, and they did not fit the angulardata equally well. Let us assum e that these simplifications are designed toenab le us to concen trate on es tablishing the significance of the phases ofVenus . This aside, one difficulty immediately strikes one. How couldCopernicus 's theory possibly be considered a special case of Ptolemy's,given that one asserts and the other denies that the earth moves? It wouldbe irrelevant and false to say (and Rosenkrantz does not) that from arelativistic stan dpo int there is no dist inction, since we and Rosenkrantz(1977, p. 140) are t ry ing to art iculate the underlying basis of the pro-Copernican argum ents g iven in Copernicus 's t ime. A s far as I know, no onein the period covered by this paperspecifically, no one before Descar-tesheld that all m otio n is relativ e. A nd anyw ay, both special and ge neralrelativity dis t inguish accelerated from unaccelerated frames of reference,and C ope rnicus said the ea rth is accelerated. N or can we say Cop ernicus'stheory is a "special case" of Ptolemy 's , m eaning ju st that it has a smallersample coverage; for Rosenkrantz ' s a rgument for the greater support ofsome special case requires defining "special case" as above in terms offixing one or m ore par am eters . But we cannot get a m oving earth by fixingthe position of C in a geostatic theory.

There is an easy way for Rosenkran t z to neu tralize this objection. A ll hehas to do is to replace the one-parameter theory of Figure 3 by a new theoryobtained by dis joining it with its t ransform at ion into a heliostatic system .Then the dis junct ion of the Copernican and Tychonic system s does becomea special case of the new theoryand, indeed, the best-fitting special case.


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222 Michael R. GardnerThis change would cohere well with Rosenkrantz ' remark that whatGalileo's observations did is to narrow "the field to the Copernican andTychonic alternatives." (1977, p. 138)We can now face the really serious problems with Rosenkrantz 'saccount. The first is that Copernicus did not in fact take him self to be facedwith a Ptolemaic alternative with a free parameter EC. (1976, prefatoryletter ; Bk. 1, chap . 10) For he w as well aware of the lon g tradition am on gPtolemiac astronom ers (section 2 above) of determ ining EC on the basis ofthe n esting-she ll hypo thesis. His objection to them on this score was notthat EC was unspecified, but that it was specified on the basis of an"inappropriate and wholly irrelevant," "fallacious" assu m ptio n that causedtheir argum ents on planetary order and distances to suffer from "weaknessand uncer ta inty ." In effect, Rosenkrantz has loaded the dice againstPtolemy and friends by inserting into their theory a nonexistent freeparameter that lowers its support . He therefore fails to give an adequateanalysis of the reasons why C oper nicus attribu ted such imp ortance to therelative merits of his and Ptolemy's determinat ions of the planetarydistances.The second serious problem with R osen krantz 's account is that he fails toconsider the bearing of the supposed prior probabilities of the Copernicanand Ptolemaic theories on their evaluation. He writes that "simplificationsof the Copernican system" such as the supposed one un de r discussion "arefrequently cited reasons for preferring it to the Ptolemaic theory. Yet,writers from the t ime of Copernicus to our own, have uniformly failed toanalyze these simplifications or account adequately for their force. TheBayesian analysis. . . fills this lacuna in earlier accounts. . .." (1977, p. 140)B ut his Bayesian analysis asserts that preference among theories isgoverned by their probab ilities, and sup po rt mu st be com bined via Bayes'stheorem with the prior probabilities of the theories and data to yield theposterior probabilities. A nd Ro senkrantz gives no indication of how thesepriors are to be computed from th e maximum entropy rule (what con-straints are to be used, etc.). N or does he show how to compute th enumerical values of the con ditional probabilities so that the Bayes-theoremcalculation can actually be don e. Finally, he n eglects to say wh at nu llhypothesis of chance and what background information define the chancedistribution.

