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Galileo GalileiFirst published Fri Mar 4, 2005; substantive revision Thu Jun 13, 2013

Galileo Galilei (15641642) has always played a key role in any history ofscience and, in many histories of philosophy, he is a, if not the, centralfigure of the scientific revolution of the 17th Century. His work in physicsor natural philosophy, astronomy, and the methodology of science stillevoke debate after over 360 years. His role in promoting the Copernicantheory and his travails and trials with the Roman Church are stories thatstill require re-telling. This article attempts to provide an overview ofthese aspects of Galileo's life and work, but does so by focusing in a newway on his discussions of the nature of matter.

1. Brief Biography2. Introduction and Background3. Galileo's Scientific Story4. Galileo and the ChurchBibliographyAcademic ToolsOther Internet ResourcesRelated Entries

1. Brief BiographyGalileo was born on February 15, 1564 in Pisa. By the time he died onJanuary 8, 1642 (but see problems with the date, Machamer 1998, pp. 245) he was as famous as any person in Europe. Moreover, when he wasborn there was no such thing as science, yet by the time he died sciencewas well on its way to becoming a discipline and its concepts and methoda whole philosophical system.

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Galileo and his family moved to Florence in 1572. He started to study forthe priesthood, but left and enrolled for a medical degree at the Universityof Pisa. He never completed this degree, but instead studied mathematicsnotably with Ostilio Ricci, the mathematician of the Tuscan court. Laterhe visited the mathematician Christopher Clavius in Rome and started acorrespondence with Guildobaldo del Monte. He applied and was turneddown for a position in Bologna, but a few years later in 1589, with thehelp of Clavius and del Monte, he was appointed to the chair ofmathematics in Pisa.

In 1592 he was appointed, at a much higher salary, to the position ofmathematician at the University of Padua. While in Padua he met MarinaGamba, and in 1600 their daughter Virginia was born. In 1601 they hadanother daughter Livia, and in 1606 a son Vincenzo.

It was during his Paduan period that Galileo worked out much of hismechanics and began his work with the telescope. In 1610 he publishedThe Starry Messenger, and soon after accepted a position asMathematician and Philosopher to the Grand Duke of Tuscany (and a non-teaching professorship at Pisa). He had worked hard for this position andeven named the moons of Jupiter after the Medici. There were manyreasons for his move but he says he did not like the wine in the Venicearea and he had to teach too many students. Late in 1610, the CollegioRomano in Rome, where Clavius taught, certified the results of Galileo'stelescopic observations. In 1611 he became a member of what is perhapsthe first scientific society, the Academia dei Lincei.

In 1612 Galileo published a Discourse on Floating Bodies, and in 1613,Letters on the Sunspots. In this latter work he first expressed his positionin favor of Copernicus. In 1614 both his daughters entered the Franciscanconvent of Saint Mathew, near Florence. Virginia became Sister MariaCeleste and Livia, Sister Arcangela. Marina Gamba, their mother, had

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been left behind in Padua when Galileo moved to Florence.

In 16134 Galileo entered into discussions of Copernicanism through hisstudent Benedetto Castelli, and wrote a Letter to Castelli. In 1616 hetransformed this into the Letter to the Grand Duchess Christina. InFebruary 1616, the Scared Congregation of the Index condemnedCopernicus' book On the Revolution of the Heavenly Orbs, pendingcorrection. Galileo then was called to an audience with Cardinal RobertBellarmine and advised not to teach or defend Copernican theory.

In 1623 Galileo published The Assayer dealing with the comets andarguing they were sublunary phenomena. In this book, he made some ofhis most famous methodological pronouncements including the claim thebook of nature is written in the language of mathematics.

The same year Maffeo Barberini, Galileo's supporter and friend, waselected Pope Urban VIII. Galileo felt empowered to begin work on hisDialogues concerning the Two Great World Systems. It was publishedwith an imprimatur from Florence (and not Rome) in 1632. Shortlyafterwards the Inquisition banned its sale, and Galileo was ordered toRome for trial. In 1633 he was condemned. There is more about theseevents and their implications in the final section of this article, Galileo andthe Church.

In 1634, while Galileo was under house arrest, his daughter, Maria Celestedied. (Cf. Sobel 1999). At this time he began work on his final book,Discourses and Mathematical Demonstrations concerning Two NewSciences. This book was smuggled out of Italy and published in Holland.Galileo died early in 1642. Due to his conviction, he was buried obscurelyuntil 1737.

