[forthcoming in The Journal of the History of Ideas]

Galileo’s Interventionist Notion of “Cause”1

Steffen Ducheyne

1. Introduction

In this essay, I shall take up the theme of Galileo’s notion of cause, which has already

received considerable attention.2 I shall argue that the participants in the debate as it stands

have overlooked a striking and essential feature of Galileo’s notion of cause. Galileo not only

reformed natural philosophy, he also – as I shall defend – introduced a new notion of causality

and integrated it in his scientific practice (hence, this new notion also has its methodological

repercussions). Galileo’s conception of causality went hand in hand with his methodology (see

section 3). This is the main message of this essay. It is my claim that Galileo was trying to

construct a new scientifically useful notion of causality. This new notion of causality is an

interventionist notion. According to such a notion, causal relations can be discovered by

actively exploring and manipulating natural processes. In order to know nature we have to

intervene in nature. Generally: If we wish to explore whether A is a cause of B, we will need to

establish whether deliberate and purposive variations in A result in changes in B. If changes in

A produce changes in B, the causal relation is established. It will be shown that this notion first

emerged from Galileo’s work in hydrostatics and came to full fecundity in his treatment of the

tides.

1 The author is Research Assistant of the Research Foundation - Flanders (FWO - Vlaanderen).

I am indebted to Erik Weber and the anonymous referee for making some interesting points

that allowed me to improve this essay.

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Let me first of all take stock of the present discussion. De Motu is one of Galileo’s early

scientific works on what we today would roughly call ‘mechanics’ (written between 1589 and

1592). That in De Motu Galileo wishes to establish a causal explanation of motion (and

acceleration) is accepted by all scholars.3 According to Galileo, falling bodies are moved by an

internal cause; projectiles by an external one.4 Galileo indeed claims that he wished to

determine the hidden causes of observable effects “for what we seek are the causes of effects,

and these causes are not given to us by experience)”.5 In dealing with the cause of acceleration,

Galileo clarifies that he wants to discover the true, essential and not the accidental cause of

acceleration.6 Acceleration is an accidental feature of motion, caused by the gradual overtaking

of the intrinsic weight of a body during fall, after being lifted (and the weight being

diminished) by an impressed force. Scholars begin to disagree however on the presence and

importance of causal explanations in the period after this early work. Edwin A. Burtt, echoing

Ernst Mach, wrote that Galileo’s studies on motion led him to focus more on the how than on

the why of motion.7 Closely connected to this is Galileo’s ban of final causes from natural

philosophy.8 Galileo, according to Burtt, treated motions as the secondary causes of natural

phenomena and the forces producing them as their primary causes (of which the nature or

essence is further unknown).9 We only know quantitative effects of forces in terms of motion.10

This implies that knowledge of primary, essential causes is impossible according to Galileo.

After Burtt, authors have gone even further: they questioned the presence of causal explanation

in toto in Galileo’s (mature) work. On the one side of the spectrum, Drake claims that Galileo

banished causal inquiries from his science, since they were speculative and unnecessary:

The word cause, frequent in this early book, is less frequent in the later ones. It

played little part in Galileo’s mature presentation of scientific material, which he

confined more and more to observational and mathematical statements.11

1

Causal claims were present in his early work (e.g. in the discourse on floating bodies (1612)),

but not in his mature work (by which Drake apparently means the Dialogo and the Discorsi).12

Pietro Redondi seems to side with Drake: Galileo was defending a docta ignorantia with

respect to causes and causal knowledge.13 There are some passages which seem to converge to

this interpretation (note that they can be made consistent with the causal interpretation as well).

2 For two of the earliest scholarly appraisals, see Edwin A. Burtt, The Metaphysical

Foundations of Modern Physical Science, A History and Critical Essay (London: Routledge &

Paul Kegan, [1924] 1967) and Ernst Mach, The Science of Mechanics, A Critical and

Historical Account of Its Development (Illinois: La Salle, [1883] 1974). For the more recent

literature see infra.

3 See for instance William R. Shea, Galileo’s Intellectual Revolution, Middle Period 1610-

1632 (New York: Neale Watson Academic Publications, 1972), 36.

4 Galileo Galilei, On Motion and On Mechanics, Translated with Introduction and Notes by

I.E. Drabkin and S. Drake (Madison: The University of Wisconsin Press, 1960), 6.

5 Ibid., 27.

6 Ibid., 87.

7 See Burtt, The Metaphysical Foundations, 80-81 and Mach, The Science of Mechanics, 155.

8 Burtt’s analysis is simply refuted by pointing to Galileo’s horror vacui explanation of

cohesion. 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 de Salvio

(New York: Dover, [1638] 1954), 11-26. For a discussion of Galileo’s argument 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.

2

For instance, after having reviewed various hypothetical 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 of our Author merely to investigate and

to demonstrate some of the properties of accelerated motion (whatever the cause

of this acceleration may be) (…).14

Ernan V. McMullin, however, correctly argues that this passage in the Discorsi does not

necessarily mean a rejection of causal explanation: It simply means that dynamics needs to be

preceded by kinematics.15 Only when the properties of motion have been described, can we

start with explaining them causally. This does not necessarily entail a rejection of causal

explanation as such.

9 Ibid., 91.

10 Ibid., 93.

11 Stillman Drake, Cause, Experiment and Science, A Galilean dialogue incorporating a new

English translation of Galileo’s “Bodies That Stay atop Water, or Move in It”

(Chicago/London: The University of Chicago Press, 1981), xxviii.