The last argume nt by R osen kran tz (1977, pp. 143-148) we shall considerrelates to a crucial passage by Co pernic us (1976, Book I, chapter 10), w hichI shall discuss later:


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R E A L I S M A N D I N S T R U M E N T A L I S M 2 2 3W e find, then, in this arrangemen t the marvel lous symm etry of theunive rse, and a sure link ing together in harm ony of the m otion andsize of the spheres, such as could be perceived in no other way. Forhere one may understand, by attentive observation, why Jupiterappears to have a larger progression and retrogression than Saturn,and smaller than Mars, and again w hy Ve n u s has larger ones thanM ercury; why such a doub ling back appears mo re frequ ently in Saturnthan in Jupi ter , and still more rarely in M a rs and Venus than inMercury; and fur thermore w hy Saturn, Jupiter and M a rs are nearer tothe E arth w hen in oppo sition than in the region of their occu ltation bythe Sun and r e - a p p e a r a n c e . . . . A ll these phenomena proceed fromthe sam e cause, wh ich lies in the m otion of the E arth . (C opern icus1976, Bk. I, chap. 10)

Rosenkrantz attempts to explain the force of the part of this argumentwhich concerns the frequencies of retrogression as follows:

. . .wi thin the Ptolemaic theory, the period of an outer planet'sepicycle can be adjusted at will to produce as many retrogressions inone circuit of the zodiac as d e s i r e d . . . . while both theories fit thisaspect of the data, the C opernican theory fits only the actuallyobserved frequency of retrogression for each p l a n e t . . . . Hence , . . .qua special case of the geostatic theory , the heliostatic theo ry is againbetter supp orted . (R osen kran tz 1977, pp. 143-148)

Let us handle the problem about "special case" as above, so that theargument is understood (as Rosenkrantz intends) as being for the disjunc-tion of the C opern ican and Tychonic theories. W e can then easily see thatthe a rg u m e n t fails for essentially the same reason as Rosenkrantz ' sargument conc erning the planetary distances. The b est P tolemaic theory ofCopernicus 's t ime did not, of course, m erely assert that a given planet hasone epicycle with some radius and some period. If this theory had beenexistentially quantified in this way, it would not have sufficed for thecom putation of the tables of observed positions, which C opernican astron-omers soug ht to improve u pon. Similarly, the C opernican theory could notfit jus t the observed frequencies of retrogression withou t specifying theradii and periods of the planets' re volutio ns. O bviously, then , Ro sen kran tzis making an irrelevant and unfair comparison: between th e Copernicantheory with its specifications of radii and speeds, and a P tolem aic theoryweaker than Copernicus's real rival because of existential quan tificationover its fixed parameters. To obtain a Copernican account of the durat ionsand ang ular wid ths of the retrograde mo tions, we need to specify radii andspeeds; and we get a Ptolem aic account of the same appearances if wespecify the comparable quantities.


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224 Michael R. GardnerI also cannot see why Rosenkrantz thinks his Bayesian account explains

the basis of Copernicus's claim that his theory exhibits a "symmetry of theuniverse , and a sure linkin g together in harm ony," or in Rosen krantz'sterm s an "economy of ex plan ation ." Cope rnicus, as he exp licitly said, wasevidently referring to the fact that his theory explains a wide variety ofphenomena on the basis of the hypothe sis that the earth moves. M etaphor-ically, his theory "symmetrizes" or "harmonizes" these phenomena. B utthis virtu e o f his theory has noth ing to do with the sup posed fact that histheory is com patible only with certain specific observations. It could havethis latter proper ty even if it accounted for different sets of theseobservations on the basis of entirely different hypotheses.

To sum up then: despite the considerable merits that Rosenkrantz'sBayesianism has in connection with other problems in the philosophy ofscience, I do not think it helps us understand the Copernican revolution.

6. BootstrapsThe last published account of the Copernican revolution I shall discuss is

based on Glymour's presentation of what he calls th e "bootstrap strategy"of testing, which he says is a common but not universal pattern in thehistory of science. (1980, chapter 5) Briefly and informally, the strategy isthis. One confirms a hypothesis by verifying an instance of it, and oneverifies th e instance by measuring or calculating th e value of each qua ntitythat occurs in it. In calculating values of quantit ies not themselvesmeasured, one may use other hypotheses of a given theoryi.e. , thetheory can "pull itself up by its bootstraps." However, no hypothesis can beconfirmed by values obtained in a manner that guarantees it will besatisfied. W e cannot, then, test "F = ma" by measuring m and a and usingthis very law to calculate F; whereas we can use this procedu re to obtain avalue of F to substitute into "F = GMm/r2" along with m easured values ofM, m , and r, and thereby test the latter law. So, Glymour concludes,Duhem-Quine holists are right in ma intainin g that hypotheses can be usedjointly in a test, but mistaken in concluding that the test is therefore anindiscriminate one of the entire set. The described procedure, e .g . , usestwo laws jointly, but tests only the latter.

