Galileo’s Interventionist Notion of ‘Cause’

Galileo’s Interventionist Notion of ‘‘Cause’’

Steffen Ducheyne

1. INTRODUCTION

In this essay, I shall take up the theme of Galileo’s notion of cause, whichhas already received considerable attention.1 I shall argue that the partici-pants in the debate as it stands have overlooked a striking and essentialfeature of Galileo’s notion of cause. Galileo not only reformed natural phi-losophy, he also introduced a new notion of causality and integrated it inhis scientific practice (hence, this new notion also has its methodologicalrepercussions). Galileo’s conception of causality went hand in hand withhis methodology (see section 3). Galileo’s new notion of causality wasclosely intertwined with a new conception of how to discover causal rela-tions. His new notion of causality focused on heuristics rather than on on-tology. This is the main message of this essay. It is my claim that Galileowas trying to construct a new scientifically useful notion of causality. Thisnew notion of causality is an interventionist notion. According to such anotion, causal relations can be discovered by actively exploring and manip-

The author is Research Assistant of the Research Foundation—Flanders (FWO—Vlaanderen). I am indebted to Erik Weber, Eric Schliesser and Paolo Palmieri, and theanonymous referee for making some interesting points that allowed me to improve thisessay.1 For two of the earliest scholarly appraisals, see Edwin A. Burtt, The Metaphysical Foun-dations of Modern Physical Science: A History and Critical Essay (1924; reprint, London:Routledge & Kegan Paul, 1967) and Ernst Mach, The Science of Mechanics: A Criticaland Historical Account of Its Development (1883; reprint, Illinois: La Salle, 1974). Forthe more recent literature see infra.

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ulating natural processes. In order to know nature, we have to intervene innature. Generally: if we wish to explore whether A is a cause of B, we willneed to establish whether deliberate and purposive variations in A result inchanges in B. If changes in A produce changes in B, the causal relation isestablished. It will be shown that this notion first emerged from Galileo’swork in hydrostatics and came to full fecundity in his treatment of the tides.

Let me first of all take stock of the present discussion. De Motu, writtenbetween 1589 and 1592, is one of Galileo’s early scientific works on whatwe today would roughly call ‘‘mechanics.’’ That in De Motu Galileo wishedto establish a causal explanation of motion (and acceleration) is acceptedby all scholars.2 According to Galileo, falling bodies are moved by an inter-nal cause; projectiles by an external one.3 Galileo indeed claimed that hewished to determine the hidden causes of observable effects ‘‘for what weseek are the causes of effects, and these causes are not given to us by experi-ence.’’4 In dealing with the cause of acceleration, Galileo clarified that hewanted to discover the true, essential and not the accidental cause of accel-eration.5 Acceleration is an accidental feature of motion, caused by thegradual overtaking of the intrinsic weight of a body during fall, after beinglifted (and the weight being diminished) by an impressed force. Scholarsbegin to disagree, however, on the presence and importance of causal expla-nations in the period after this early work. Edwin A. Burtt, echoing ErnstMach, wrote that Galileo’s studies on motion led him to focus more on thehow than on the why of motion.6 Closely connected to this is Galileo’s banof final causes from natural philosophy.7 Galileo, according to Burtt,treated motions as the secondary causes of natural phenomena and theforces producing them as their primary causes (of which, further, the nature

2 See for instance William R. Shea, Galileo’s Intellectual Revolution, Middle Period1610–1632 (New York: Neale Watson Academic Publications, 1972), 36.3 Galileo Galilei, On Motion and On Mechanics, translated with introduction and notesby I. E. Drabkin and S. Drake (Madison: The University of Wisconsin Press, 1960), 6.4 Ibid., 27.5 Ibid., 87.6 See Burtt, The Metaphysical Foundations, 80–81 and Mach, The Science of Mechanics,155.7 Burtt’s analysis is simply refuted by pointing to Galileo’s horror vacui explanation ofcohesion. Bodies cohere in order to prevent a vacuum to occur in nature. Galileo Galilei,Dialogues Concerning Two New Sciences, translated by Henry Crew and Alfonso deSalvio (1638; reprint, New York: Dover, 1954), 11–26. For a discussion of Galileo’sargument containing the rota Aristotelis, see H. E. Le Grand, ‘‘Galileo’s Matter Theory,’’in New Perspectives on Galileo, eds. R. E. Butts and J. C. Pitt (Dordrecht / Boston: Reidel,1978), 197–208.

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Ducheyne ✦ Galileo’s Interventionist Notion of ‘‘Cause’’

or essence is unknown).8 We only know quantitative effects of forces interms of motion.9 This implies that knowledge of primary, essential causesis impossible according to Galileo. After Burtt, authors have gone even fur-ther: they questioned the presence of causal explanation in toto in Galileo’s(mature) work. On one side of the spectrum, Drake claims that Galileobanished causal inquiries from his science, since they were speculative andunnecessary:

The word cause, frequent in this early book, is less frequent in thelater ones. It played little part in Galileo’s mature presentation ofscientific material, which he confined more and more to observa-tional and mathematical statements.10

Causal claims were present in his early work (e.g. in the Discourse on Float-ing Bodies [1612]), but not in his mature work, by which Drake apparentlymeans the Dialogo and the Discorsi.11 Pietro Redondi seems to side withDrake: Galileo was defending a docta ignorantia with respect to causes andcausal knowledge.12 There are some passages which seem to conform withthis interpretation, although note that they can be made consistent with thecausal interpretation as well. For instance, after having reviewed varioushypothetical explanations of the cause of gravity, Salviati says:

Now, all these fantasies, and others too, ought to be examined;but it is not really worth while. At present it is the purpose ofour Author merely to investigate and to demonstrate some of theproperties of accelerated motion (whatever the cause of this accel-eration may be) ( . . . ).13