12 Drake noted that Galileo’s usage of the word “cause” after 1600 had a “man-in-the-street

ring”, rather than a technical Aristotelian connotation. See Stillman Drake, Galileo at Work,

His Scientific Biography (Chicago/London: The University of Chicago Press, 1978), 33.

13 Pietro Redondi, “From Galileo to Augustine,” in: The Cambridge Companion to Galileo, ed.

P. K. Machamer (Cambridge: Cambridge University Press, 1998), 175-210, 185.

14 Galilei, Dialogues, 166-67; For the original quote see Galileo Galilei, Le Opere di Galileo

Galilei, Nuova Ristampa della Edizione Nazionale (20 vol.), edited by Antonio Favaro

[Giuseppe Saragat] (Florence: Barbèra, 1968), VIII, 202.

3

On the other side, there are authors who stress the importance of causal explanation and

causal reasoning in Galileo’s work and relate them to past traditions where causal knowledge

was important. Peter K. Machamer argued that Galileo’s notion of cause is that of the tradition

of the mixed sciences (“scientiae mixtae”):

I shall attempt to show that though Galileo does use such causal language with

serious intent, there is a sense in which Drake is right about Galileo’s unconcern

for causes; Galileo is, for the most part but not all always, unconcerned about

extrinsic, efficient causes. This is one aspect familiar to those who deal with the

mixed sciences. Galileo is concerned very much with formal and final causes, and

sometimes material causes.16

He admits that his analysis is primarily based on the Discorsi.17 According to Machamer,

proper (causal) explanations refer to formal, final and material (necessitating) causes.18

William W. Wallace has connected Galileo’s notion of cause to the Aristotelian tradition.19

Galileo frequently uses causal parlance which is in agreement with Aristotle’s views of causes

and his ideas on scientific method laid down in the Posterior Analytics. Galileo’s scientific

demonstrations agree to and are derived from, as John H. Randall first argued, the regressus

strategy in the Aristotelian tradition.20 Wallace’s main message is that Galileo’s nuove scienze

were not created de novo. Jacopo Zabarella was, as Randall claimed, “the methodologist who

stood behind Galileo’s early account of demonstrative methodology”.21 Galileo continued to

use the regressus throughout his career with various modifications.22

Causal explanations are certainly present in Galileo’s work.23 That is presently not the issue

at stake:

4

The problem of causality in his science is clearly not whether he sought causal

explanations, but rather how he sought them and how he thought they could lead

to certain and unrevisable knowledge about the physical world.24

I would add to that list that in addition to this we also need to clarify what Galileo’s notion of

cause was. In this essay, I shall not directly evaluate Wallace’s and Machamer’s readings. My

point is rather different: instead of solely focussing on past traditions from which much of

Galileo’s terminology appears to be derived, we should pay more attention to some of the

innovative features of Galileo’s notion of causality. There are prima facie parallels with past

traditions and indeed Galileo frequently used Aristotelian terminology. But, let us not

equivocate Galileo’s notion of ‘cause’ with that of a past tradition too fast. Let us also look at

possibly original contributions of Galileo to the idea of cause.25 This is the aim of the present

essay: to point to the interventionist strand in Galileo’s conception of cause.

In section 2 I shall therefore begin by carefully looking at some of Galileo’s causal reasoning

strategies. I shall discuss Galileo’s treatment of the 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 explicit on his causal reasoning and his notion of ‘cause’. These cases will pave the way

for a more elaborate understanding of Galileo’s notion of cause. In section 3, I shall compare

Galileo’s interventionist notion of cause with James Woodward’s recent theory of causation,

presently one of the most developed interventionist accounts of causation. In the final section

(4), I shall briefly point to the significance of Galileo’s interventionist notion of cause in

connection to the idea of what Antonio Pérez-Ramos has called an “active science”.26

2. Galileo and the Occurrence of Physical Causes in his Scientific Work

5

In 2.1.1 and 2.2.1, we shall look at two case-studies in Galileo’s works (one stemming from

the mid-period of his scientific career and one from his later work) where he explicitly

discusses the notion of physical cause. These cases will give us access to Galileo’s notion of

cause. This will set the stage for a fuller discussion of Galileo’s notion of physical cause in

sections 2.1.2 and 2.2.2. The goal of this section (2) is to penetrate the deeper conceptual strata

of Galileo’s notion of ‘cause’. I attempt to characterize Galileo’s notion of “cause” in the form

of three general statements, which are meta-level descriptions of Galileo’s notion of “cause”.

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

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

Galileo’s discourse on floating bodies (first edition: 1612) was a best-selling book in its own

time. Unfortunately, it has received relatively little attention by scholars.27 It is certainly

relevant for an understanding of Galileo’s notion of physical cause, since Galileo explicitly

addresses the problem of finding true causes. Stillman Drake suggests that, when Galileo first

sharply defined the word “cause” for use in scientific inquiries, the “process by which causes

gave way to laws in science may be considered as having begun”.28 In this discourse Galileo

refuted the Aristotelian explanation of floating. The Aristotelians, like Lodovico delle

Colombe, asserted that bodies floated on water because of their flat shape which prevents its

piercing the water’s resistance to division.29 Lodovico delle Colombe claimed to have refuted

Galileo by the following experimentum crucis: a flat ebony chip floats, while an ebony ball of

the same weight cannot do so.30 The central tenet of the Aristotelians was water’s resistance to

division. This tenet was based rather on the metaphysical assumption that all motion requires

an opposing medium, and not on experiments.31 Galileo claimed – in agreement with

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Archimedes – that “only greater or lesser heaviness in relation to water” is the cause of floating

or sinking.32 Both parties claimed to have inferred the cause of floating bodies. How do we

know what is the true cause?