For detailed biographical material, the best and classic work dealing withGalileo's life and scientific achievements is Stillman Drake's Galileo at

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Work (1978). More recently, J.L. Heilbron has written a magnificentbiography, Galileo, that touches on all the multiple facets of Galileo's life(2010).

2. Introduction and BackgroundFor most people, in the 17th Century as well as today, Galileo was and isseen as the hero of modern science. Galileo discovered many things:with his telescope, he first saw the moons of Jupiter and the mountains onthe Moon; he determined the parabolic path of projectiles and calculatedthe law of free fall on the basis of experiment. He is known for defendingand making popular the Copernican system, using the telescope toexamine the heavens, inventing the microscope, dropping stones fromtowers and masts, playing with pendula and clocks, being the first realexperimental scientist, advocating the relativity of motion, and creating amathematical physics. His major claim to fame probably comes from histrial by the Catholic Inquisition and his purported role as heroic rational,modern man in the subsequent history of the warfare between scienceand religion. This is no small set of accomplishments for one 17th-centuryItalian, who was the son of a court musician and who left the University ofPisa without a degree.

One of the good things about dealing with such momentous times andpeople is that they are full of interpretive fecundity. Galileo and his workprovide one such occasion. Since his death in 1642, Galileo has been thesubject of manifold interpretations and much controversy. The use ofGalileo's work and the invocations of his name make a fascinating history(Segre 1991, Palmerino and Thijssen 2004, Finocchiaro 2005), but this isnot our topic here.

Philosophically, Galileo has been used to exemplify many differentthemes, usually as a side bar to what the particular writer wished to make

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the hallmark of the scientific revolution or the nature of good science.Whatever was good about the new science or science in general, it wasGalileo who started it. One early 20th Century tradition of Galileoscholarship used to divvy up Galileo's work into three or four parts: (1) hisphysics, (2) his astronomy, and (3) his methodology, which could includehis method of Biblical interpretation and his thoughts about the nature ofproof or demonstration. In this tradition, typical treatments dealt with hisphysical and astronomical discoveries and their background and/or whowere Galileo's predecessors. More philosophically, many would ask howhis mathematics relates to his natural philosophy? How did he produce atelescope and use his telescopic observations to provide evidence in favorof Copernicanism (Reeves 2008)? Was he an experimentalist (Settle 1961,196, 1983, 1992; Palmieri 2008), a mathematical Platonist (Koyr 1939),an Aristotelian emphasizing experience (Geymonat 1954), precursor ofmodern positivist science (Drake 1978), or maybe an Archimedean(Machamer 1998), who might have used a revised Scholastic method ofproof (Wallace 1992)? Or did he have no method and just fly like an eaglein the way that geniuses do (Feyerabend 1975)? Behind each of theseclaims there was some attempt to place Galileo in an intellectual contextthat brought out the background to his achievements. Some emphasizedhis debt to the artisan/engineer practical tradition (Rossi 1962), others hismathematics (Giusti 1993, Feldhay 1998, Palmieri 2001, 2003, Renn2002), some his mixed mathematics (Machamer 1978, 1998, Lennox1986, Wallace 1992), others his debt to atomism (Shea 1972, Redondi1983), and some his use of Hellenistic and Medieval impetus theory(Duhem 1954, Claggett 1966, Shapere 1974).

Yet most everyone in this tradition seemed to think the three areasphysics, astronomy and methodologywere somewhat distinct andrepresented different Galilean endeavors. More recent historical researchhas followed contemporary intellectual fashion and shifted foci bringingnew dimensions to our understanding of Galileo by studying his rhetoric

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(Moss 1993, Feldhay 1998, Spranzi 2004), the power structures of hissocial milieu (Biagioli 1993, 2006), his personal quest foracknowledgment (Shea and Artigas 2003) and more generally hasemphasized the larger social and cultural history, specifically the court andpapal culture, in which Galileo functioned (Redondi 1983, Biagioli 1993,2006, Heilbron 2010).

In an intellectualist recidivist mode, this entry will outline hisinvestigations in physics and astronomy and exhibit, in a new way, howthese all cohered in a unified inquiry. In setting this path out I shall showwhy, at the end of his life, Galileo felt compelled (in some sense ofnecessity) to write the Discourses Concerning the Two New Sciences,which stands as a true completion of his overall project and is not just areworking of his earlier research that he reverted to after his trial, when hewas blind and under house arrest. Particularly, I shall try to show whyboth of the two new sciences, especially the first, were so important (atopic not much treated except recently by Biener 2004). In passing, I shalltouch on his methodology and his mathematics (and here refer you tosome of the recent work by Palmieri 2001, 2003). At the end I shall havesome words about Galileo, the Catholic Church and his trial.

