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First published Fri Mar 4, 2005; substantive revision Fri Jun 4, 2021

Galileo Galilei (1564–1642) has always played a key role in anyhistory of science, as well as many histories of philosophy. He isa—if not the—central figure of the ScientificRevolution of the seventeenth century. His work in physics (or“natural philosophy”), astronomy, and the methodology ofscience still evoke debate after more than 400 years. His role inpromoting the Copernican theory and his travails and trials with theRoman Church are stories that still require re-telling. This articleattempts to provide an overview of these aspects of Galileo’slife and work, but does so by focusing in a new way on his argumentsconcerning the nature of matter.

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1. Brief Biography

Galileo was born in Pisa on February 15, 1564. By the time he died onJanuary 8, 1642 (but for problems with the date, see Machamer 1998b,24–25), he was as famous as any person in Europe. Moreover, whenhe was born there was no such thing as ‘science’; yet bythe time he died, science was well on its way to becoming adiscipline, and its concepts and method a complete philosophicalsystem.

Galileo’s father Vincenzo, though of noble heritage, was asemi-itinerant court musician and composer of modest means, who alsoauthored treatises on music theory; his mother, Giulia Ammannati,descended from Pisan cloth merchants. In 1572, they resettled thefamily in Florence. As a boy, Galileo was tutored privately and, for atime, by the monks at Vallombrosa, where he considered a religiousvocation and may have started a novitiate. He returned home, however,and then enrolled for a medical degree at the University of Pisa in1580. He never completed this degree, but instead studied mathematics,notably with Ostilio Ricci, a mathematics teacher attached to theTuscan court and the Florentine Accademia del Disegno.

After leaving university, Galileo worked as a private mathematicstutor around Florence and Siena and cultivated the support of leadingmathematicians. He visited Christoph Clavius, professor at the JesuitCollegio Romano, and corresponded with the engineer Guildobaldo delMonte, Marchese of Urbino. In 1588, he applied and was turned down fora professorship in Bologna, but a year later, with the help of Claviusand del Monte, he was appointed lecturer in mathematics at Pisa. In1592, he obtained, at a much higher salary, a chair of mathematics atthe University of Padua, in the Venetian Republic. Galileo alsosupplemented his income by producing a calculating instrument of hisown design (see Galilei 1606) and other devices in a householdworkshop, and by private tutoring and consulting on practicalmathematics and engineering. During this period, he began arelationship with Marina Gamba, and their daughter Virginia was bornin 1600. In 1601, they had another daughter, Livia, and a son,Vincenzo, in 1606.

Daughter

In Padua, Galileo worked out much of the mechanics he would publishlater in life, and which constitute his primary lastingcontribution to physical science. However, these projects wereinterrupted in 1609, when Galileo heard about the recently inventedspyglass, invented an improved telescope, and used it to makeastounding celestial discoveries. He rushed these into print inSidereus Nuncius (Starry Messenger), which appearedin March 1610 and launched Galileo onto the world stage. Among others,Johannes Kepler, Imperial Mathematician at Prague, lauded the work(Kepler 1610). Clavius and his colleagues at the Collegio Romanoconfirmed its results and threw a celebratory banquet when Galileovisited in 1611. During the same Roman sojourn, Galileo was admittedto what was perhaps the first scientific society, the Accademia deiLincei; he would style himself “Lincean Academician” forthe rest of his life. Some fascinating treatments of this periodof Galileo’s life and motivations have recently appeared(Biagioli 2006; Reeves 2008; Wilding 2014).

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Galileo also used the Starry Messenger to solicit patronagein his native Tuscany, naming the moons of Jupiter he had found the“Medicean” stars, in honor of the ruling Medici family.His negotiations were ultimately successful, and Galileo moved toFlorence as “Chief Mathematician and Philosopher to the GrandDuke” and holder of a sinecure professorship at Pisa. Hisdaughters moved with him and were shortly placed in the convent ofSaint Matthew at Arcetri, near Florence. Vincenzo and his mother,Marina, were left behind in Venice.

Once a courtier, Galileo entered into several debates on scientifictopics. In 1612, he published a Discourse on Floating Bodies,and in 1613, Letters on Sunspots, where he first openlyexpressed support for Copernican heliocentrism. In 1613–14,Galileo entered into discussions of Copernicanism through his studentBenedetto Castelli, and wrote a Letter to Castellidefending the doctrine from theological objections. Meanwhile, ithad become known that Copernicanism was under scrutiny by Churchauthorities. Galileo lectured and lobbied against its condemnation,expanding his Letter to Castelli into the widelycirculated Letter to the Grand Duchess Christina in 1615and travelling to Rome late that year. Nevertheless, in March 1616,Copernicus’s On the Revolutions of the Heavenly Orbswas suspended (i.e., temporarily censored), pending correction,by the Congregation of the Index of Prohibited Books. Galileo himselfwas called to an audience with Cardinal Robert Bellarmine, a leadingtheologian and member of the Roman Inquisition, who admonished him notto teach or defend Copernican theory. (The details of this episode arefar from straightforward, and remain disputed even today. See Shea andArtigas 2003; Fantoli 2005.)