Galileo, in defending his position, often argued about what a ‘(proper) cause’ precisely is. In

his notes early in the hydrostatic discussion (and not in the discourse itself), Galileo wrote that

“Causa è quella, la qual posta, sèguita l’effetto; e rimossa, si rimuove l’effetto” (“Cause is that

15 Ernan V. McMullin, “The Conception of Science in Galileo’s Work”, in New Perspectives

on Galileo, ed. R. E. Butts and J. C. Pitt (Dordrecht/Boston: Reidel, 1978), 209-258, 238.

16 Peter K. Machamer, “Galileo and the Causes”, in New Perspectives on Galileo, ed. R. E.

Butts and J. C. Pitt (Dordrecht/Boston: Reidel, 1978), 161-180, 162.

18 Machamer, Galileo and the Causes, 173.

19 See William A. Wallace, Galileo's Early Notebooks: The Physical Questions, A Translation

from the Latin, with Historical and Paleographical commentary (Notre Dame: University of

Notre Dame Press, 1977); William A. Wallace. Galileo and his Sources: the Heritage of the

Collegio Romano in Galileo’s Science (Princeton: Princeton University Press, 1984); William

A. Wallace, “Randall Redivivus Galileo and the Paduan Aristotelians,” Journal of the History

of Ideas 49 (1988), 133-149; William A. Wallace, Galileo’s Logical Treatises, A Translation,

with Notes and Commentary of His Appropriated Latin Questions on Aristotle’s Posterior

Analytics, (Dordrecht/Boston/London: Kluwer, 1992); and, William A. Wallace, Galileo, the

Jesuits, and the Medieval Aristotle (Aldershot: Ashgate, 1999).

17 Ibid., 161.

20 See John H. Randall, “The Development of Scientific Method in the School of Padua,”

Journal of the History of Ideas 1 (1940), 177-206; and Wallace, Galileo’s Logical Treatises,

166-167. The Paduan Aristotelians – exemplified by Jacopo Zabarella – are usually credited

with elaborating Aristotle’s logic of demonstration into a scientific method of demonstration in

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which put [placed], the effect follows; and removed, the effect is removed.” (sic)).33 This

definition seems to have guided him in his scientific research. Galileo set out to search for the

“true, intrinsic, and entire cause of the rising and floating of some solid bodies in water”.34 He

wrote:

With a different method and other means I shall seek to reach the same conclusion

[as Archimedes], reducing the causes of such effects to principles more intrinsic

which one first reasons from the effects to the causes (resolution), and then from the causes to

the effects (composition). Demonstrative regressus is a procedure which combines an inference

from an observed effect to its proximate cause with an inference from the proximate cause to

the observed effect. See Nicolas Jardine, “Epistemology of the Sciences,” in The Cambridge

History of Renaissance Philosophy, ed. Charles B. Schmitt (Cambridge: Cambridge University

Press, 1988), 685-711. As Peter Dear notes: “By no means wholly original with Zabarella but

closely associated with his name throughout Europe in the later sixteenth and seventeenth

centuries, the technique had developed from a commentary tradition that focused on Aristotle’s

Posterior Analytics, and in particular on Aristotle’s distinction between two forms of

demonstration: apodeixis tou dioti and apodeixis tou hoti, usually latinized as demonstration

propter quid and demonstratio quia.” (Peter Dear, Discipline and Experience, The

Mathematical Way in the Scientific Revolution (Chicago/London: University of Chicago Press,

1995), 27). Randall was unaware of Galileo’s Logical Treatises (BNF MS Gal. 27) (see

Wallace, Randall Redivivus, 133).

21 Wallace, Randall Redivivus, 145.

22 Ibid.

23 See Wallace, Galileo’s Logical Treatises, for several examples ranging from different

periods in Galileo’s career.

24 Wallace, Galileo, the Jesuits, and the Medieval Aristotle, 624.

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and immediate, in which are perceived also the causes of some admirable and

almost incredible events, as that a very small quantity of water may raise up and

sustain with its small weight a solid body that is a hundred of thousand times

heavier = the famous hydrostatical paradox. And since demonstrative advance

requires it I shall define some terms and then explain some propositions from

which, as from things true and noted, I may then serve my own purposes.35

25 I admit that Wallace points to some innovative changes Galileo made to the regressus

methodology. The first is the use of experimental models (Wallace, Galileo, the Jesuits, and

the Medieval Aristotle, 627). The second concentrates on the “various quantitative modalities

of cause-and-effect phenomena” and the use of these “to reason mathematically to the

existence of a physical cause for an observed physical effect” (Ibid., 629). A.C. Crombie has

also hinted to the importance of Galileo of varying the conditions and isolating the causes. See

A. C. Crombie, The History of Science, From Augustine to Galileo (2 vol.) (New York: Dover,

[1952] 1995), II, 147.