3. Galileo's Scientific StoryThe philosophical thread that runs through Galileo's intellectual life is astrong and increasing desire to find a new conception of what constitutesnatural philosophy and how natural philosophy ought to be pursued.Galileo signals this goal clearly when he leaves Padua in 1611 to return toFlorence and the court of the Medici and asks for the title Philosopher aswell as Mathematician. This was not just a status-affirming request, butalso a reflection of his large-scale goal. What Galileo accomplished by theend of his life in 1642 was a reasonably articulated replacement for thetraditional set of analytical concepts connected with the Aristotelian

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tradition of natural philosophy. He offered, in place of the Aristoteliancategories, a set of mechanical concepts that were accepted by mosteveryone who afterwards developed the new sciences, and which, insome form or another, became the hallmark of the new philosophy. Hisway of thinking became the way of the scientific revolution (and yes, therewas such a revolution pace Shapin 1996 and others, cf. selections inLindberg 1990, Osler 2000.)

Some scholars might wish to describe what Galileo achieved inpsychological terms as an introduction of new mental models (Palmieri2003) or a new model of intelligibility (Machamer 1998). Howeverphrased, Galileo's main move was to de-throne the Aristotelian physicalcategories of the one celestial (the aether or fifth element) and fourterrestrial elements (fire, air, water and earth) and their differentialdirectional natures of motion (circular, and up and down). In their placehe left only one element, corporeal matter, and a different way ofdescribing the properties and motions of matter in terms of themathematics of the equilibria of proportional relations (Palmieri 2001) thatwere typified by the Archimedian simple machinesthe balance, theinclined plane, the lever, and, he includes, the pendulum (Machamer 1998,Machamer and Hepburn 2004, Palmieri 2008). In doing so Galileochanged the acceptable way of talking about matter and its motion, and soushered in the mechanical tradition that characterizes so much of modernscience, even today. But this would take more explaining (Dijksterhuis1950, Machamer et al. 2000, Gaukroger 2009).

As a main focus underlying Galileo's accomplishments, it is useful to seehim as being interested in finding a unified theory of matter, amathematical theory of the material stuff that constitutes the whole of thecosmos. Perhaps he didn't realize that this was his grand goal until thetime he actually wrote the Discourses on the Two New Sciences in 1638.Despite working on problems of the nature of matter from 1590 onwards,

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he could not have written his final work much earlier than 1638, certainlynot before The Starry Messenger of 1610, and actually not before theDialogues on the Two Chief World Systems of 1632. Before 1632, he didnot have the theory and evidence he needed to support his claim aboutunified, singular matter. He had thought deeply about the nature of matterbefore 1610 and had tried to work out how best to describe matter, but theidea of unified matter theory had to wait on the establishment of principlesof matter's motion on a moving earth. And this he did not do until theDialogues.

Galileo began his critique of Aristotle in the 1590 manuscript, De Motu.The first part of this manuscript deals with terrestrial matter and arguesthat Aristotle's theory has it wrong. For Aristotle, sublunary or terrestrialmatter is of four kinds [earth, air, water, and fire] and has two forms,heavy and light, which by nature are different principles of (natural)motion, down and up. Galileo, using an Archimedian model of floatingbodies and later the balance, argues that there is only one principle ofmotion, the heavy (gravitas), and that lightness (or levitas) is to beexplained by the heavy bodies moving so as to displace or extrude otherbits of matter in such a direction that explains why the other bits rise. Soon his view heaviness (or gravity) is the cause of all natural terrestrialmotion. But this left him with a problem as to the nature of the heavy, thenature of gravitas? In De Motu, he argued that the moving arms of abalance could be used as a model for treating all problems of motion. Inthis model heaviness is the proportionality of weight of one object on onearm of a balance to that of the weight of another body on the other arm ofthe balance. In the context of floating bodies, weight is the weight of onebody minus weight of the medium.

Galileo realized quickly these characterizations were insufficient, and sobegan to explore how heaviness was relative to the different specificgravities of bodies having the same volume. He was trying to figure out

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what is the concept of heaviness that is characteristic of all matter. Whathe failed to work out, and this was probably the reason why he neverpublished De Motu, was this positive characterization of heaviness. Thereseemed to be no way to find standard measures of heaviness that wouldwork across different substances. So at this point he did not have usefulreplacement categories.