8 Ibid., 91.9 Ibid., 93.10 Stillman Drake, Cause, Experiment and Science: A Galilean dialogue incorporating anew English translation of Galileo’s ‘‘Bodies That Stay atop Water, or Move in It’’(Chicago / London: The University of Chicago Press, 1981), xxviii.11 Discourse on Floating Bodies, Opere, 4: 57–143; Dialogue, Opere, 7: 21–521; Dis-course, Opere, 8: 39–319. Drake noted that Galileo’s usage of the word ‘‘cause’’ after1600 had a ‘‘man-in-the-street ring,’’ rather than a technical Aristotelian connotation.See Stillman Drake, Galileo at Work: His Scientific Biography (Chicago / London: TheUniversity of Chicago Press, 1978), 33.12 Pietro Redondi, ‘‘From Galileo to Augustine,’’ in The Cambridge Companion to Gali-leo, ed. P. K. Machamer (Cambridge: Cambridge University Press, 1998), 175–210, 185.13 Galilei, Dialogues, 166–67. For the original quote see Galileo Galilei, Le Opere diGalileo Galilei, Nuova Ristampa della Edizione Nazionale, ed. Antonio Favaro, 20 vol-umes (Florence: Barbera, 1968), 8: 202.

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Ernan V. McMullin, however, correctly argues that this passage in the Dis-corsi does not necessarily mean a rejection of causal explanation: it simplymeans that dynamics needs to be preceded by kinematics.14 Only when theproperties of motion have been described, can we start with explainingthem causally. This does not necessarily entail a rejection of causal explana-tion as such.

On the other side, there are authors who stress the importance ofcausal explanation and causal reasoning in Galileo’s work and relate themto past traditions where causal knowledge was important. Peter K. Ma-chamer argued that Galileo’s notion of cause is that of the tradition of themixed sciences (scientiae mixtae):

I shall attempt to show that though Galileo does use such causallanguage with serious intent, there is a sense in which Drake isright about Galileo’s unconcern for causes; Galileo is, for the mostpart but not always, unconcerned about extrinsic, efficient causes.This is one aspect familiar to those who deal with the mixedsciences. Galileo is concerned very much with formal and finalcauses, and sometimes material causes.15

He admits that his analysis is primarily based on the Discorsi.16 Accordingto Machamer, proper (causal) explanations refer to formal, final, and mate-rial (necessitating) causes.17 William W. Wallace has connected Galileo’snotion of cause to the Aristotelian tradition.18 Galileo frequently uses causalparlance which is in agreement with Aristotle’s views of causes and hisideas on scientific method laid down in the Posterior Analytics. Galileo’sscientific demonstrations agree with and are derived from the regressus

14 Ernan V. McMullin, ‘‘The Conception of Science in Galileo’s Work,’’ in New Perspec-tives on Galileo, ed. R. E. Butts and J. C. Pitt (Dordrecht / Boston: Reidel, 1978), 209–58,238.15 Peter K. Machamer, ‘‘Galileo and the Causes,’’ in New Perspectives on Galileo, 161–180, 162.16 Ibid., 161.17 Machamer, Galileo and the Causes, 173.18 See William A. Wallace, Galileo’s Early Notebooks: The Physical Questions. A Trans-lation from the Latin, with Historical and Paleographical Commentary (Notre Dame:University of Notre Dame Press, 1977); William A. Wallace. Galileo and his Sources: TheHeritage of the Collegio Romano in Galileo’s Science (Princeton: Princeton UniversityPress, 1984); William A. Wallace, ‘‘Randall Redivivus Galileo and the Paduan Aristoteli-ans,’’ JHI 49 (1988), 133–49; William A. Wallace, Galileo’s Logical Treatises: A Transla-tion, with Notes and Commentary of His Appropriated Latin Questions on Aristotle’sPosterior Analytics, (Dordrecht / Boston / London: Kluwer, 1992); and, William A. Wal-lace, Galileo, the Jesuits, and the Medieval Aristotle (Aldershot: Ashgate, 1999).

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strategy in the Aristotelian tradition, as John H. Randall first argued.19 ThePaduan Aristotelians—exemplified by Jacopo Zabarella—are usually cred-ited with elaborating Aristotle’s logic of demonstration into a scientificmethod of demonstration in which one first reasons from the effects to thecauses (resolution), and then from the causes to the effects (composition).Demonstrative regressus is a procedure which combines an inference froman observed effect to its proximate cause with an inference from the proxi-mate cause to the observed effect.20 Wallace’s main message is that Galileo’snuove scienze were not created de novo. Jacopo Zabarella was, as Randallclaimed, ‘‘the methodologist who stood behind Galileo’s early account ofdemonstrative methodology.’’21 Galileo continued to use the regressusthroughout his career with various modifications.22

Causal explanations are certainly present in Galileo’s work.23 That ispresently not the issue at stake:

The problem of causality in his science is clearly not whether hesought causal explanations, but rather how he sought them andhow he thought they could lead to certain and unrevisable knowl-edge about the physical world.24

I would add to that list that in addition to this we also need to clarify whatGalileo’s notion of cause was. In this essay, I shall not directly evaluate

19 See John H. Randall, ‘‘The Development of Scientific Method in the School of Padua,’’JHI 1 (1940): 177–206; and Wallace, Galileo’s Logical Treatises, 166–67. See NicolasJardine, ‘‘Epistemology of the Sciences,’’ in The Cambridge History of Renaissance Phi-losophy, ed. Charles B. Schmitt (Cambridge: Cambridge University Press, 1988), 685–711. As Peter Dear notes: ‘‘By no means wholly original with Zabarella but closelyassociated with his name throughout Europe in the later sixteenth and seventeenth centu-ries, the technique had developed from a commentary tradition that focused on Aristotle’sPosterior Analytics, and in particular on Aristotle’s distinction between two forms ofdemonstration: apodeixis tou dioti and apodeixis tou hoti, usually latinized as demon-stration propter quid and demonstratio quia.’’ Peter Dear, Discipline and Experience,The Mathematical Way in the Scientific Revolution (Chicago/London: University of Chi-cago Press, 1995), 27. Randall was unaware of Galileo’s Logical Treatises (BNF MS Gal.27) (see Wallace, Randall Redivivus, 133). Randall was unaware of Galileo’s LogicalTreatises (BNF MS Gal. 27) (see Wallace, Randall Redivivus, 133).20 See Nicolas Jardine, ‘‘Epistemology of the Sciences,’’ in The Cambridge History ofRenaissance Philosophy, ed. Charles B. Schmitt (Cambridge: Cambridge University Press,1988), 685–711.21 Wallace, Randall Redivivus, 145.22 Ibid.23 See Wallace, Galileo’s Logical Treatises, for several examples ranging from differentperiods in Galileo’s career.24 Wallace, Galileo, the Jesuits, and the Medieval Aristotle, 624.