26 Antonio Pérez-Ramos, Francis Bacon's Idea of Science and the Maker's Knowledge

Tradition (Oxford: Clarendon Press, 1988); and Antonio Pérez-Ramos, “Bacon’s Forms and

the Maker’s Knowledge,” in The Cambridge Companion to Bacon, ed. M. Peltonen, Markuu

(Cambridge: Cambridge University Press, 1996), 99-120.

27 However, see Paolo Palmieri, “The Cognitive Devolopment of Galileo’s Theory of

Buoyancy,” Archives for the History of the Exact Sciences 50 (2005), 189-222.

28 Drake, Cause, Experiment and Science, xxv.

29 Ibid., xvii.

30 Ibid., xix. Today we would explain this phenomenon by the surface tension of the water. This

was only discovered in the eighteenth century.

31 Ibid., xxiii.

32 Ibid., 23.

9

The terms Galileo refers to are specific weight, i.e. the weight of a body in a given volume,

absolute weight, i.e. the ‘normal’ weight of a body, and the moment. On “moment” Galileo

writes:

Moment, among mechanics, means that force, that power, that efficacy, with

which the mover moves and the moved resists, which force depends not simply on

weight, but on speed of motion [and] on different inclinations of the spaces over

which motion is made – for a heavy body descending makes greater impetus in a

steeper space than in one less steep. And in short, whatever be the cause of such

force, it always keeps this name of moment.36

The first proposition that follows from these concepts is that if two bodies on a balance have

equal absolute weight, their moment will be equal. Hence, they make equilibrium.37 The

second proposition is that the moment and the power of heaviness is increased by the speed of

motion.38 Then Galileo started laying down further physico-mathematical theorems and

experiments, which confirmed that the sinking or floating of bodies is dependent on their

specific heaviness.39 These propositions indeed “opened the road to the contemplation of the

true, intrinsic, and proper cause of the diverse motions and of rest of different solid bodies in

various mediums”.40 Galileo claimed that bodies sink or float irrespective of their form.41 This

can be shown by experiments where the (specific) weight is kept fixed and the form is varied:

33 Ibid., 217. Drake draws an analogy with the expression “causam tollere” that Galileo

probably learned as a medical student (Ibid., xxvii).

34 Ibid., 25.

36 Ibid., 29; Opere, IV, 68.

10

Therefore, commencing to investigate with examination by exact experiment how

true it is that shape does not at all affect the sinking or not sinking of the same

solids, and having already demonstrated how a greater heaviness of the solid with

respect to the heaviness of the medium is the cause of its ascending or

descending, [then] whenever we want to make a test of what effect diversity of

shape has on the latter, it will be necessary to make the experiment with materials

in which variety of heaviness does not exist. For were we to make use of materials

that could vary in specific weight from one to another, when we encountered

variation in the fact of descent or ascent we would always remain with ambiguous

reasoning as to whether the difference derived truly from shape alone, or also

from different heaviness.42

Form is a cause secundum quid, it functions as an assisting or concomitant cause.43 It can

influence the speed of descent or ascent, but it is not as such the cause of its upward and

downward motion. It is a secondary cause, not a primary cause.44 The prima facie anomalous

floating of the chip is then explained as follows. The chip, upon closer inspection, is immersed

under the water level with a layer of air above it. This layer and the original chip form an

aggregate which is specifically lighter than water. Hence its will (nearly) float. The form of the

chip is not the true cause of its floating. The form does allow for the air to take its space above

the chip, but it is the presence of the air that produces the lighter-than-water-aggregate. This

lighter-than-water-aggregate is the true cause. Scientific understanding for Galileo was

discovering the proximate and immediate causes of phenomena. True causes are the immediate

causes not the mediate ones.45

11

2.1.2. A More Systematic Analysis of Galileo’s Causal Intuitions in the Discourse on

Floating Bodies

Let us take stock and characterize Galileo’s notion of cause in the discourse on floating

bodies. We have seen that Galileo conceived of a true cause as the most proximate and

immediate factor that brings an effect about. Without that factor the effect would not occur.

Whether an effect is directly produced by a property can be established by varying this

property, while keeping all other properties fixed. If the effect follows, the property under

investigation is the true cause. If the effect does not follow, the property is not the true cause. A

true cause needed to refer to some essential property of the object under investigation (of

course, distinguishing between essential properties and accidental ones is sometimes a

precarious work).46 In the discourse form is an accidental property, while specific weight is not.

Based on this, we can see that one of the Galileo’s early strategies for causal reasoning is

isolating and varying the presumed causal factor (IVC):

(IVC):

If, when keeping fixed all other relevant causal factors (Px), varying property P1 (= the

assumed causal factor) results in an alteration of property E1 (= the effect), then we may

conclude that P1 is a causal factor for E1 (or as Galileo would formulate it “a true

cause”).

46 This topic is far too complex to spell out here. For the different ways Galileo considered

properties as accidental, see Noretta Koertge, “Galileo and the Problem of Accidents,” Journal

of the History of Ideas 38 (1977), 389-408.

12

In Bodies That Stay Atop Water or Move in It, Galileo typically assumes that a true cause is

universal in the sense that is responsible for all observable floating or sinking behaviour. This

is, what I would call, the universality and 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 or the 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 of all bodies under all circumstances).

In other words, two generalisations are made: (1) the causal relation as such 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 similar phenomena cannot be caused by different causes).