A while later, in his 1600 manuscript, Le Mecaniche (Galileo 1600/1960)he introduces the concept of momento, a quasi force concept that appliesto a body at a moment and which is somehow proportional to weight orspecific gravity (Galluzzi 1979). Still, he has no good way to measure orcompare specific gravities of bodies of different kinds and his notebooksduring this early 17th-century period reflect his trying again and again tofind a way to bring all matter under a single proportional measuring scale.He tries to study acceleration along an inclined plane and to find a way tothink of what changes acceleration brings. In this regard and during thisperiod he attempts to examine the properties of percussive effect of bodiesof different specific gravities, or how they have differential impacts. Yetthe details and categories of how to properly treat weight and movementelude him.

One of Galileo's problems was that the Archimedian simple machines thathe was using as his model of intelligibility, especially the balance, are noteasily conceived of in a dynamic way. Except for the inclined plane, timeis not a property of the action of simple machines that one would normallyattend to. In discussing a balance, one does not normally think about howfast an arm of the balance descends nor how fast a body on the oppositearm is rising (though Galileo in his Postils to Rocco ca. 163445 does; seePalmieri 2005). The converse is also true. It is difficult to modeldynamic phenomena that deal with the rate of change of different bodiesas problems of balance arms moving upwards or downwards because ofdifferential weights. So it was that Galileo's classic dynamic puzzle about

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how to describe time and the force of percussion, or the force of body'simpact, would remain unsolved, He could not, throughout his life findsystematic relations among specific gravities, height of fall and percussiveforces. In the Fifth Day of the Discouses, he presciently explores theconcept of the force of percussion. This concept will become, after hisdeath, one of the most fecund ways to think about matter.

In 16039, Galileo worked long at doing experiments on inclined planesand most importantly with pendula. The pendulum again exhibited toGalileo that acceleration and, therefore, time is a crucial variable.Moreover, isochronyequal times for equal lengths of string, despitedifferent weightsgoes someway towards showing that time is a possibleform for describing the equilibrium (or ratio) that needs to be madeexplicit in representing motion. It also shows that in at least one case timecan displace weight as a crucial variable. Work on the force of percussionand inclined planes also emphasized acceleration and time, and during thistime (ca. 1608) he wrote a little treatise on acceleration that remainedunpublished.

We see from this period that Galileo's law of free fall arises out of thisstruggle to find the proper categories for his new science of matter andmotion. Galileo accepts, probably as early as the 1594 draft of LeMecaniche, that natural motions might be accelerated. But that acceleratedmotion is properly measured against time is an idea enabled only later,chiefly through his failure to find any satisfactory dependence on placeand specific gravity. Galileo must have observed that the speeds of bodiesincrease as they move downwards and, perhaps, do so naturally,particularly in the cases of the pendulum, the inclined plane, in free fall,and during projectile motion. Also at this time he begins to think aboutpercussive force, the force that a body acquires during its motion thatshows upon impact. For many years he thinks that the correct science ofthese changes should describe how bodies change according to where they

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are on their paths. Specifically, it seems that height is crucial. Percussiveforce is directly related to height and the motion of the pendulum seems toinvolve essentially equilibrium with respect to the height of the bob (andtime also, but isochrony did not lead directly to a recognition of time'simportance.)

The law of free fall, expressed as time squared, was discovered by Galileothrough the inclined plane experiments (Drake 1999, v. 2), but heattempted to find an explanation of this relation, and the equivalent meanproportional relation, through a velocity-distance relation. His later andcorrect definition of natural acceleration as dependent on time is an insightgained through recognizing the physical significance of the meanproportional relation (Machamer and Hepburn 2004; for a differentanalysis of Galileo's discovery of free fall see Renn et al. 2004.) YetGalileo would not publish anything making time central to motion until1638, in Discourses on the Two New Sciences (Galileo 1638/1954.) But letus return to the main matter.

In 1609 Galileo begins his work with the telescope. Many interpretershave taken this to be an interlude irrelevant to his physics. The StarryMessenger, which describes his early telescopic discoveries, waspublished in 1610. There are many ways to describe Galileo's findings butfor present purposes they are remarkable as his start at dismantling of thecelestial/terrestrial distinction (Feyerabend 1975). Perhaps the mostunequivocal case of this is when he analogizes the mountains on the moonto mountains in Bohemia. The abandonment of the heaven/earthdichotomy implied that all matter is of the same kind, whether celestial orterrestrial. Further, if there is only one kind of matter there can be only onekind of natural motion, one kind of motion that this matter has by nature.So it has to be that one law of motion will hold for earth, fire and theheavens. This is a far stronger claim than he had made back in 1590. Inaddition, he described of his discovery of the four moons circling Jupiter,

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which he called politically the Medicean stars (after the ruling family inFlorence, his patrons). In the Copernican system, the earth having a moonrevolve around it was unique and so seemingly problematic. Jupiter'shaving planets made the earth-moon system non-unique and so again theearth became like the other planets. Some fascinating background andtreatments of this period of Galileo's life and motivations have recentlyappeared (Biagoli 2006, Reeves 2008, and the essays in Hessler and DeSimone 2013).