The falsification of an instance of a hypothesis may result solely from thefalsity of other hypotheses used in testing it . Again, confirmation mayresult from comp ensatory errors in two or more hypotheses. Hence there isa demand fo r variety of evidence: preferably, a hypothesis is tested in many


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different waysi .e . , in conjunct ion wi th m any different sets of addit ionalhypotheses. Preferably also, these addit ional hypotheses are themselvestested.A s G l y m o u r points out , his strategy of test ing makes it possible toun de rsta nd , e. g. , why T hirring's theory of gravitation is not taken seriouslyby physicists. I t contains a quanti ty

which can be calculated from m easu rem ents using rods, c locks, testparticles, etc. But the quant i t ies i]; and T)^ can be nei ther measured norcalculated from quantities that can. Either may be assigned any valuewhatsoever , as long as compensatory changes are made in the other . W emigh t express this by saying these quant i t ies are indeterminate: nei thermeasurable nor computable from measured quanti t ies via well-testedhypotheses . Consequent ly no hypotheses containing them can be con-f i rmed, and Thirrings's theory is rejected.1

G l y m o u r a t tempts to establish the importance of the bootstrap strategyby sho w ing that it played a role in a variety o f episodes in the histor y ofscience. He also applies it to the comparison of the Ptolemaic andCopernican planetary theories, but says that in this case (unlike his others)his arg um en ts are m ere ly intend ed as i l lustrative of the strategy and not ashistorically accurate acco unts of argu m en ts actually given around Co perni-cus's t ime. (Glymour 1980, chapter 6) I shall therefore not discuss herewhat Glymour does, but I shall consider instead to what extent thebootstrap strategy is helpful in enabl ing one to see the basis of Copernicus 'sow n argu m ents against Ptolemaic ast ronom y and in favor of his ow n theory.Copernicus gives a helpful s u m m a r y of his negat ive a rguments in hisprefatory let ter:

. . . I was impelled to think out ano ther w ay of calculating the m otionsof the spheres of the universe by no thing else than the realisation tha tthe math emat i c i ans t h emse lves are inconsi s ten t in invest igat ingthem. For first, the m athem aticians are so un ce rtain of the mo tion ofthe Sun and Moon that they cannot represent or even be consistentwith the constant len gth of the seasonal year. Second ly, in establishingthe m otions both of the Sun and M oon and of the other five wander ingstars they do not use the same principles or assumptions, or explana-t ions of their ap paren t revo lutions and m otions. For som e use onlyhomocentric circles, others eccentric circles and epicycles, fromwhich however the required consequences do not completely follow.


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226 Michael R. GardnerFor those who have relied on hom oce ntric circles, a lthough they haveshown that diverse motions can be constructed from them, have notfrom that been able to establish a ny thin g certain, w hich wouldwithout doubt correspond w ith the phen om ena. B ut those who havedevised e ccen tric circles, althou gh they seem to a great ext en t to haveextracted from them the apparent motions, with numerical agree-m ent, nevertheless have in the process adm itted m uch which seemsto contravene the first principle of regularity of motion. Also they havenot been able to discover or deduce from them the chief thin g, that isthe form of the univ erse, and the clear sy m m etr y of its parts. They arejust like someone including in a picture hands, feet, head, and otherl imbs from different places, well painted indeed, but not modelledfrom the same body, and no t in the least matc hing each other , so that amo nster would be produced from them rather than a m an. Thu s in theprocess of their de m on stratio ns, wh ich they call their sy stem , they arefound either to have missed out something essential, or to havebrought in something inappropriate and wholly irrelevant, whichwould not have happened to them if they had followed properprinciples. For if the hypotheses which they assumed had not beenfallacious, everything which follows from them could be indisputablyverified. (1976, p. 25)