Post factum, we might of course say that Galileo’s universality assumption was incorrect, since

it is not unimaginable to find similar effects which are produced by different causes. It is not

possible to explain all phenomena of sinking and floating solely by specific weight. According

to the modern explanation, the direct cause of the floating anomalous chip is the surface

tension of the water. This is a case where one causal factor (surface tension) nullifies another

causal factor (greater specific heaviness with respect to water). According to Galileo’s

reasoning the lighter-than-water-aggregate of ebony and air is the direct cause of the floating of

the chip. This explanation is introduced ad hoc, after Galileo’s statement that specific

13

heaviness with respect to water 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 few attention47, the theory was

to Galileo’s mind the “principal event” in the Dialogo.48 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 in 1616: Discorso del flusso e reflusso del mare.49 I shall focus on the later version

from the Dialogo. The tides were to Galileo’s mind a physical proof that the earth moved.50

Salviati (Galileo’s spokesman) stresses that in dealing with questions like these “a knowledge

of the effects is what leads to an investigation and discovery of the causes”.51 Such an

investigation may lead to the “true and primary”52, or “universal causes”53 of the effects we

observe. Galileo acknowledges that not “all proper and sufficient causes” will be adduced. In

renouncing other alleged explanations, which Galileo calls “occult qualities” or “idle

imaginations”54 (e.g. various depths of the sea, attraction or heat produced by the Moon),

Salviati formulates a positive criterion for a true cause (“vera causa”), namely artificial

reproduction:

But I believe that you have not any stronger indication that the true cause of the

tides is one of those incomprehensibles than the mere fact that among all things so

far adduced as verae causae there is not one which we can duplicate for ourselves

by means of appropriate artificial device. For neither by the light of the moon or

14

sun, nor by temperate heat, nor by differences of depth can we ever 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 the vessel in motion, I can represent for you

without any artifice at all precisely those changes which are perceived in the

waters of the sea, why should you reject this cause and take refuge in miracles?55

Galileo even claimed to have “a mechanical model” of the tides.56 Unfortunately, he did not

further discuss it.57 Galileo then presented his kinematical model of the tides.58 He explicitly

renounced an explanation involving attractions of the Moon like the one favoured by Kepler.59

The uniform annual motion60 of the Earth from west to east (depicted by circle BC) and the

uniform diurnal motion of the Earth from west to east (depicted by circle DEFG), result in an

uneven mixed motion in the different parts on the earth (see figure 1).

Figure 1. The earth’s annual and diurnal motion.

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

direction. At point F the contrary will occur. At points E and G the absolute motion remains

35 Ibid., 26; Opere, IV, 67.

37 Ibid.

38 Ibid., 31.

39 Ibid., 35-49.

40 Ibid., 59.

41 Ibid., 23.

42 Ibid., 74 (emphasis added); Opere, IV, 89.

43 Ibid., 164.

15

equal to the simple annual motion. The cause of the tides is the acceleration and deceleration of

different parts of the earth which results from its diurnal and annual rotation. Paolo Palmieri

uses the expression “tide-generating acceleration”.61 Indeed, when we accelerate and decelerate

a vessel with water contained in it, we observe that the water will run back and forth.62 Galileo

notes that:

44 In BNF MS 27 (referred to as the Logical Questions) which was written between 1588 and

1591, Galileo introduced various classifications of different causes, among which are the

following: verae causae versus virtual ones, universal versus particular ones, internal versus

external ones, proximate versus immediate ones, … (Wallace, Galileo, the Jesuits, and the

Medieval Aristotle, 611-613).

45 Ibid., 70.

48 Galileo Galilei, S.J. Gould ed., Dialogue Concerning the Two Chief World Systems,

Translated and with revised notes by Stillman Drake, (New York: The Modern Library, [1632]

2001), 479. The most complete and up-to-date treatment is Palmieri, Re-examining. I owe a lot

to Palmieri’s insightful analysis.

49 See Opere, V, 377-395.

47 Paolo Palmieri, “Re-examining Galileo’s Theory of the Tides,” Archives for the History of

the Exact Sciences 53 (1998), 223-375.

50 William R. Shea, “Galileo’s Copernicanism,” in The Cambridge Companion to Galileo, ed.

P. K. Machamer (Cambridge: Cambridge University Press, 1998), 211-243, 224-226. It should

be kept in mind, however, that Galileo’s explanation of the tides is one of his “earliest original

physical ideas” (Wallace Hooper, “Seventeenth-Century Theories of the Tides as a Gauge of

Scientific Change,” in The Reception of the Galilean Science of Motion 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 the tides were a relevant problem to Copernicus’s

16

Now this is the most fundamental and effective cause of the tides, without which

they would not take place. But the particular events observed at different times

and places are many and varied; these must depend upon diverse concomitant

causes, though all must have some connection63 with the fundamental cause. So

our next business is to bring up and examine the different phenomena which may

be the causes of such diverse effects.64

theory by 1595.

51 Galilei, Diaologue, 484.

52 Ibid., 485.

53 Ibid., 533.

54 Ibid., 516.

55 Ibid., 489 (emphasis added); Opere, VII, 447.

56 Galilei, Dialogue, 500.

57 There seems to be historical evidence that Galileo built several mechanical models of the

tides; the details on these devices are lacking (Palmieri, Re-examining, 318-325).