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Wallace’s and Machamer’s readings. My point is rather different: insteadof solely focusing on past traditions from which much of Galileo’s terminol-ogy appears to be derived, we should pay more attention to some of theinnovative features of Galileo’s notion of causality. There are prima facieparallels with past traditions, and indeed Galileo frequently used Aristote-lian terminology. But we should not associate Galileo’s notion of ‘‘cause’’with that of a past tradition too quickly. Let us also look at possibly originalcontributions of Galileo to the idea of cause.25 I admit that Wallace hasalready pointed to some innovative changes Galileo made to the regressusmethodology. The first is the use of experimental models.26 The second con-centrates on the ‘‘various quantitative modalities of cause-and-effect phe-nomena’’ and the use of these ‘‘to reason mathematically to the existenceof a physical cause for an observed physical effect.’’27 This is the aim of thepresent essay: to point to the interventionist strand in Galileo’s conceptionof cause.

In section 2, I shall therefore begin by carefully looking at some ofGalileo’s causal reasoning strategies. I shall discuss Galileo’s treatment ofthe floating and sinking of bodies in water and his explanation of the tides.I have chosen these cases because on these occasions Galileo is very expliciton his causal reasoning and his notion of ‘‘cause.’’ These cases will pavethe way for a more elaborate understanding of Galileo’s notion of cause. Insection 3, I shall compare Galileo’s interventionist notion of cause withJames Woodward’s recent theory of causation, presently one of the mostdeveloped interventionist accounts of causation. In the final section (4), Ishall briefly point to the significance of Galileo’s interventionist notion ofcause in connection with the idea of what Antonio Perez-Ramos has calledan ‘‘active science.’’28

2. GALILEO AND THE OCCURRENCE OF PHYSICALCAUSES IN HIS SCIENTIFIC WORK

In 2.1.1 and 2.2.1, we shall look at two case-studies in Galileo’s works, onestemming from the mid-period of his scientific career and one from his later

25 A. C. Crombie has hinted to the importance for Galileo of varying the conditions andisolating the causes. See A. C. Crombie, The History of Science, From Augustine to Gali-leo (1952; reprint, New York: Dover, 1995), 2: 147.26 Wallace, Galileo, the Jesuits, and the Medieval Aristotle, 627.27 Ibid., 629.28 Antonio Perez-Ramos, Francis Bacon’s Idea of Science and the Maker’s KnowledgeTradition (Oxford: Clarendon Press, 1988); and Antonio Perez-Ramos, ‘‘Bacon’s Formsand the Maker’s Knowledge,’’ in The Cambridge Companion to Bacon, ed. M. Peltonen,Markuu (Cambridge: Cambridge University Press, 1996), 99–120.

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work, where he explicitly discusses the notion of physical cause. These caseswill give us access to Galileo’s notion of cause. This will set the stage for afuller discussion of Galileo’s notion of physical cause in sections 2.1.2 and2.2.2. The goal of section 2 is to penetrate the deeper conceptual strata ofGalileo’s notion of ‘‘cause.’’ I attempt to characterize Galileo’s notion of‘‘cause’’ in the form of three general statements, which are meta-level de-scriptions of Galileo’s notion of ‘‘cause.’’

2.1. The Emergence of ‘‘Cause’’ in the Discourseon Floating Bodies (1612)

2.1.1. Galileo’s Causal Intuitions in the Discourse on Floating Bodies

Galileo’s Discourse on Floating Bodies (1612) was a best-selling book in itsown time. Unfortunately, it has received relatively little attention by schol-ars.29 It is certainly relevant for an understanding of Galileo’s notion ofphysical cause, since Galileo explicitly addresses the problem of finding truecauses. Stillman Drake suggests that, when Galileo first sharply defined theword ‘‘cause’’ for use in scientific inquiries, the ‘‘process by which causesgave way to laws in science may be considered as having begun.’’30 In thisdiscourse Galileo refuted the Aristotelian explanation of floating. The Aris-totelians, like Lodovico delle Colombe, asserted that bodies float on waterbecause of their flat shape, which prevents them from piercing the water’sresistance to division.31 Lodovico delle Colombe claimed to have refutedGalileo by the following experimentum crucis: a flat ebony chip floats,while an ebony ball of the same weight cannot do so.32 The central tenet ofthe Aristotelians was water’s resistance to division. This tenet was basedrather on the metaphysical assumption that all motion requires an opposingmedium, and not on experiments.33 Galileo claimed—in agreement withArchimedes—that ‘‘only greater or lesser heaviness in relation to water’’ isthe cause of floating or sinking.34 Both parties claimed to have inferred thecause of floating bodies. How do we know what is the true cause?

Galileo, in defending his position, often argued about what a ‘‘(proper)

29 However, see Paolo Palmieri, ‘‘The Cognitive Devolopment of Galileo’s Theory ofBuoyancy,’’ Archives for the History of the Exact Sciences 50 (2005): 189–222.30 Drake, Cause, Experiment and Science, xxv.31 Ibid., xvii.32 Ibid., xix. Today we would explain this phenomenon by the surface tension of thewater. This was only discovered in the eighteenth century.33 Ibid., xxiii.34 Ibid., 23.