A s C opern icus said more explicitly elsewhere, his first point is that hisoppo nents had inacc urate theories of the precession of the equinox es,wh ich (w ith the solstices) de fine the seasons. (1976, Book III, chapters 1,13) In particular, Ptolem y attem pted to define a constant year by referenceto the equinoxes, failing to account for the supposed fact that they recu r (asCo pernicus tho ug ht) at uneq ual inter vals, and that only the sidereal year(with respect to the stars) is co nsta nt. C ope rnicus's second com plaint is thathis opp one nts d isagreed a m on g them selv es in regard to the use ofhomocentric spheres as against epicycles and eccentrics. Moreover, heargued, those who used hom ocentrics had failed to achieve observationalaccuracy, because "the pla ne ts. . . appear to us some tim es to mo un t higherin the heavens, sometimes to descend; and this fact is incom patible withthe principle of concentricity." (Rosen 1959, p. 57) C ope rnicu s un do ub t-edly was referr ing here not to variations in plan etary latitude, whose limits(but not t imes) E udox us could account fo r (Dreyer 1953, p. 103), but tovariations in planetary distance ("height") and brig htne ss, a long-stand ingproblem for hom ocentrics. A lthoug h those who used epicycles and eccen-trics (realistically inte rpr ete d) could hand le this prob lem , they also usedthe eq uan t, which violates the principle that the basic celestial m otion s are


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of uniform linear speed and which m akes their system "neither sufficientlyabsolute nor sufficiently pleasing to the mind." (Rosen 1959, p. 57)

A t first glance, it seems difficult to be sympathetic to this last argu-mentthat is, to try (like Lakatos and Zahar) to find some generallyacceptable pattern of scientific reason ing in to which it fits. K uh n explainspart of what is going on at this point when he says that here Copernicusshowed himself to be intellectually conservativeto feel that on thisquestion at least "our ancestors" were right. (Copernicus, in Rosen, 1959,p. 57) Copernicus also evidently felt that his principle of uniformity had a"pleasing" intellectual beauty that lent it plausibility. The principle alsoderived some of its appeal from the false idea that trajectories that "passthrough i r regular i t ies . . . in accordance with a definite law and with fixedreturns to their original positions" must necessarily be compounded ofuniform circular motions. Finally, he had arguments based on vague,implicit physical principles: irregularity would require "changes in themoving power" or "unevenness in the revolving body," both of which are"unacceptable to reason." (Copernicus 1976, Book I, chapter 4) Theprinciple of uniform circularity does, then, rest after all upon considera-tions of a sort generally con sidered scientifically respectable: theoreticalconservativism, theoretical beauty, mathematical necessities imposed bythe p heno m ena, and consistency with physical principles and conditions.

In the rem ainde r of the long quotation above, Co pernicus m ade a fourthand a fifth critical point, w ithout d isting uish ing them clearly. The fourth isthat his opponents were not able satisfactorily to compute from theirprinciples (toge ther, pre sum ably , with observational data) the distances ofthe planets from the earth and therefore the overall arrangement ("form")of th e planetary system. They either omitted these "essential" quantitiesaltogether, or else computed them using an "inappropriate" and "irrele-vant" assumptionviz. , the nes ting- she ll hyp othe sis (stated and criticizedexplicitly in Book I, chapter 10).

It is plain that we can interpret this Copernican criticism (which heregarded as his most important"the chief thing") in the light of theprinciple, suggested by Glymour 's theory, that it is an objection to theacceptance of a theory that it contains indeterminate quant i t iesi.e . ,nonmeasurable quantities that either cannot be computed from observa-tional data at all, or canno t be co m puted via well-tested hy poth eses. I wishto leave it open for the moment, however, whether we ll-testedness in theCopernican context can be interpreted on the basis of Glymour 's approach.


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228 Michael R. GardnerLet us first consider why Copernicus thinks his own theory avoids his

fourth objection to Ptolem y's. C opern icus showed how to use his heliostat-ic system of orbits, together with such data as the m axim um angle betweenan inferior planet and the sun , to compute the relative distances betweenthe sun and each planet. (1976, Book V; see also Kuh n 1957, pp. 174-176)He was referring to this fact about his theory when he said that it "linkstogether th e arrangement of all the stars and spheres, and their sizes, andth e very heaven, so that nothing can be moved in any part of it withoutupsett ing the other parts and the whole u niv ers e." (1976, prefatory letter)Contrary to K uhn , this argument has little if anything to do with "aestheticharmony, " but concerns the determinateness of quanti t ies. B ut were thehypotheses used to obtain the radii of these orbits well tested in a way inwhich the nesting-shell hypothesis w as not? A nd does the bootstrapstrategy describe this way? O r does the more familiar hypothetico-deductive (H D) strategy round ly cri ticized by Glymour (1980, chapter 2)provide a better basis for the comparison?