58 Ibid., 495-496.

59 Ibid., 536.

60 In contrast to Aiton, Clavelin, Mach and Shea, Palmieri argues that there is no contradiction

between the principle of relativity formulated in the Second Day of the Dialogo and Galileo’s

theory of the tides (Palmieri, Re-examining, 236-243). The principle of relativity which states

that there is no observable difference of motion applies to uniform motions or motions at rest;

in this case the Earth is a vessel that has a continuous but non-uniform motion (since it is

accelerated and retarded). Differences in motion in this last case can be noticed.

61 Ibid., 232.

62 Galilei, Dialogue, 496-497, 499-500.

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Next, Galileo discusses the concomitant or particular causes. The first of these concomitant

causes is the tendency of water “by its own weight” to return to equilibrium and pass beyond it

and to continue to do so until its impetus has diminished. The second is the length of the

vessel: in shorter vessels 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 more frequent than in

less deeper ones. The fourth is that the oscillations produce two motions: a rising and falling at

either extremity (= vertical displacement) and the horizontal running to and fro (= horizontal

current). The fifth is the inequality of the acceleration and deceleration communicated to

different parts at great distance from each other at the same moment. The effects of the fifth

concomitant cause are so fine-grained that “it is impossible for us to duplicate its effects by any

practical experiment”.65 These secondary causes are adduced to explain the six-hour periods in

the Mediterranean (the primary cause would by itself give rise to a twelve-hour period).

Galileo states that:

These causes, although they do not operate to move the waters (that action being

from the primary cause alone, without which there would be no tides), are

nevertheless the principal factors in limiting the duration of the reciprocations,

and operate so powerfully that the primary cause must bow to them.66

Galileo strengthens his claim by pointing out that “from one uniform cause only one single

uniform effect can follow” and that “effects, being contrary and irregular, you can never

deduce from one uniform and constant cause”.67 Galileo used a principle of superposition to

explain the interaction of the tide-generating acceleration and the oscillatory properties of the

seabed. He did not have the mathematical tools to deal with this problem. According to Galileo

66 Ibid., 502; Opere, VII, 458.

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“there is only one true and primary cause for one effect”.68 That Galileo’s kinematical model is

highly connected with his ideas 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 constant connection, then

whenever a fixed and constant alteration is seen in the effect, there must be a

fixed and constant variation in the cause. Now since the alterations which take

place in the tides at different times of the year and of the month have their fixed

and constant periods, it must be that regular changes occur simultaneously in the

primary cause of the tides. Next, the alterations in the tides at the said times

consist of nothing more than changes in their size; that is in the rising and

lowering of the water a greater or lesser amount, and its running with greater or

lesser impetus. Hence it is necessary that whatever the primary cause of the tides

is, it should increase or diminish its force at the specific times mentioned.69

Again we encounter Galileo’s universality assumption. Let us use this presentation of Galileo’s

theory of the tides as starting point for an analysis of Galileo’s notion of physical cause.

2.2.2. A More Systematic Treatment of These Intuitions

Being able to reproduce the observed effect by means of a mechanical model is 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 kinematical properties of the earth. Therefore, Galileo

uses what he thinks is a representative small-scale model which reproduces and isolates the

kinematical properties of the earth. This model is similar qua kinematical properties to the

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earth. The model obviously does not take into account the form of the seabed. The motions of

the model indeed result in to and fro motion. Hence, Galileo concludes that the tides are caused

by a similar acceleration. I refer to this strategy as artificial reproduction (AR):

(AR):

If a representative physical model M, similar qua property P to a physical system

φ, produces in virtue of P certain regular effects EM, then P is the primary cause of

the similar and regular Eφ’s.

Galileo uses a replica or simulacrum, which easily allows manipulative operations, to model a

physical system which is physically impossible to manipulate directly. In cases where human

interventions are impossible, Galileo instead manipulates a representative replica in order to

answer his scientific questions. William R. Shea correctly noted:

It is one of Galileo’s great contributions to the development of the scientific

method that he clearly recognised the necessity of isolating the true cause by

creating artificial conditions where one element is varied at a time.70

70 Shea, Galileo’s Intellectual Revolution, 40.

63 This supposes what we call today a “principle of superimposition” of waves which explains

the interaction of the tide-generating acceleration and the internal properties of the vessel

(Palmieri, Re-examining, 263).

64 Ibid., 497; Opere, VII, 454.

65 Galilei, Dialogue, 498.

67 Galilei, Dialogue, 515.

68 Ibid., 488.

69 Ibid., 517 (emphasis added); Opere, VII, 471.

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Bear in mind that it was Galileo’s main point to show that the tides are produced by a mixed

motion. Galileo’s strategy is strongly based on his principle that “there is only one true and

primary cause for one effect”. Since Galileo accepts this principle as a true maxim he may

easily infer that the cause of the effects of the model is identical to the cause of the effects of

the physical system. Since they are the same effects, they are produced by the same cause (cf.

Galileo’s U assumption). Despite Galileo’s insistence on finding universal causes, he had to

take into account secondary causes to explain the tides. The observed effects are highly

irregular. To 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 with one of the

central contemporary interventionist accounts on causation in the philosophy of science.