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cause’’ precisely is. In his notes early in the hydrostatic discussion (and notin the discourse itself), Galileo wrote that ‘‘Causa e quella, la qual posta,seguita l’effetto; e rimossa, si rimuove l’effetto’’ (‘‘Cause is that which put[placed], the effect follows; and removed, the effect is removed’’ [sic]).35

This definition seems to have guided him in his scientific research. Galileoset out to search for the ‘‘true, intrinsic, and entire cause of the rising andfloating of some solid bodies in water.’’36 He wrote:

With a different method and other means I shall seek to reach thesame conclusion [as Archimedes], reducing the causes of such ef-fects to principles more intrinsic and immediate, in which are per-ceived also the causes of some admirable and almost incredibleevents, as that a very small quantity of water may raise up andsustain with its small weight a solid body that is a hundred or athousand times heavier [� the famous hydrostatical paradox].And since demonstrative advance requires it I shall define someterms and then explain some propositions from which, as fromthings true and noted, I may then serve my own purposes.37

The terms Galileo refers to are specific weight, i.e. the weight of a body ina given volume, absolute weight, i.e. the ‘‘normal’’ weight of a body, andthe moment. On ‘‘moment’’ Galileo writes:

Moment, among mechanics, means that force, that power, thatefficacy, with which the mover moves and the moved resists, whichforce depends not simply on weight, but on speed of motion [and]on different inclinations of the spaces over which motion ismade—for a heavy body descending makes greater impetus in asteeper space than in one less steep. And in short, whatever be thecause of such force, it always keeps this name of moment.38

The first proposition that follows from these concepts is that if two bodieson a balance have equal absolute weight, their moment will be equal.Hence, they make equilibrium.39 The second proposition is that the moment

35 Ibid., 217. Drake draws an analogy with the expression causam tollere that Galileoprobably learned as a medical student (ibid., xxvii).36 Ibid., 25.37 Ibid., 26; Opere, 4: 67.38 Ibid., 29; Opere, 4: 68.39 Ibid.

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and the power of heaviness is increased by the speed of motion.40 ThenGalileo started laying down further physico-mathematical theorems andexperiments, which confirmed that the sinking or floating of bodies is de-pendent on their specific heaviness.41 These propositions indeed ‘‘openedthe road to the contemplation of the true, intrinsic, and proper cause of thediverse motions and of rest of different solid bodies in various mediums.’’42

Galileo claimed that bodies sink or float irrespective of their form.43 Thiscan be shown by experiments where the (specific) weight is kept fixed andthe form is varied:

Therefore, commencing to investigate with examination by exactexperiment how true it is that shape does not at all affect the sink-ing or not sinking of the same solids, and having already demon-strated how a greater heaviness of the solid with respect to theheaviness of the medium is the cause of its ascending or descend-ing, [then] whenever we want to make a test of what effect diver-sity of shape has on the latter, it will be necessary to make theexperiment with materials in which variety of heaviness does notexist. For were we to make use of materials that could vary inspecific weight from one to another, when we encountered varia-tion in the fact of descent or ascent we would always remain withambiguous reasoning as to whether the difference derived trulyfrom shape alone, or also from different heaviness.44

Form is a cause secundum quid, it functions as an assisting or concomitantcause.45 It can influence the speed of descent or ascent, but it is not as suchthe cause of its upward and downward motion. It is a secondary cause, nota primary cause.46 The prima facie anomalous floating of the chip is thenexplained as follows. The chip, upon closer inspection, is immersed underthe water level with a layer of air above it. This layer and the original chip

40 Ibid., 31.41 Ibid., 35–49.42 Ibid., 59.43 Ibid., 23.44 Ibid., 74 (emphasis added); Opere, 4: 89.45 Ibid., 164.46 In BNF MS 27 (referred to as the Logical Questions) which was written between 1588and 1591, Galileo introduced various classifications of different causes, among which arethe following: verae causae versus virtual ones, universal versus particular ones, internalversus external ones, proximate versus immediate ones, . . . (Wallace, Galileo, the Jesuits,and the Medieval Aristotle, 611–13).

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form an aggregate which is specifically lighter than water. Hence it will(nearly) float. The form of the chip is not the true cause of its floating. Theform does allow for the air to take its space above the chip, but it is thepresence of the air that produces the lighter-than-water-aggregate. Thislighter-than-water-aggregate is the true cause. Scientific understanding forGalileo was discovering the proximate and immediate causes of phenom-ena. True causes are the immediate causes, not the mediate ones.47

2.1.2. A More Systematic Analysis of Galileo’s CausalIntuitions in the Discourse on Floating Bodies

Let us take stock and characterize Galileo’s notion of cause in the discourseon floating bodies. We have seen that Galileo conceived of a true cause asthe most proximate and immediate factor that brings about an effect. With-out that factor the effect would not occur. Whether an effect is directlyproduced by a property can be established by varying this property, whilekeeping all other properties fixed. If the effect follows, the property underinvestigation is the true cause. If the effect does not follow, the property isnot the true cause. A true cause needs to refer to some essential property ofthe object under investigation (of course, distinguishing between essentialproperties and accidental ones is sometimes a precarious work).48 In thediscourse form is an accidental property, while specific weight is not. Basedon this, we can see that one of the Galileo’s early strategies for causal rea-soning is isolating and varying the presumed causal factor (IVC):

(IVC):If, when keeping fixed all other relevant causal factors (Px), vary-ing property P1 (� the assumed causal factor) results in an alter-ation of property E1 (� the effect), then we may conclude that P1

is a causal factor for E1 (or as Galileo would formulate it ‘‘a truecause’’).

In Bodies That Stay Atop Water or Move in It, Galileo typically assumesthat a true cause is universal in the sense that it is responsible for all observ-

47 Ibid., 70.48 This topic is far too complex to spell out here. For the different ways Galileo consideredproperties as accidental, see Noretta Koertge, ‘‘Galileo and the Problem of Accidents,’’JHI 38 (1977): 389–408.

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able floating or sinking behaviour. This is what I would call the universalityand uniqueness assumption (U2) of Galileo’s notion of ‘‘cause’’:

(U2general):

If P1 is a true cause of E1, then P1 is a universal and unique cause,i.e. it explains all E’s similar to E1 (under all circumstances).