One of the cardinal points of the bootstrap strategy is that a hypothesiscannot be confirmed by values of its quantities that are obtained in amanner that guarantees they will agree with the hypothesis. By thisstandard the nesting-shell hypothesis was almost entirely untested. E xceptfor the case of the sun (see section 2 ), P tole m y had only one way to com puteplanetary distancesvia the nesting-shell hypothesisand there w astherefore no w ay he could possibly obtain planetary distances that wouldviolate it. If we ignore the difficulties in stating the HD method and followour i n tu i t i ons about it , we will say similarly that the nest ing-shel lhypo thesis was untes ted by H D standard s; for it was not used (perhap s inconjunction with other hypotheses) to deduce observational claims whichwere then verified. Ptolemy adopted it on the entirely theoretical groundthat a vacuum between the shells is impossible (section 2 above).

But were the hypotheses Copernicus used in computing planetarydistances well testedand, if so, in what sense(s)? Let us begin with hisprincipal axiom that the earth mo ves (in a specified w ay). In his prefa toryletter Copernicus had made a fifth and last criticism of his oppo ne nts: thatthey treated the apparent motion of each planet as an entirely separateproblem rather than exhibiting the "symmetry" or "harmony" of theuniverse by ex plainin g a wide variety of plane tary phe no m ena o n the basisof a single assumption used repeatedly. A s the long qu otation in section 5(above) makes clear, Copernicus thought that his own theory did have this


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particular sort of uni ty . Essent ia l ly his claim w as that his hypothesis Econcern ing the actual m otion (arou nd the su n) of the earth is used inconjunction with his hypothesis P^ describing the actual motion of eachplanet k in order to deduce a description O /< of the observed motion ofplanet k.

(* ) E E EP I P 2 P 3.-.Q! :.O2 .-.O,3, etc.

From the O^'s one can deduce various relat ions among the planets' sizesand f requencies of retrograde loops, and the correlation of max imumbrightness with opposit ion in the case of the superior planets. One ofCo pernicus's m ain argum en ts for his theory , th en , is that is very welltested in that i t is used (in con junction with other hyp otheses) to deducethe occurren ce of al l these observe d p hen om en a. A s he put i t : "All thesephenomena proceed from the same cause, which lies in the motion of theEarth." (Copernicus 1976, Book I, Chap. 10)A lthough Copern icus did notsay so explici t ly, the p he no m en a he l isted are n ot only nu m er ou s, but alsovaried. Perhaps the phrase "all these phenomena" was in tended to expressthis . A nd althou gh he invoke d no cri terion of variety explici t ly, a criterionthat his a r g u m e n t satisfies is: the derivat ions (* ) provide varied tests for because different sets of hypotheses are conjoined with to deduce theOj. s. In any case, the appeal in the a rgumen t from "harmony" is not merelyto the "aesthetic sense and to that alone" (Kuhn 1957, p. 180), but to thenature of the observat ional support for the hypothesis .

Despite the cogency of Copernicus 's argument , Ptolemy could havemade the reply that each of his de term ination s of a plane tary angle wasbased on the hypothesis that the earth is stationary at the approximatecenter of the p lanet 's m otio n, and that his hypo thesis was therefor e welltested in the same way was. But I am ju st t rying to discern Copernicus'stest ing strategy, and so shall ignore possible replies to it .

N ow in some respects the argument from h armony sounds like thebootst rap st ra tegy in opera t ion : for Glymour 's principle of variety ofevidence also favors a hypo thesis that is tested in m ore w ays (other thingsbeing equal) , where the ways are ind iv idua ted by the sets of additionalhypotheses used in the test. But the bootstrap strategy requires them easu rem en t or compu tation (using other hypotheses) of every quant i tyocc urring in a hyp othesis in order to see if it holds in a given in stan ce . A nd


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230 Michael R. Gardnerthis does not appear to be what Copernicus had in mind in the argument weare discussing. W e are not to observe the apparent position of some planetk at some time and then use this in conjunction w ith P^ to compute th eactual position of the earth at that time to see if holds then. Rather, thedeductions are to proceed in the opposite direction: the "phenomenaproceed from the cause" E, as Copernicus put it, and not vice versa. Hismethod here is hypothetico-deductive, and involves no bootstrapping.That Copernicus thought his argument for the earth's motion was HD isalso show n clearly by his state m en t (1976, Book I, chapter 11): "so m an yand substantial pieces of eviden ce from the w ande ring stars agree with themobility of the Earth. . . the appearances are explained by it as by ahypothesis."