Contemporary philosophers of science have attempted to develop and elaborate an

interventionist or manipulationist account of causation and explanation.71 I shall focus on

James Woodward’s account. His account is meant as a theory of causal explanation. Such an

account holds that causal and explanatory relations are “relationships that are potentially

exploitable for purposes of manipulation and control” and that these relationships are

“invariant under interventions”.72 It is my claim that Galileo had similar interventionist or

manipulationist intuitions on causation. Let us first look at Woodward’s modern interventionist

71 For the relevant literature see James Woodward, Making Things Happen, A Theory of Causal

Explanation (Oxford: Oxford University Press, 2003).

72 Ibid., v.

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intuitions.73 It is not my aim here to present a complete survey of Woodward’s theory of

causation, nor to evaluate Woodward’s proposal, but only to touch upon those matters that are

relevant to a fruitful comparison with Galileo. To Woodward’s mind causes are “potential

handles or devices for bringing about effects”.74 Judea Pearl labels causal networks as “oracles

of intervention”.75 Of crucial importance are Woodward’s notions of intervention variable and

invariance. If X and Y are two variables with different values, I is an intervention variable for

X with respect to Y, if and only if, the following criteria hold:

(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, X ceases to depend on the values of other variables

that cause X and instead depends only on the value taken by I.

I.3. Any directed path from I to Y goes through X. That is, I does not directly cause Y and

is not a cause of any causes of Y that are distinct from X except, of course, for those

causes of Y, if any, that are built into the I-X-Y connection itself; that is except for (a) any

74 Ibid., 12.

75 Judea Pearl, Causality, Models, Reasoning, and Inference, (Cambridge: Cambridge

University Press, 2000), 22.

73 Woodward refers to the twentieth-century pioneering work in the area of manipulability

theories of causation of R. G. Collingwood, Douglas Gasking and Georg Henrik von Wright

(Ibid., 12). He correctly states the importance of manipulating or controlling nature in the

development of the history of science. Neglect of this, according to Woodward, originates from

the sharp dichotomy between (pure) science and technology (Ibid., 11).

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causes of Y that are effects of X (i.e., variables that are causally between X and Y) and (b)

any causes of Y that are between I and Y and have no effect on Y independently of X.

I.4 I is (statistically) independent of any variable Z that causes Y and that is on a directed

path that does not go through X.76

Some explanation is in order here.77 The intuitive idea is that I is an intervention variable for X

with respect to Y, when all changes that occur in the value Y are produced only by changes in

the value of X (which are directly brought about by I). I.1 states that the changes in X are

produced by the intervention I. I.2 tells us that for some values of I, the value of X depends

only on the value of I. In this way, we are able to rule out all other causes of X. I.3 informs us

that I cannot directly cause Y and that I cannot be the cause of another variable (Z) that causes

Y. Finally, I.4 says that there are no other variables, other than I, which produce Y. Woodward

further distinguishes between direct causes and contributing causes: (1) X is a direct cause of

X with respect to some variable set V, if there is a possible intervention of X that will change

Y when all other variables in V besides X and Y are held fixed78; (2) X is a contributing cause

of Y, if there is a directed path from X to Y such that each link in this path is a causal

relationship.79 The relations we encounter in manipulating nature need to be stable.80 The

second important notion, besides intervention, for Woodward’s account is invariance. Very

crudely, this notion refers to the fact that the changes produced in Y through X continue to

hold under a certain range of interventions. An invariant relation remains stable as other

changes occur. Typically, we will generalize the result produced by our intervention.

Invariance has to do with the fact that “the generalization should continue to hold under an

intervention that changes its independent variables sufficiently (or in such a way) that the value

of its dependent variable is predicted by the generalization to change under the intervention”.81

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Obviously, it is not my claim that Galileo endorsed exactly the same ideas on causation as

Woodward. Galileo’s notion of causation clearly did not incorporate such notions as

“(in)dependent variable”, “statistical probability”, or “invariance under manipulation”. And

that is only for starters. I shall not go into detail and discuss all the differences here, since my

claim focuses on the similarities. What is important is the following. Galileo endorsed the same

intuition on which Woodward’s programme is based: that in order to establish causal relations

we need, while keeping all other possible factors fixed, to manipulate and vary the presumed

cause, whose manipulation 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 to control the

effect, we should manipulate its cause. This interventionist stratum of causation in Galileo’s

natural philosophy has not received much scholarly interest. This intuition, which is explicitly

developed by Woodward (see his definition of direct cause), is embedded in Galileo’s

scientific practice (see section 3.2). It played a highly significant role in Galileo’s practice of

science. This should be clear by now from the discussion in section 3.2. It is one of Galileo’s

strategies for inferring causal relations (IVC). In The Assayer (1623) Galileo explicitly

discusses discovering causal links by intervention:

To discover the true cause I reason as follows: “If we do not achieve an effect

which others achieved, then it must be that in our operations we lack something

that produces their success [“nostro operare manchiamo di quello che fu causa

della riuscita d'esso effetto”]. And if there is just one single thing we lack, then

that alone can be the true cause. (…)”82

Woodward’s idea of direct83/contributing cause roughly corresponds to Galileo’s idea of

proximate/remote cause.