In 1611, at the request of Cardinal Robert Bellarmine, the professors at theCollegio Romano confirmed Galileo's telescopic observations, with aslight dissent from Father Clavius, who felt that the moon's surface wasprobably not uneven. Later that year Clavius changed his mind.

A few years later in his Letters on the Sunspots (1612), Galileoenumerated more reasons for the breakdown of the celestial/terrestrialdistinction. Basically the ideas here were that the sun has spots (maculae)and rotated in circular motion, and, most importantly Venus had phasesjust like the moon, which was the spatial key to physically locating Venusas being between the Sun and the earth, and as revolving around the Sun.In these letters he claimed that the new telescopic evidence supported theCopernican theory. Certainly the phases of Venus contradicted thePtolemaic ordering of the planets.

Later in 1623, Galileo argued for a quite mistaken material thesis. In TheAssayer, he tried to show that comets were sublunary phenomena and thattheir properties could be explained by optical refraction. While this workstands as a masterpiece of scientific rhetoric, it is somewhat strange thatGalileo should have argued against the super-lunary nature of comets,which the great Danish astronomer Tycho Brahe had demonstrated earlier.

Yet even with all these changes, two things were missing. First, he needed

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to work out some general principles concerning the nature of motion forthis new unified matter. Specifically, given his Copernicanism, he neededto work out, at least qualitatively, a way of thinking about the motions ofmatter on a moving earth. The change here was not just the shift from aPtolemaic, Earth-centered planetary system to a Sun-centered Copernicanmodel. For Galileo, this shift was also from a mathematical planetarymodel to a physically realizable cosmography. It was necessary for him todescribe the planets and the earth as real material bodies. In this respectGalileo differed dramatically from Ptolemy, Copernicus, or even TychoBrahe, who had demolished the crystalline spheres by his comets-as-celestial argument and flirted with physical models (Westman 1976). Soon the new Galilean scheme there is only one kind of matter, and it mayhave only one kind of motion natural to it. Therefore, he had to devise (orshall we say, discover) principles of local motion that will fit a central sun,planets moving around that sun, and a daily whirling earth.

This he did by introducing two new principles. In Day One of hisDialogues on the Two Chief World Systems (Galileo 1632) Galileo arguedthat all natural motion is circular. Then, in Day Two, he introduced hisversion of the famous principle of the relativity of observed motion. Thislatter held that motions in common among bodies could not be observed.Only those motions differing from a shared common motion could be seenas moving. The joint effect of these two principles was to say that allmatter shares a common motion, circular, and so only motions differentfrom the common, say up and down motion, could be directly observed.Of course, neither of the principles originated with Galileo. They hadpredecessors. But no one needed them for the reasons that he did, namelythat they were necessitated by a unified cosmological matter.

In Day Three, Galileo dramatically argues for the Copernican system.Salviati, the persona of Galileo, has Simplicio, the ever astoundedAristotelian, make use of astronomical observations, especially the facts

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that Venus has phases and that Venus and Mars are never far from theSun, to construct a diagram of the planetary positions. The resultingdiagram neatly corresponds to the Copernican model. Earlier in Day One,he had repeated his claims from The Starry Messenger, noting that theearth must be like the moon in being spherical, dense and solid, andhaving rugged mountains. Clearly the moon could not be a crystallinesphere as held by some Aristotelians.

In the Dialogues, things are more complicated than I have just sketched.Galileo, as noted, argues for a circular natural motion, so that all things onthe earth and in the atmosphere revolve in a common motion with theearth so that the principle of the relativity of observed motion will apply tophenomena such as balls dropped from the masts of moving ships. Yet healso introduces at places a straight-line natural motion. For example, inDay Three, he gives a quasi account for a Coriolis-type effect for thewinds circulating about the earth by means of this straight-line motion.(David Miller discovered this in the text; see also Hooper 1998.) Further,in Day Four, when he is giving his proof of the Copernican theory bysketching out how the three-way moving earth mechanically moves thetides, he nuances his matter theory by attributing to the element water thepower of retaining an impetus for motion such that it can provide areciprocal movement once it is sloshed against a side of a basin. This wasnot Galileo's first dealing with water. We saw it in De Motu in 1590, withsubmerged bodies, but more importantly he learned much more whileworking through his dispute over floating bodies. (Discourse on FloatingBodies, 1612). In fact a large part of this debate turned on the exact natureof water as matter, and what kind of mathematical proportionality could beused to correctly describe it and bodies moving in it (Cf. Palmieri, 1998,2004a).