(U2sinking or floating):

If P1 (specific weight) is a true cause of E1 (the sinking of lead orthe floating of olive oil) then P1 is a universal and unique cause, i.e.it explains all E’s similar to E1 (the floating or sinking behaviour ofall bodies under all circumstances).

In other words, two generalizations are made: (1) the causal relation assuch and (2) the fact that the inferred cause is assumed to be a unique cause,i.e. that it explains all similar phenomena (or put differently, that similarphenomena cannot be caused by different causes). Post factum, we mightof course say that Galileo’s universality assumption was incorrect, since itis not unimaginable to find similar effects which are produced by differentcauses. It is not possible to explain all phenomena of sinking and floatingsolely by specific weight. According to the modern explanation, the directcause of the floating anomalous chip is the surface tension of the water.This is a case where one causal factor (surface tension) nullifies anothercausal factor (greater specific heaviness with respect to water). Accordingto Galileo’s reasoning the lighter-than-water-aggregate of ebony and air isthe direct cause of the floating of the chip. This explanation is introducedad hoc, after Galileo’s statement that specific heaviness with respect towater is the true cause. Galileo’s true cause turned out not to be unique.

2.2. The Causal Explanation of the Tides in the Dialogo (1632)

2.2.1. The Causal Intuitions in the Explanation of the Tides

Although Galileo’s theory of the tides has received relatively little atten-tion,49 the theory was to Galileo’s mind the ‘‘principal event’’ in the Dia-

49 Paolo Palmieri, ‘‘Re-examining Galileo’s Theory of the Tides,’’ Archives for the Historyof the Exact Sciences 53 (1998): 223–375.

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logo.50 In the Fourth Day of the Dialogo (1632), Galileo presents his geo-kinetic theory of the tides. An early version of this theory was written in1616: Discorso del flusso e reflusso del mare.51 I shall focus on the laterversion from the Dialogo. The tides were to Galileo’s mind a physical proofthat the earth moved.52 Salviati (Galileo’s spokesman) stresses that in deal-ing with questions like these, ‘‘a knowledge of the effects is what leads toan investigation and discovery of the causes.’’53 Such an investigation maylead to the ‘‘true and primary,’’54 or ‘‘universal causes’’55 of the effects weobserve. Galileo acknowledges that not ‘‘all proper and sufficient causes’’will be adduced. In renouncing other alleged explanations, which Galileocalls ‘‘occult qualities’’ or ‘‘idle imaginations’’56 (e.g. various depths of thesea, attraction or heat produced by the Moon), Salviati formulates a posi-tive criterion for a true cause (vera causa), namely artificial reproduction:

But I believe that you have not any stronger indication that thetrue cause of the tides is one of those incomprehensibles than themere fact that among all things so far adduced as verae causaethere is not one which we can duplicate for ourselves by means ofappropriate artificial device. For neither by the light of the moonor sun, nor by temperate heat, nor by differences of depth can weever make water contained in a motionless vessel run to and fro,or rise and fall in but a single place. But if, by simply setting thevessel in motion, I can represent for you without any artifice at allprecisely those changes which are perceived in the waters of thesea, why should you reject this cause and take refuge in miracles?57

50 Galileo Galilei, Dialogue Concerning the Two Chief World Systems, ed. S. J. Gould,translated and with revised notes by Stillman Drake (1632; reprint, New York: The Mod-ern Library, 2001), 479. The most complete and up-to-date treatment is Palmieri, ‘‘Re-examining Galileo’s Theory of the Tides.’’ I owe a lot to Palmieri’s insightful analysis.51 See Opere, 5: 377–95.52 William R. Shea, ‘‘Galileo’s Copernicanism,’’ in The Cambridge Companion to Gali-leo, ed. P. K. Machamer (Cambridge: Cambridge University Press, 1998), 211–43, 224–26. It should be kept in mind, however, that Galileo’s explanation of the tides is one ofhis ‘‘earliest original physical ideas.’’ Wallace Hooper, ‘‘Seventeenth-Century Theories ofthe Tides as a Gauge of Scientific Change,’’ in The Reception of the Galilean Science ofMotion in Seventeenth-Century Europe, eds. C. R. Palmerino and J. M. M. H Thijssen(Dordrecht / Boston / London: Kluwer, 2004), 199–242, 206. Galileo was aware that thetides were a relevant challenge to Copernicus’s theory by 1595.53 Galilei, Diaologue, 484.54 Ibid., 485.55 Ibid., 533.56 Ibid., 516.57 Ibid., 489 (emphasis added); Opere, 7: 447.

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FIGURE 1: the earth’s annual and diurnal motion.

Galileo even claimed to have ‘‘a mechanical model’’ of the tides.58 Unfortu-nately, he did not further discuss it.59 Galileo then presented his kinematicalmodel of the tides.60 He explicitly renounced an explanation involving at-tractions of the Moon like the one favoured by Kepler.61 The uniform an-nual motion of the Earth from west to east (depicted by circle BC) and theuniform diurnal motion of the Earth from west to east (depicted by circleDEFG), result in an uneven mixed motion in the different parts of the earth(see figure 1). In contrast to Aiton, Clavelin, Mach and Shea, Palmieri ar-gues that there is no contradiction between the principle of relativity formu-lated in the Second Day of the Dialogo and Galileo’s theory of the tides.62

The principle of relativity, which states that there is no observable differ-ence of motion, applies to uniform motions or motions at rest; in this casethe Earth is a vessel that has a continuous but non-uniform motion (sinceit is accelerated and retarded). Differences in motion in this last case can benoticed.

At point D the absolute motion will be the swiftest, since both motions

58 Galilei, Dialogue, 500.59 There seems to be historical evidence that Galileo built several mechanical models ofthe tides; the details on these devices are lacking (Palmieri, ‘‘Re-examining Galileo’s The-ory of the Tides,’’ 318–25).60 Ibid., 495–96.61 Ibid., 536.62 Palmieri, ‘‘Re-examining Galileo’s Theory of the Tides,’’ 236–43.