In 1623, Galileo published The Assayer, which deals withthe nature of comets and argues they are sublunary phenomena. Thisbook includes some of Galileo’s most famous methodologicalpronouncements, including the claim that the book of nature is writtenin the language of mathematics. It also contains passages suggestiveof atomism, a heretical doctrine, for which the book was referred tothe Inquisition, which dismissed the charge.

Also in 1623, Maffeo Barberini, Galileo’s supporter and friend,was elected Pope Urban VIII. Galileo felt empowered to begin work onhis Dialogue Concerning the Two Chief World Systems. The“two systems” are the Ptolemaic and Copernican, and thetext clearly, though not explicitly, favors the latter. Printing wascompleted in Florence by February 1632. Shortly afterwards, theInquisition banned its sale, and Galileo was ordered to Rome fortrial. In June 1633, Galileo was convicted of “vehementsuspicion of heresy,” and a sentence of imprisonment wasimmediately commuted to perpetual house arrest. (There is more aboutthese events and their implications in the final section of this article, Galileo and the Church.)

In 1634, while Galileo was confined to his villa in Arcetri, hisbeloved eldest daughter died (Sobel 1999). Around this time, he beganwork on his final book, Discourses and MathematicalDemonstrations Concerning Two New Sciences, based on themechanics he had developed early in his career. The manuscript wassmuggled out of Italy and published in Holland by the Elzeviers in1638. Galileo died early in 1642, and due to his condemnation, hisburial place was obscure until he was re-interred in 1737.

For detailed biographical material, the best and classic work dealingwith Galileo’s scientific achievements is StillmanDrake’s Galileo at Work (1978). Morerecently, J. L. Heilbron has written a magnificentbiography, Galileo (2010), that touches on all themultiple facets of his life.

2. Introduction and Background

From the seventeenth century onward, Galileo has been seen by many asthe “hero” of modern science. He is renowned for hisdiscoveries: he was the first to report telescopic observations of themountains on the moon, the moons of Jupiter, the phases of Venus, andthe rings of Saturn. He invented an early microscope and a predecessorto the thermometer. In mathematical physics—a discipline hehelped create—he calculated the law of free fall, conceived ofan inertial principle, determined the parabolic trajectory ofprojectiles, and advocated the relativity of motion. He is thought tobe the first “real” experimental scientist, who droppedstones from towers and ships’ masts, and played with magnets,clocks, and pendulums (noting the isochrony of the latter). Much ofhis cultural stature also arises from his advocacy and popularizationof Copernicanism and the resulting condemnation by the CatholicInquisition, which has made him a purported “martyr” tothe cause of rationality and enlightened modernity in the subsequenthistory of a supposed “warfare” between science andreligion. This is no small set of accomplishments for oneseventeenth-century Italian, who was the son of a court musician andwho left the University of Pisa without a degree.

Momentous figures living in momentous times are full of interpretivefecundity, and Galileo has been the subject of manifoldinterpretations and much controversy. The use of Galileo’s workand the invocations of his name make a fascinating history(Segre 1991; Palmerino and Thijssen 2004; Finocchiaro 2005; Sheaand Artigas 2006), but this is not our topic, which are thephilosophical implications of his work.