The final chapter of Galileo's scientific story comes in 1638 with thepublication of Discourses of the Two New Sciences. The second science,

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discussed (so to speak) in the last two days, dealt with the principles oflocal motion. These have been much commented upon in the Galileanliterature. Here is where he enunciates the law of free fall, the parabolicpath for projectiles and his physical discoveries (Drake 1999, v. 2). Butthe first two days, the first science, has been much misunderstood andlittle discussed. This first science, misleadingly, has been called thescience of the strength of materials, and so seems to have found a place inhistory of engineering, since such a course is still taught today. However,this first science is not about the strength of materials per se. It is Galileo'sattempt to provide a mathematical science of his unified matter. (SeeMachamer 1998, Machamer and Hepburn 2004, and the detailed workspelling this out by Biener 2004). Galileo realizes that before he can workout a science of the motion of matter, he must have some way of showingthat the nature of matter may be mathematically characterized. Both themathematical nature of matter and the mathematical principles of motionhe believes belong to the science of mechanics, which is the name he givesfor this new way of philosophizing. Remember that specific gravities didnot work.

So it is in Day One that he begins to discuss how to describe,mathematically (or geometrically), the causes of how beams break. He issearching for the mathematical description of the essential nature ofmatter. He rules out certain questions that might use infinite atoms as basisfor this discussion, and continues on giving reasons for various propertiesthat matter has. Among these are questions of the constitution of matter,properties of matter due to its heaviness, the properties of the media withinwhich bodies move and what is the cause of a body's coherence as a singlematerial body. The most famous of these discussions is his account ofacceleration of falling bodies, that whatever their weight would fallequally fast in a vacuum. The Second Day lays out the mathematicalprinciples concerning how bodies break. He does this all by reducing theproblems of matter to problems of how a lever and a balance function.

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Something he had begun back in 1590, though this time he believes he isgetting it right, showing mathematically how bits of matter solidify andstick together, and do so by showing how they break into bits. Theultimate explanation of the sticking eluded him since he felt he wouldhave to deal with infinitesimals to really solve this problem.

The second science, Days Three and Four of Discorsi, dealt with properprinciples of local motion, but this was now motion for all matter (not justsublunary stuff) and it took the categories of time and acceleration asbasic. Interestingly Galileo, here again, revisited or felt the need to includesome anti-Aristotelian points about motion as he had done back in 1590.The most famous example of his doing this, is his beautiful thoughtexperiment, whereby he compares two bodies of the same material ofdifferent sizes and points out that according to Aristotle they fall atdifferent speeds, the heavier one faster. Then, he says, join the bodiestogether. In this case the lightness of the small one ought to slow down thefaster larger one, and so they together fall as a speed less than the heavyfell in the first instance. Then his punch line: but one might also conceiveof the two bodies joined as being one larger body, in which case it wouldfall even more quickly. So there is a contradiction in the Aristotelianposition (Palmieri 2005). His projected Fifth Day would have treated thegrand principle of the power of matter in motion due to impact. He calls itthe force of percussion, which deals with two bodies interacting. Thisproblem he does not solve, and it won't be solved until Descartes,probably following Beeckman, turns the problem into finding theequilibrium points for colliding bodies.

The sketch above provides the basis for understanding Galileo's changes.He has a new science of matter, a new physical cosmography, and a newscience of local motion. In all these he is using a mathematical mode ofdescription based upon, though somewhat changed from, the proportionalgeometry of Euclid, Book VI and Archimedes (for details on the change

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see Palmieri 2002).

It is in this way that Galileo developed the new categories of themechanical new science, the science of matter and motion. His newcategories utilized some of the basic principles of traditional mechanics, towhich he added the category of time and so emphasized acceleration. Butthroughout, he was working out the details about the nature of matter sothat it could be understood as uniform and treated in a way that allowedfor coherent discussion of the principles of motion. That a unified matterbecame accepted and its nature became one of the problems for the newscience that followed was due to Galileo. Thereafter, matter reallymattered.