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act in the same direction. At point F the contrary will occur. At points Eand G the absolute motion remains equal to the simple annual motion. Thecause of the tides is the acceleration and deceleration of different parts ofthe earth which results from its diurnal and annual rotation. Paolo Palmieriuses the expression ‘‘tide-generating acceleration.’’63 Indeed, when we ac-celerate and decelerate a vessel with water contained in it, we observe thatthe water will run back and forth.64 Galileo notes that:

Now this is the most fundamental and effective cause of the tides,without which they would not take place. But the particular eventsobserved at different times and places are many and varied; thesemust depend upon diverse concomitant causes, though all musthave some connection65 with the fundamental cause. So our nextbusiness is to bring up and examine the different phenomenawhich may be the causes of such diverse effects.66

Next, Galileo discusses the concomitant or particular causes. The first ofthese concomitant causes is the tendency of water ‘‘by its own weight’’ toreturn to equilibrium and pass beyond it and to continue to do so until itsimpetus has diminished. The second is the length of the vessel: in shortervessels the oscillations will be more frequent; in longer ones less frequent.The third is the depth of the vessel: in deep vessels oscillations will be morefrequent than in less deep ones. The fourth is that the oscillations producetwo motions: a rising and falling at either extremity (� vertical displace-ment) and the horizontal running to and fro (� horizontal current). Thefifth is the inequality of the acceleration and deceleration communicated todifferent parts at great distance from each other at the same moment. Theeffects of the fifth concomitant cause are so fine-grained that ‘‘it is impossi-ble for us to duplicate its effects by any practical experiment.’’67 These sec-ondary causes are adduced to explain the six-hour periods in theMediterranean, whereas the primary cause would by itself give rise to atwelve-hour period. Galileo states that:

63 Ibid., 232.64 Galilei, Dialogue, 496–97, 499–500.65 This supposes what we call today a ‘‘principle of superimposition’’ of waves whichexplains the interaction of the tide-generating acceleration and the internal properties ofthe vessel (Palmieri, ‘‘Re-examining Galileo’s Theory of the Tides,’’ 263).66 Ibid., 497; Opere, 7: 454.67 Galilei, Dialogue, 498.

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These causes, although they do not operate to move the waters(that action being from the primary cause alone, without whichthere would be no tides), are nevertheless the principal factors inlimiting the duration of the reciprocations, and operate so power-fully that the primary cause must bow to them.68

Galileo strengthens his claim by pointing out that ‘‘from one uniform causeonly one single uniform effect can follow’’ and that ‘‘effects, being contraryand irregular, you can never deduce from one uniform and constantcause.’’69 Galileo used a principle of superposition to explain the interactionof the tide-generating acceleration and the oscillatory properties of the sea-bed. He did not have the mathematical tools to deal with this problem.According to Galileo ‘‘there is only one true and primary cause for oneeffect.’’70 That Galileo’s kinematical model is closely connected with hisideas on physical causes can be seen from the following fragment:

Thus I say if it is true that one effect can have only one basic cause,and if between the cause and the effect there is a fixed and constantconnection, then whenever a fixed and constant alteration is seenin the effect, there must be a fixed and constant variation in thecause. Now since the alterations which take place in the tides atdifferent times of the year and of the month have their fixed andconstant periods, it must be that regular changes occur simultane-ously in the primary cause of the tides. Next, the alterations in thetides at the said times consist of nothing more than changes intheir size; that is in the rising and lowering of the water a greateror lesser amount, and its running with greater or lesser impetus.Hence it is necessary that whatever the primary cause of the tidesis, it should increase or diminish its force at the specific times men-tioned.71

Again, we encounter Galileo’s universality assumption. Let us use this pre-sentation of Galileo’s theory of the tides as a starting point for an analysisof Galileo’s notion of physical cause.

68 Ibid., 502; Opere, 7: 458.69 Galilei, Dialogue, 515.70 Ibid., 488.71 Ibid., 517 (emphasis added); Opere, 7: 471.

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2.2.2. A More Systematic Treatment of These Intuitions

Being able to reproduce the observed effect by means of a mechanical modelis one of Galileo’s criteria for establishing causal relations between events.In the case of the tides it is impossible to manipulate or control the kinemat-ical properties of the earth. Therefore, Galileo uses what he thinks is arepresentative small-scale model which reproduces and isolates the kine-matical properties of the earth. This model is similar qua kinematical prop-erties to the earth. The model obviously does not take into account theform of the seabed. The motions of the model indeed result in to and fromotion. Hence, Galileo concludes that the tides are caused by a similaracceleration. I refer to this strategy as artificial reproduction (AR):

(AR):If a representative physical model M, similar qua property P to aphysical system �, produces in virtue of P certain regular effectsEM, then P is the primary cause of the similar and regular E�’s.

Galileo uses a replica or simulacrum, which easily allows manipulative op-erations, to model a physical system which is physically impossible to ma-nipulate directly. In cases where human interventions are impossible,Galileo instead manipulates a representative replica in order to answer hisscientific questions. William R. Shea correctly noted:

It is one of Galileo’s great contributions to the development of thescientific method that he clearly recognised the necessity of isolat-ing the true cause by creating artificial conditions where one ele-ment is varied at a time.72

Bear in mind that it was Galileo’s main point to show that the tides areproduced by a mixed motion. Galileo’s strategy is strongly based on hisprinciple that ‘‘there is only one true and primary cause for one effect.’’Since Galileo accepted this principle as a true maxim, he may easily inferthat the cause of the effects of the model is identical to the cause of theeffects of the physical system. Since they are the same effects, they are pro-duced by the same cause (cf. Galileo’s U 2 assumption). Despite Galileo’sinsistence on finding universal causes, he had to take into account second-ary causes to explain the tides. The observed effects are highly irregular. To

72 Shea, Galileo’s Intellectual Revolution, 40.

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explain these irregularities Galileo ad hoc adduces the secondary causes:the tendency of water to equilibrate itself, the depth of the sea, the breadth,. . . etc. These secondary causes disturb the regular effects.