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A further important difference between Galileo and Woodward is that Galileo does not only

have an interventionist concept of causation, but that he also has a direct interventionist

methodology. Let me clarify what I mean by that. In his insistence on using a scale-model of

the kinetic properties of the earth, Galileo seems to suggest that proper scientific knowledge

presupposes actually realizable interventions. By contrast, Woodward allows that we may

meaningfully make use of counterfactual claims about what would happen under interventions,

even when such interventions are not physically possible.84 Hence, it makes sense to claim

doubling the moon’s orbit would cause changes in the motion of the tides. Although we cannot

change the moon’s orbit, Newton’s theory shows what would happen to the tides under an

intervention that doubles the moon’s orbit, and “this is enough for counterfactual claims about

what would happen under such interventions to be legitimate and to allow us to assess their

truth”.85

4. In Conclusion: Galileo as an “Operative Scientist”

In the seventeenth century scientific practice was increasingly portrayed as a practice

wherein we manipulate and reproduce natural phenomena. In the literature on the emergence of

the idea of science as an operative science (“scientia operativa”), Francis Bacon is usually

given credit for this transformation.86 A knower, according to Bacon, is essentially a maker.

84 Woodward, Making Things Happen, 132.

85 Ibid., 131.

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True knowledge refers to knowledge which is made or can be made (reproduced, modelled,

fabricated, …).87 In order to know a phenomenon we should be able to (re)produce it.88 Put

more precisely: “The capacity of (re)producing Nature’s ‘effects’ was perceived as the

epistemological guarantee of man’s knowledge of natural processes in the external world.”89.

Accordingly, Bacon reacted to the Aristotelian dichotomy between products of nature

(“naturalia”) and human arts (“artificialia”), by showing that there is no ontological difference

between the spontaneous workings of nature and the workings which are directed or

manipulated by man’s purposive action.90 Nature always maintains the same modus operandi.

In his third Letter on the Sunspots (1613) Galileo subscribed to this idea:

Nature, deaf to our entreaties, will not alter or change the course of her effects;

and those things that we are here trying to investigate have not just occurred once

and then vanished, but have always proceeded and will always proceed in the

same style.91

Hence, there is no fundamental difference between what nature produces herself and what is

brought about by men.

I have argued that there is a significant interventionist component in Galileo’s causal

reasoning and practice. This component played an essential role in Galileo’s scientific practice

and his articulation of the notion of ‘cause’, as can be seen from the examples discussed above.

Galileo subscribed to the idea that if we wish to really understand nature we have to

76 Woodward, Making Things Happen, 98.

77 Ibid., 99-102.

78 Ibid., 55.

79 Ibid., 57.

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manipulate and reproduce her. “Nostro operare” is what provides us with a causal

understanding of the world. Galileo was indeed a highly self-conscious operative scientist.

Ghent University, Belgium

80 Pearl also stresses the stability inherent in causal relationships. According to Pearl causal

relations are stable, ontological relations, describing objective physical constraints in our world

(Pearl, Causality, Models, Reasoning, and Inference, 25).

81 Woodward, Making Things Happen, 250.

82 Stillman Drake, Discoveries and Opinions of Galileo (New York: Doubleday & Company,

1957, 272 (emphasis added); Opere, VI, 340.

83 Woodward defines a direct cause as follows: X is a direct cause of Y with respect to some

variable set V, if and only if, there is a possible intervention on X that will change Y when all

other variables in V besides X and Y are held fixed at some value by interventions (Woodward,

Making Things Happen, 55). “Possible” does not refer to “realizable by humans”, it refers to

all possible interventions that are logically possible or well-defined (Ibid., 128).

86 See Pérez-Ramos, Francis Bacon's Idea of Science; Pérez-Ramos, Bacon’s Forms and the

Maker’s Knowledge. The tradition of the maker’s knowledge is referred to by Pérez-Ramos as

“one of those ‘subterranean’ currents in Western thought which are only made explicit from

time to time” (Pérez-Ramos, Francis Bacon's Idea of Science, 150). In her innovating work,

Pamela H. Smith also nuances the credit which is usually given 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 Dürer, Leonardo, Pailissy, to the makers of the works of

art that filled art and curiosity cabinets, and to the writings and persona of Paracelsus. These

artisans and practitioners appealed to nature as the basis of their science.” (Pamela H Smith,

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The Body of the Artisan, Art and Experience in the Scientific Revolution (Chicago: The

University of Chicago Press, 2004), 239). William Eamon further stresses the importance of

the books of secrets (“libri secretorum”), which exhibit a strong utilitarian tendency, in the

constitution of a “maker’s knowledge” (William Eamon, Science and the Secrets of Nature,

Books of Secrets in Medieval and Early Modern Culture (Princeton/New Jersey: Princeton

University Press, 1996), 10). These books were based upon a ““down-to-earth”, experimental

outlook: they did not affirm underlying principles but taught “how to”” (Ibid., 4, cf. 126-134).

87 Pérez-Ramos, Bacon’s Forms and the Maker’s Knowledge, 110.

88 Ibid., 115.

89 Pérez-Ramos, Francis Bacon's Idea of Science, 59.

90 Ibid., 109; see also Pérez-Ramos, Bacon’s Forms and the Maker’s Knowledge, 110-116.

William R. Newman, however, tempers Pérez-Ramos’s view by showing that Aristotle already

referred to manufactured analogues of rainbows and that Themo Judaei (fourteenth century)

already testified of a maker’s conception of knowledge (William Newman, Promethean

Ambitions, Alchemy and the Quest to Perfect Nature (Chicago/London: The University of

Chicago Press, 2004), 242, 247-248.

91 Drake, Discoveries and Opinions of Galileo, 136; Opere, V, 218-219.

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