Philosophically, Galileo has been used to exemplify many differentthemes, usually as a personification of whatever the writer wished tomake the hallmark of the Scientific Revolution or of the nature ofgood science—whatever was good about the new science or sciencein general, it was Galileo who started it. One tradition of Galileoscholarship has divided Galileo’s work into three or four parts:(1) his physics, (2) his astronomy, and (3) his methodology, whichmight include his method of Biblical interpretation and/or histhoughts about the nature of proof or demonstration. In thistradition, typical treatments deal with his physical and astronomicaldiscoveries and their background and/or who were Galileo’spredecessors. More philosophically, many ask how his mathematicalpractice relates to his natural philosophy. Was he a mathematicalPlatonist (Jardine 1976; Koyré 1978), an experimentalist(Settle 1967; Settle 1983; Settle 1992; Palmieri 2008), anAristotelian emphasizing experience (Geymonat 1954), a precursor ofmodern positivist science (Drake 1978), or maybe an Archimedean(Machamer 1998a), who might have used a revised Scholastic method ofproof (Wallace 1992; Miller 2018)? Or did he have no method and justfly like an eagle in the way that geniuses do (Feyerabend 1975)?Alongside these claims there have been attempts to place Galileo in anintellectual context that brings out the background to hisachievements. Some have emphasized his debt to the artisan/engineerpractical tradition (Rossi 1962; Valleriani 2010), others hismathematics (Giusti 1993; Feldhay 1998; Renn, et al. 2000; Palmieri2001; Palmieri 2003; Peterson 2011; Palmerino 2016), his mixed (orsubalternate) mathematics (Machamer 1978; Lennox 1986; Wallace 1992;Dear 1995; Machamer 1998a), his debt to atomism (Shea 1972; Redondi1983), his use of Hellenistic and Medieval impetus theory (Moody 1951;Duhem 1954; Clagett 1959; Shapere 1974), or the idea that discoveriesbring new data into science (Wootton 2015).

Still, almost everyone working in this tradition seems to think thethree areas—physics, astronomy, and methodology—aresomewhat distinct and represent different Galilean endeavors. Morerecent historical research has followed contemporary intellectualfashion and shifted foci, bringing new dimensions to our understandingof Galileo by studying his rhetoric (Finocchiaro 1980; Moss 1993;Feldhay 1998; Spranzi 2004), the power structures of his social milieu(Biagioli 1993; Biagioli 2006), his personal quest for acknowledgment(Shea and Artigas 2003), and more generally emphasizing the largersocial and cultural history (Reeves 2008; Bucciantini, et al. 2015),in particular the court and papal culture in which Galileofunctioned (Redondi 1983; 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 out this path, weshall show why, at the end of his life, Galileo felt compelled (insome sense of necessity) to write the Two New Sciences,which stands as a true completion of his overall project and is notjust a reworking of his earlier research that he reverted to after histrial, when he was under house arrest and going blind. Particularly,we shall try to show why both of the two new sciences,especially the first, were so important—a topic not muchtreated except recently (Biener 2004; Raphael 2011). Inpassing, we shall touch on his methodology and his mathematics, andhere refer you to some of the recent work by Palmieri (2001; 2003). Atthe end, we shall add some words about Galileo, the Catholic Church,and his trial.

3. Galileo’s Scientific Story

The philosophical thread that runs through Galileo’sintellectual life is a strong and increasing desire to find a newconception of what constitutes natural philosophy and how naturalphilosophy ought to be pursued. Galileo signaled this goal clearlywhen he left Padua in 1610 to return to Florence and the court of theMedici. He asked for and received the designation‘Philosopher’, in addition to ‘Mathematician’.This was not just a status-affirming request, but also a reflection ofhis programmatic aims. What Galileo accomplished by the end of hislife was a reasonably articulated replacement for the traditional setof analytical concepts connected with the Aristotelian tradition ofnatural philosophy. He offered, in place of the Aristoteliancategories, a set of mechanical archetypes that were accepted by mosteveryone who afterwards developed the “new sciences,” andwhich, in some form or another, became the hallmark of the newphilosophy. His way of thinking became the way of the ScientificRevolution (and yes, there was such a revolution, pace Shapin1996 and others; see the selections in Lindberg and Westman 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 1994; Machamer,1998a; Adams, et al. 2017). However phrased, Galileo’s main movewas to dethrone the Aristotelian physical categories; namely, the onecelestial element (aether, or quintessence—i.e.,“fifth element”) and the four terrestrial ones (fire, air,water, and earth), along with their respective motive natures(circular, and up and down). In their place, he left only oneelement, corporeal matter, whose properties and motions he describedusing the mathematics of proportional relations typified by theArchimedian simple machines—the balance, the inclined plane, andthe lever—to which Galileo added the pendulum (Machamer 1998a;Machamer and Hepburn 2004; Palmieri 2008). In doing so, Galileochanged the acceptable way of talking about matter and its motion, andso ushered in the mechanical tradition that characterizes so much ofmodern science, even today. See Dijksterhuis 1961; Machamer, et al.2000; Gaukroger 2006; Roux and Garber 2013.