3. CONTEMPORY INTERVENTIONIST INTUITIONS

In this section, I shall briefly compare Galileo’s intuitions on causation withone of the central contemporary interventionist accounts on causation inthe philosophy of science. Contemporary philosophers of science have at-tempted to develop and elaborate an interventionist or manipulationist ac-count of causation and explanation.73 I shall focus on James Woodward’saccount. His account is meant as a theory of causal explanation. Such anaccount holds that causal and explanatory relations are ‘‘relationships thatare potentially exploitable for purposes of manipulation and control’’ andthat these relationships are ‘‘invariant under interventions.’’74 It is my claimthat Galileo had similar interventionist or manipulationist intuitions oncausation. Let us first look at Woodward’s modern interventionist intu-itions. Woodward refers to the twentieth-century pioneering work in thearea of manipulability theories of causation of R. G. Collingwood, DouglasGasking, and Georg Henrik von Wright.75 He correctly states the impor-tance of manipulating or controlling nature in the development of the his-tory of science. Neglect of this, according to Woodward, originates fromthe sharp dichotomy between (pure) science and technology.76 It is not myaim here to present a complete survey of Woodward’s theory of causation,nor to evaluate Woodward’s proposal, but only to touch upon those mat-ters that are relevant to a fruitful comparison with Galileo. To Woodward’smind causes are ‘‘potential handles or devices for bringing about effects.’’77

Judea Pearl labels causal networks as ‘‘oracles of intervention.’’78 Of crucialimportance are Woodward’s notions of intervention variable and invari-ance. If X and Y are two variables with different values, I is an interventionvariable for X with respect to Y, if and only if, the following criteria hold:

73 For the relevant literature see James Woodward, Making Things Happen: A Theory ofCausal Explanation (Oxford: Oxford University Press, 2003).74 Ibid., v.75 Ibid., 12.76 Ibid., 11.77 Ibid., 12.78 Judea Pearl, Causality, Models, Reasoning, and Inference (Cambridge: Cambridge Uni-versity Press, 2000), 22.

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(IV)I1. I causes X.I2. I acts as a switch for all other variables that cause X. That is,certain values of I are such that when I attains those values, Xceases to depend on the values of other variables that cause X andinstead depends only on the value taken by I.I.3. Any directed path from I to Y goes through X. That is, I doesnot directly cause Y and is not a cause of any causes of Y that aredistinct from X except, of course, for those causes of Y, if any, thatare built into the I-X-Y connection itself; that is except for (a) anycauses of Y that are effects of X (i.e., variables that are causallybetween X and Y) and (b) any causes of Y that are between I andY and have no effect on Y independently of X.I.4 I is (statistically) independent of any variable Z that causes Yand that is on a directed path that does not go through X.79

Some explanation is in order here.80 The intuitive idea is that I is an inter-vention variable for X with respect to Y, when all changes that occur in thevalue Y are produced only by changes in the value of X (which are directlybrought about by I). I.1 states that the changes in X are produced by theintervention I. I.2 tells us that for some values of I, the value of X dependsonly on the value of I. In this way, we are able to rule out all other causesof X. I.3 informs us that I cannot directly cause Y and that I cannot be thecause of another variable (Z) that causes Y. Finally, I.4 says that there areno other variables, other than I, which produce Y. Woodward further dis-tinguishes between direct causes and contributing causes: (1) X is a directcause of X with respect to some variable set V, if there is a possible interven-tion of X that will change Y when all other variables in V besides X and Yare held fixed81; (2) X is a contributing cause of Y, if there is a directed pathfrom X to Y such that each link in this path is a causal relationship.82 Therelations we encounter in manipulating nature need to be stable.83 The sec-ond important notion, besides intervention, for Woodward’s account is in-variance. Very crudely, this notion refers to the fact that the changes

79 Woodward, Making Things Happen, 98.80 Ibid., 99–102.81 Ibid., 55.82 Ibid., 57.83 Pearl also stresses the stability inherent in causal relationships. According to Pearlcausal relations are stable, ontological relations, describing objective physical constraintsin our world (Pearl, Causality, Models, Reasoning, and Inference, 25).

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produced in Y through X continue to hold under a certain range of inter-ventions. An invariant relation remains stable as other changes occur. Typi-cally, we will generalize the result produced by our intervention. Invariancehas to do with the fact that ‘‘the generalization should continue to holdunder an intervention that changes its independent variables sufficiently (orin such a way) that the value of its dependent variable is predicted by thegeneralization to change under the intervention.’’84

Obviously, it is not my claim that Galileo endorsed exactly the sameideas on causation as Woodward. Galileo’s notion of causation clearly didnot incorporate such notions as ‘‘(in)dependent variable,’’ ‘‘statistical prob-ability,’’ or ‘‘invariance under manipulation.’’ And that is only for starters.I shall not go into detail and discuss all the differences here, since my claimfocuses on the similarities. What is important is the following. Galileo en-dorsed the same intuition on which Woodward’s program is based: that inorder to establish causal relations we need, while keeping all other possiblefactors fixed, to manipulate and vary the presumed cause, whose manipula-tion and variation will result, if it is a real cause, in a variation of the effect(a variation in the cause will result in a variation of the effect). In order tocontrol the effect, we should manipulate its cause. This interventionist stra-tum of causation in Galileo’s natural philosophy has not received muchscholarly attention. This intuition, which is explicitly developed by Wood-ward (see his definition of direct cause), is embedded in Galileo’s scientificpractice. It played a highly significant role in Galileo’s practice of science.This should be clear by now from the discussion in sections 2.1.2 and 2.2.2.It is one of Galileo’s strategies for inferring causal relations (IVC). In TheAssayer (1623) Galileo explicitly discusses discovering causal links by inter-vention:

To discover the true cause I reason as follows: ‘‘If we do notachieve an effect which others achieved, then it must be that in ouroperations we lack something that produces their success [‘‘nostrooperare manchiamo di quello che fu causa della riuscita d’esso ef-fetto’’]. And if there is just one single thing we lack, then that alonecan be the true cause. [. . .]’’85

Woodward’s idea of direct/contributing cause roughly corresponds to Gali-leo’s idea of proximate/remote cause. Woodward defines a direct cause as

84 Woodward, Making Things Happen, 250.85 Stillman Drake, Discoveries and Opinions of Galileo (New York: Doubleday & Com-pany, 1957), 272 (emphasis added); Opere, 6: 340.