The set of deduct ions (* ) can be thought of as parts of HD tests not only ofE, but also of the descriptions P^ of the motions of the other planets. These,how ever, are not tested as thor ou ghly by (* ) and the relevant data, each onebeing used to obtain only one of the O^ . But Copernicus also had othertests aimed more directly at the P / , , and they tu rn out to involve a complexcombination of bootstrapping and hypothetico-deduction. We can illus-trate his procedure by examining his t rea tment of Saturn (Copernicus1976, Book V, chapter 5-9), which has the same pattern as his treatm en t ofth e other tw o superior planets, (see also Armitage 1962, chapter 6.) Hebegan w ith thr ee longitud es of Sa turn observed at opposition by Ptolem y.He then hypothesized a circular orbit for Saturn eccentric to the earth's.From these data and hypotheses he deduced the length and orientation ofthe line betwe en the two orbits' centers. He then repeated the procedureusing three longitudes at opposition observed by himself, and noted withsatisfaction that he obtained about the same length for the line between thecenters. (Its orien tation, how ever, seemed to have shifted considerablyover the interven ing centuries.) This is a boo tstrap test o f his hypothe sis hconcerning th e length of the line. He used one triple of data and otherhypotheses to obtain the quanti ty (length) in h. To have a test, the lengthhad then to be obtained in a way that could falsify h; hence he used anothertriple of data and the sam e auxiliary hypotheses, computed the lengthanew, and thereby verified h.

This bootstrapping was only a prelim inary step. Copernicus's final movewas to use the computed length and orientation of the line between thecenters to construct what he considered an exact description P 5 of Saturn'sorbit (with one epicycle), and showed that P 5 and E yield (very nearly) the


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R E A L I S M A N D I N S T R U M E N T A L I S M 231triples of data: "A ssumin g these [comp uted values] as correct and borrow-in g them for our hypothesis, we shall show that they agree with theobserved appearances." (Book V, chapter 5) The positive results gaveCopernicus sufficient confidence in P 5 to use it (with ) to constructextensive tables of observed positions fo r Saturn.

This pro ced ure is som ewh at peculiar, since Co pernicus u sed the verysame triples of data to obtain some of the parameters in P,5 and also to testP , 5 . Still the exercise is nontrival since (a) one of the parameters could beobtained from either triple of data; and (b) the additional param eters of P 5might have resulted in inconsistency with the original data.

Peculiarities aside, the final step of the procedure is plainly HD:deducing from P 5 and values for certain angles, comp aring these w ith thedata, and finally conclud ing that the hypotheses, because they agree "withwhat has been found visually [are] considered reliable and confirmed."(1976, Book V, chapter 12)

In argu ing that Co pernicus's m ethod w as m ainly the H D and not thebootstrap, I have not been a rgu ing against G lym ou r. For he freely admits(1980, pp. 169-172) that despite the difficulties in giving a precisecharacterization of the HD strategy, a great m any scientists have nonethe-less (somehow) managed to use it. What, then, are the morals of my story?The first moral is that the principle suggested by the bootstrap strategy,that ind ete rm ina te q uan tities are objectionab le, has a range of applicationthat tran sce nd s the applicability of the boo tstrap concept of we ll-tested-ness. That is, we can see from Copernicus's arguments concerning th eplanetary distances that the computabili ty of quantit ies from measuredones via well-tested hypo theses is considered desirable even if the testingin que stion is done m ainl y by the HD me thod. Indeed, Copernicus himselfmad e this connection between the HD method and determinateness whenhe wrote that if his hypothesis is adopted, "not only do the phenomenaagree with the result, but also it links togethe r the arr ang em en t of all thestars and spheres and their sizes. . . . " (1976, prefatory letter) Unfortu-nately the rationale for this principle w ithin th e bootstrap strategy that itssatisfaction mak es tests possible or make s them betteris unavailable in anHD framework. What its rationale there might be I do not know.