As a way of understanding Galileo’s accomplishments, it isuseful to see him as being interested in finding a unified theory ofmatter—a mathematical theory of the material stuff thatconstitutes the whole of the cosmos. Perhaps he did not realize thatthis was his grand project until the time he actually wrote theTwo New Sciences in the mid-1630s. Despite working onproblems of the nature of matter from 1590 onwards, he could not havewritten his final work much earlier than 1638; certainly notbefore the Starry Messenger of 1610, and probablynot before the Dialogue Concerning the Two Chief WorldSystems of 1632. He had thought deeply about the nature ofmatter before 1610 and had tried to work out how best to describematter, but before 1632, he did not have the theory and evidence heneeded to support his claims about a unified, singular matter. Theidea of unified matter theory had to wait for theestablishment of principles of matter’s motion on a movingEarth. And this he did not accomplish untilthe Dialogue.

Galileo began his critique of Aristotle in a treatise he draftedaround 1590, titled De Motu (On Motion). Thefirst part of this manuscript deals with terrestrial matter and arguesthat Aristotle’s theory has it wrong. For Aristotle, the matterof the terrestrial realm within the sphere of the moon is of fourelemental kinds—earth, water, air, and fire. These possess twoformal principles that give rise to their natural motion: heaviness(gravitas; in earth and water) and lightness(levitas; in air and fire). Galileo, using an Archimedeanmodel of floating bodies, and later the balance, argues that there isonly one principle of motion—heaviness. Bodies move upward notbecause they have a natural lightness, he says, but because they aredisplaced or extruded by other heavier bodies moving downward. So onhis view, heaviness is the cause of all natural terrestrialmotion.

This move left Galileo with a problem: what is heaviness and how is itto be described? In De Motu, he argued that the movingarms of a balance could be used as a model for treating all problemsof natural motion. In this model, heaviness is the proportionality ofthe weight of an object on one arm of the balance to the weight ofanother body on the other arm. In the context of floating bodies,heaviness is the weight of one body minus the weight of the medium.Galileo quickly realized these characterizations were insufficient,and so began to explore how heaviness might be related to specificgravities; i.e., the comparative weights of bodies having equalvolume. He was trying to figure out the concept of heaviness that ischaracteristic of all matter. What he failed to work out—andthis was probably the reason why he never published DeMotu—was this positive characterization of heaviness. Thereseemed to be no way to find a standard measure of heaviness that wouldwork across different substances. At this point, he did not have auseful replacement for Aristotelian gravitas.

A while later, in his 1600 manuscript version of LeMeccaniche (On Mechanics), Galileo introduced theconcept of momento, a quasi forcethat applies to a body at a moment, and which is somehow proportionalto weight or specific gravity (Galluzzi 1979). Still, he had no goodway to measure or compare specific gravities of bodies of differentkinds, and his notebooks during this early seventeenth-century periodreflect his trying again and again to find a way to bring all matterunder a single proportional measuring scale. He tried to studyacceleration along an inclined plane and to find a way to think ofwhat changes acceleration brings to momento. Yet the detailsand categories of how to properly treat weight and movement eludedhim.

We see from this period that Galileo’s law of free fall arisesout of this struggle to find the proper categories for his new scienceof matter and motion. Galileo accepted, probably as early as the 1594draft of Le Meccaniche, that natural motions might beaccelerated. Particularly in the cases of the pendulum, the inclinedplane, free fall, and projectile motion, Galileo must have observedthat the speeds of bodies increase as they move downwards and,perhaps, do so naturally. But that accelerated motion is properlymeasured against time is an idea he realized only later, chieflythrough his failure to find any satisfactory dependence on place andspecific gravity. Also at this time, he began to think aboutpercussive force. For many years, he thought that the correct scienceof these phenomena should describe how bodies change according towhere they are on their paths. Specifically, it seemed that height iscrucial. Percussive force is directly related to height and the motionof the pendulum seems to involve equilibrium with respect to theheight of the bob (and time also, but isochrony did not lead directlyto a recognition of time’s importance).

One of Galileo’s problems was that the Archimedian simplemachines he was using as his models of intelligibility, especially thebalance, are not easily conceived of in a dynamic way (but seeMachamer and Woody 1994). Since they generally work by establishingstatic equilibrium, time is not a feature of their action one wouldnormally attend to. In discussing a balance, for instance, one doesnot normally think about how fast an arm of the balance descends, norhow fast a body on the opposite arm is rising (though Galileo does inhis Postils to Rocco circa 1634–45; seePalmieri 2005). The converse is also true. It is difficult to modeldynamic phenomena that involve rates of change as balance arms movingupwards or downwards because of differential weights. So it was thatGalileo’s puzzle about how to describe time and the force ofpercussion (the force of body’s impact) would remain unsolved.Throughout his life, he could not find systematic relations amongspecific gravities, heights of fall, and percussive forces. Even whilethe Two New Sciences was going to press in 1638, Galileo waslaboring on an additional “Fifth Day” (not published until1718) that presciently explored the concept of the force ofpercussion, which would become, after his death, one of the mostfecund ways to think about matter and its motion.