4. Galileo and the ChurchNo account of Galileo's importance to philosophy can be complete if itdoes not discuss Galileo's condemnation and the Galileo affair(Finocchiaro 1989). The end of the episode is simply stated. In late 1632,after publishing Dialogues on the Two Chief World Systems, Galileo wasordered to go to Rome to be examined by the Holy Office of theInquisition. In January 1633, a very ill Galileo made an arduous journey toRome. Finally, in April 1633 Galileo was called before the Holy Office.This was tantamount to a charge of heresy, and he was urged to repent(Shea and Artigas, 183f). Specifically, he had been charged with teachingand defending the Copernican doctrine that holds that the Sun is at thecenter of the universe and that the earth moves. This doctrine had beendeemed heretical in 1616, and Copernicus' book had placed on the indexof prohibited books, pending correction.

Galileo was called four times for a hearing; the last was on June 21, 1633.The next day, 22 June, Galileo was taken to the church of Santa Mariasopra Minerva, and ordered to kneel while his sentence was read. It was

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declared that he was vehemently suspect of heresy. Galileo was made torecite and sign a formal abjuration:

Galileo was not imprisoned but had his sentence commuted to housearrest. In December 1633 he was allowed to retire to his villa in Arcetri,outside of Florence. During this time he finished his last book, Discourseson the Two New Sciences, which was published in 1638, in Holland, byLouis Elzivier. The book does not mention Copernicanism at all, andGalileo professed amazement at how it could have been published. Hedied on January 8, 1642.

There has been much controversy over the events leading up to Galileo'strial, and it seems that each year we learn more about what actuallyhappened. There is also controversy over the legitimacy of the chargesagainst Galileo, both in terms of their content and judicial procedure. Thesummary judgment about this latter point is that the Church most probablyacted within its authority and on good grounds given the condemnationof Copernicus, and, as we shall see, the fact that Galileo had been warnedby Cardinal Bellarmine earlier in 1616 not to defend or teachCopernicanism. There were also a number of political factors given theCounter Reformation, the 30 Years War (Miller 2008), and the problemswith the papacy of Urban VIII that served as further impetus to Galileo's

I have been judged vehemently suspect of heresy, that is, of havingheld and believed that the sun in the centre of the universe andimmoveable, and that the earth is not at the center of same, andthat it does move. Wishing however, to remove from the minds ofyour Eminences and all faithful Christians this vehement suspicionreasonably conceived against me, I abjure with a sincere heart andunfeigned faith, I curse and detest the said errors and heresies, andgenerally all and every error, heresy, and sect contrary to the HolyCatholic Church. (Quoted in Shea and Artigas 194)

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condemnation (McMullin, ed. 2005). It has even been argued (Redondi1983) that the charge of Copernicanism was a compromise plea bargain toavoid the truly heretical charge of atomism. Though this latter hypothesishas not found many willing supporters.

Legitimacy of the content, that is, of the condemnation of Copernicus, ismuch more problematic. Galileo had addressed this problem in 1615,when he wrote his Letter to Castelli (which becomes known as the Letterto the Grand Duchess Christina). In this letter he had argued that, ofcourse, the Bible was an inspired text, yet two truths could not contradictone another. So in cases where it was known that science had achieved atrue result, the Bible ought to be interpreted in such a way that makes itcompatible with this truth. The Bible, he argued, was an historicaldocument written for common people at an historical time, and it had to bewritten in language that would make sense to them and lead them towardsthe true religion.

Much philosophical controversy, before and after Galileo's time, revolvesaround this doctrine of the two truths and their seeming incompatibility.Which of course, leads us right to such questions as: What is truth? andHow is truth known or shown?

Cardinal Bellarmine was willing to countenance scientific truth if it couldbe proven or demonstrated (McMullin 1998). But Bellarmine held that theplanetary theories of Ptolemy and Copernicus (and presumably TychoBrahe) were only hypotheses and due to their mathematical, purelycalculatory character were not susceptible to physical proof. This is a sortof instrumentalist, anti-realist position (Duhem 1985, Machamer 1976).There are any number of ways to argue for some sort of instrumentalism.Duhem (1985) himself argued that science is not metaphysics, and so onlydeals with useful conjectures that enable us to systematize the phenomena.Subtler versions, without an Aquinian metaphysical bias, of this position

Peter Machamer


have been argued subsequently and more fully by van Fraassen (1996) andothers. Less sweepingly, it could reasonably be argued that both Ptolemyand Copernicus' theories were primarily mathematical, and that whatGalileo was defending was not Copernicus' theory per se, but a physicalrealization of it. In fact, it might be better to say the Copernican theorythat Galileo was constructing was a physical realization of parts ofCopernicus' theory, which, by the way, dispensed with all themathematical trappings (eccentrics, epicycles, Tusi couples and the like).Galileo would be led to such a view by his concern with matter theory. Ofcourse, put this way we are faced with the question of what constitutesidentity conditions for a theory, or being the same theory. There is clearlya way in which Galileo's Copernicus is not Copernicus and most certainlynot Kepler.