To say exactly when a hypothesis is well tested in HD fashion would be atask beyond my means. B ut Copernicus 's arg um ent for a mo ving earth doesat least suggest one principle whose applicability in othe r historica l cases isworth examiningnamely, that a hypothesis is better tested (other things


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232 Michael R. Gardnerequal) if it is used in conjunction with a larger number o f sets o f otherhypotheses to deduce statements confirmed by observation. This principleof variety of evidence has a rationale similar to the one G lym our gives fo rhis: that its satisfaction reduces the chance that one hypothesis is HD-confirmed in conjunc tion with a set of others only because of compensatoryerrors in them both.

7. Copernicus's Realistic AcceptanceHaving completed our survey of various ways of accounting fo r such

acceptance as the Copernican theory enjoyed down through th e t ime ofGalileo, and hav ing mad e some pr elim inar y sugg estions about why thetheory appealed to its author, I should now like to refine the problem byasking whether various astronom ers accepted the theory as true or as ju st adevice to determine observables such as angles, and what their reasonswere. I shall begin with Copernicus himself.

It is wel l known tha t the ques t ion of Copern icus ' s ow n att i tudeconcerning the status of his theory was initially made difficult by ananonymous preface to D e Revolutionibus, which turn ed out to have beenwritten by Osiander. The preface rehearses a number of the traditionalarguments discu ssed earlier against the accep tability of a plan etary the ory(Cop ernicus's in this case) on a realistic inte rpr etatio n: that "the tru e lawscannot be reached by the use of reason"; that the realistically interpre tedtheory has "absurd" observational conseque nces e.g. , that V enu s's ap-parent diameter varies by a factor of four (Osiander ignored th e phases'compensatory effect.); and that "different hypotheses are sometimesavailable to explain one and the same motion." (Copernicus 1976, pp. 22-23) Hence, Osiander concluded, Copernicus (like any other astronom er)did not put forward his hyp othes es "w ith the aim of per suad ing anyo ne thatthey are valid, but only to provide a correct basis for calculation." A nd forthis purpose it is not "necessary that these hypo theses should be tru e, norindeed even probable." However, the older hypotheses are "no moreprobable"; and the newer have the advantage of being "easy." W e shouldnote that there is an ambivalence in O siander's p osit ion. A t some points heseems to be saying that wh ile Cope rnicus's theory is at least as probable asPtolemy's, we are unc ertain and should be u ncon cerned w hether i t or anyastronomical theory is true . B ut at other p oints he seems to be saying thatthe new theory is plainly false.

Despite Osiander's efforts, as he put it in a letter, to "mollify the


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R E A L I S M A N D I N S T R U M E N T A L I S M 2 3 3pe ripa tetics and theologians" (Rose n 1959, p. 23), it is qu ite clear thatCo pernicus believed that his hypothesis that the earth moves (leaving asidefor the mo men t some of his other assertions) is a literally tru e statem ent andnot ju st a con ven ient device. For exam ple, in his stateme nt of his sevenbasic assum ptions in Commentariolus, he distinguished carefully betweenthe apparent motions of the stars and sun, which he said do not in factmove, and the actual motions of the earth, which explain these mereappearances. (Rosen, pp. 58-59) Moreover , he felt compelled to answer theancients' physical objections to the earth's motion, which would beunnecessary on an inst rum ental ist interpretation of this hypo thesis . (1976,Book I, chap. 8)

Unconvinced by such evidence, Gingerich claims that Copernicus'swri t ings are in general ambiguous as to whether his theory, or al lastronomical theories, are put forth as true or as only computational"models." However, Gingerich holds that in at least three places, Coperni-cus was clearly thinking of his geometrical con structions as mere models"with no claim to reality": Copernicus sometimes mentioned alternativeschemes (e .g . , an epicycle on an eccentric vs. an eccentric on an eccentric)and "could have hardly claimed that one case was more real than theother"; and he did no t use the same constructions to account for the planet 'slatitudes as for their longitudes. (Gingerich 1973b, pp. 169-170)

But the mere fact that someone mentions alternative theories does notshow that he thin ks that neither is truei.e., that each is a mere device.He may simply think the available evidence is insufficient to enable one todecide which is true. Contrary to Gingerich, such an attitude towardsparticular alternatives is no evidence of a tendency in Copernicus to thinkthat all his con

realism and instrumentalism

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