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follows: X is a direct cause of Y with respect to some variable set V, if andonly if, there is a possible intervention on X that will change Y when allother variables in V besides X and Y are held fixed at some value by inter-ventions.86 ‘‘Possible’’ does not refer to ‘‘realizable by humans,’’ it refers toall possible interventions that are logically possible or well-defined.87

A further important difference between Galileo and Woodward is thatGalileo does not only have an interventionist concept of causation, but thathe also has a direct interventionist methodology. Let me clarify what I meanby that. In his insistence on using a scale-model of the kinetic properties ofthe earth, Galileo seems to suggest that proper scientific knowledge presup-poses actually realizable interventions. By contrast, Woodward allows thatwe may meaningfully make use of counterfactual claims about what wouldhappen under interventions, even when such interventions are not physi-cally possible.88 Hence, it makes sense to claim that doubling the moon’sorbit would cause changes in the motion of the tides. Although we cannotchange the moon’s orbit, Newton’s theory shows what would happen tothe tides under an intervention that doubles the moon’s orbit, and ‘‘this isenough for counterfactual claims about what would happen under suchinterventions to be legitimate and to allow us to assess their truth.’’89

4. IN CONCLUSION: GALILEO ASAN ‘‘OPERATIVE SCIENTIST’’

In the seventeenth century scientific practice was increasingly portrayed asa practice wherein we manipulate and reproduce natural phenomena. Inthe literature on the emergence of the idea of science as an operative science(scientia operativa), Francis Bacon is usually given credit for this transfor-mation.90 The tradition of the maker’s knowledge is referred to by Perez-Ramos as ‘‘one of those ‘subterranean’ currents in Western thought whichare only made explicit from time to time.’’91 A knower, according to Bacon,is essentially a maker. True knowledge refers to knowledge which is madeor can be made (reproduced, modelled, fabricated, . . . ).92 In order to know

86 Woodward, Making Things Happen, 55.87 Ibid., 128.88 Woodward, Making Things Happen, 132.89 Ibid., 131.90 See Perez-Ramos, Francis Bacon’s Idea of Science; Perez-Ramos, ‘‘Bacon’s Forms andthe Maker’s Knowledge.’’91 Perez-Ramos, Francis Bacon’s Idea of Science, 150.92 Perez-Ramos, ‘‘Bacon’s Forms and the Maker’s Knowledge,’’ 110.

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a phenomenon, we should be able to (re)produce it.93 Put more precisely:‘‘The capacity of (re)producing Nature’s ‘effects’ was perceived as the epis-temological guarantee of man’s knowledge of natural processes in the ex-ternal world.’’94 Accordingly, Bacon reacted to the Aristotelian dichotomybetween products of nature (naturalia) and human arts (artificialia), byshowing that there is no ontological difference between the spontaneousworkings of nature and the workings which are directed or manipulated byman’s purposive action.95 Nature always maintains the same modus ope-randi. In his third Letter on the Sunspots (1613) Galileo explicitly sub-scribed to this idea:

Nature, deaf to our entreaties, will not alter or change the courseof her effects; and those things that we are here trying to investi-gate have not just occurred once and then vanished, but have al-ways proceeded and will always proceed in the same style.96

Hence, there is no fundamental difference between what nature producesherself and what is brought about by men. Despite the value of Perez-Ramos’s view, recent historical research has nuanced his claims. In her in-novative work Pamela H. Smith also nuances the credit which is usuallygiven to Bacon from a totally different perspective:

The idea of an ‘‘active science,’’ however, goes back not to Bacon,but to the writings and of work of art of Durer, Leonardo, Pailissy,to the makers of the works of art that filled art and curiosity cabi-nets, and to the writings and persona of Paracelsus. These artisansand practitioners appealed to nature as the basis of their science.97

William Eamon further stresses the importance of the books of secrets (librisecretorum), which exhibit a strong utilitarian tendency, in the constitutionof a ‘‘maker’s knowledge.’’98 These books were based upon a ‘‘ ‘down-to-earth,’ experimental outlook: they did not affirm underlying principles but

93 Ibid., 115.94 Perez-Ramos, Francis Bacon’s Idea of Science, 59.95 Ibid., 109; see also Perez-Ramos, ‘‘Bacon’s Forms and the Maker’s Knowledge,’’110–16.96 Drake, Discoveries and Opinions of Galileo, 136; Opere, 5: 218–19.97 Pamela H. Smith, The Body of the Artisan: Art and Experience in the Scientific Revolu-tion (Chicago: The University of Chicago Press, 2004), 239.98 William Eamon, Science and the Secrets of Nature: Books of Secrets in Medieval andEarly Modern Culture (Princeton: Princeton University Press, 1996), 10.

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taught ‘how to.’ ’’99 William R. Newman also tempers Perez-Ramos’s viewby showing that Aristotle already referred to manufactured analogues ofrainbows and that Themo Judaei (fourteenth century) already attested to amaker’s conception of knowledge.100 This, at present, suffices to show thata ‘‘maker’s conception of knowledge’’ was by no means a prerequisite ofBacon.

In the present essay, I have explored one of the crucial strands of the‘‘maker’s conception of knowledge’’: (causal) interventionism. I have ar-gued that there is a significant interventionist component in Galileo’s causalreasoning and practice. This component played an essential role in Galileo’sscientific practice and his articulation of the notion of ‘‘cause,’’ as can beseen from the examples discussed above. Galileo subscribed to the idea thatif we wish really to understand nature we have to manipulate and repro-duce her. Nostro operare is what provides us with a causal understandingof the world. Galileo was indeed a highly self-conscious operative scientist.

Ghent University, Belgium.

99 Ibid., 4, cf. 126–34.100 William Newman, Promethean Ambitions, Alchemy and the Quest to Perfect Nature(Chicago / London: The University of Chicago Press, 2004), 242, 247–48.

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Galileo’s Interventionist Notion of ‘Cause’

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