The other aspect of all this which has been hotly debated is: whatconstitutes proof or demonstration of a scientific claim? In 1616, the sameyear that Copernicus' book was placed on the Index of Prohibited Books,Galileo was called before Cardinal Robert Bellarmine, head of the HolyOffice of the Inquisition and warned not to defend or teachCopernicanism. During this year Galileo also completed a manuscript, Onthe Ebb and Flow of the Tides. The argument of this manuscript will turnup 17 years later as day Four of Galileo's Dialogues concerning the TwoChief World Systems. This argument, about the tides, Galileo believedprovided proof of the truth of the Copernican theory. But insofar as itpossibly does, it provides an argument for the physical plausibility ofGalileo's Copernican theory. Let's look more closely at his argument.

Galileo argues that the motion of the earth (diurnal and axial) is the onlyconceivable (or maybe plausible) physical cause for the reciprocal regularmotion of the tides. He restricts the possible class of causes to mechanicalmotions, and so rules out Kepler's attribution of the moon as a cause. Howcould the moon without any connection to the seas cause the tides to ebb

Galileo Galilei


and flow? Such an explanation would be the invocation of magic or occultpowers. So the motion of the earth causes the waters in the basins of theseas to slosh back and forth, and since the earth's diurnal and axial rotationis regular, so are the periods of the tides; the backward movement is due tothe residual impetus built up in the water during its slosh. Differences intidal flows are due to the differences in the physical conformations of thebasins in which they flow (for background and more detail, see Palmieri1998).

Albeit mistaken, Galileo's commitment to mechanically intelligiblecausation makes this is a plausible argument. One can see why Galileothinks he has some sort of proof for the motion of the earth, and thereforefor Copernicanism. Yet one can also see why Bellarmine and theinstrumentalists would not be impressed. First, they do not acceptGalileo's restriction of possible causes to mechanically intelligible causes.Second, the tidal argument does not directly deal with the annual motionof the earth about the sun. And third, the argument does not touchanything about the central position of the sun or about the periods of theplanets as calculated by Copernicus. So at its best, Galileo's argument isan inference to the best partial explanation of one point in Copernicus'theory. Yet when this argument is added to the earlier telescopicobservations that show the improbabilities of the older celestial picture, tothe fact that Venus has phases like the moon and so must revolve aroundthe sun, to the principle of the relativity of perceived motion whichneutralizes the physical motion arguments against a moving earth, it wasenough for Galileo to believe that he had the necessary proof to convincethe Copernican doubters. Unfortunately, it was not until after Galileo'sdeath and the acceptance of a unified material cosmology, utilizing thepresuppositions about matter and motion that were published in theDiscourses on the Two New Sciences, that people were ready for suchproofs. But this could occur only after Galileo had changed the acceptableparameters for gaining knowledge and theorizing about the world.

Peter Machamer


To read many of the documents of Galileo's trial see Finocchiaro 1989,and Mayer 2012. To understand the long, tortuous, and fascinatingaftermath of the Galileo affair see Finocchiaro 2005, and for John Paul II'sattempt see George Coyne's article in McMullin 2005.

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Galileo Galilei


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Other Internet ResourcesGalileo Galilei's Notes on Motion, Joint Project of BibliotecaNazionale Centrale, Florence Istituto e Museo di Storia della Scienza,Florence Max Planck Institute for the History of Science, Berlin.The Galileo Project, contains Dava Sobel's translations of all 124letters from Suor Maria Celeste to Galileo in the sequence in whichthey were written, maintained by Albert Van Helden.Galileo Galilei, The Institute and Museum of the History of Scienceof Florence, Italy.

Related EntriesCopernicus, Nicolaus | matter | natural philosophy: in the Renaissance |religion: and science

Acknowledgements

Thanks to Zvi Biener and Paolo Palmieri for commenting on earlier draftsof this entry.

Copyright 2013 by the author Peter Machamer

Project (InPhO).Enhanced bibliography for this entry at PhilPapers, with linksto its database.

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galileo galilei - machamer,2013.leibniz.stanford

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