In the period 1603–9, Galileo experimented with inclined planesand, most importantly, pendulums. These studies again exhibited toGalileo that acceleration and, therefore, time is a crucial variable.Moreover, the isochrony of the pendulum—the period depends onlyon the length of the cord, regardless of the weight of thebob—went some way towards showing that time is a possible termin the equilibrium (or ratio) that needs to be made explicit torepresent motion. It also shows that, in at least one case, time candisplace weight as a crucial variable.

The law of free fall—i.e., a body in free fall from resttraverses a distance proportional to the square of the timeelapsed—was discovered by Galileo through the inclined planeexperiments (Drake 1999, v. 2). At first, Galileo attempted torepresent this phenomenon with a velocity-distance relation, and theequivalent mean proportional relation. His later and correctdefinition of natural acceleration dependent on time was an insightgained through recognizing the physical significance of that meanproportional relation (Machamer and Hepburn 2004; for a differentanalysis of Galileo’s discovery of free fall see Renn, et al.2000). Yet Galileo would not publish anything making time central tohis analysis of motion until 1638, in the Two NewSciences.

In 1609, Galileo began his work with the telescope. There are manyways to describe Galileo’s findings, and many interpreters havetaken this to be an interlude irrelevant to his physics. However,they are remarkable insofar as they are his start at dismantling thecelestial-terrestrial distinction entrenched in Aristotelian cosmology(Feyerabend 1975). Perhaps the most unequivocal case of this is whenhe analogizes the mountains on the moon to mountains in Bohemia in theStarry Messenger. Also crucial was his discovery of the fourmoons circling Jupiter, which lent credence to the Copernican systemsince it meant that a planet-moon arrangement was not unique to theEarth. The abandonment of the dichotomy between heavens and earthimplied that all matter, whether celestial or terrestrial, is of thesame kind. Further, if there is only one kind of matter, there can beonly one kind of natural motion—one kind of motion that thismatter has by nature. So it has to be that one law of motion will holdthroughout the terrestrial and celestial realms. This is a farstronger claim than he had made in 1590, which concerned only theterrestrial elements.

A few years later, in his Letters onSunspots (1613), Galileo offered new telescopic evidencethat supported the Copernican theory. But these observations alsoserved as additional reasons for dissolving the celestial-terrestrialdistinction. One was that the sun is not an immutable aetherialsphere, but has changing spots (maculae) on its surface.Another was that the sun rotates circularly around its axis, like theEarth. A third was the discovery that Venus undergoes a full sequenceof phases (like the moon), which entails that Venus revolves aroundthe sun, and suggests that the Earth is likewise a celestial bodymoving around the sun. Certainly the phases of Venus contradicted thePtolemaic ordering of the planets.

Later, in 1623, Galileo argued for a quite mistaken material thesis.In The Assayer, he tried to show that comets aresublunary phenomena and that their properties could be explained byoptical refraction. While this work stands as a masterpiece ofscientific rhetoric, it is somewhat strange that Galileo should haveargued against the superlunary nature of comets, which the greatDanish astronomer Tycho Brahe had demonstrated earlier.

Yet even with all these developments, Galileo still needed to work outgeneral principles concerning the nature of motion for this newlyunified matter. In this respect, Galileo differed from Ptolemy (atleast of the Almagest), Copernicus, or even Tycho Brahe, whotreated their planetary systems—be they Earth- orsun-centered—merely as models of the planets’ observedmotions; that is, as mathematical conceits for calculating observablepositions. For Galileo, by contrast, Copernicanism was also acommitment to a physically realizable cosmography. Consequently, heneeded to work out, at least qualitatively, a way of thinking aboutthe actual motions of matter. He had to devise (or shall we say,discover) principles of local motion that would fit a central sun,planets moving around that sun, a whirling Earth, and everything onit.

This he did by introducing two new principles. In Day One ofhis Dialogue Concerning the Two Chief WorldSystems (1632), Galileo argues that matter will movenaturally along circular trajectories, neither speeding up nor slowingdown. Then, in Day Two, he introduces his version of the famousprinciple of the relativity of observed motion. This latter holds thatobservers cannot detect uniform motions they share with objects underobservation; only differential motion can be seen. Of course, neitherof these principles was entirely original with Galileo. They hadpredecessors. But no one needed them for the reasons that he did,namely that they were necessitated by a unified cosmologicalmatter.

One key effect of these principles is that the diurnal terrestrialrotation asserted by the Copernican system is unobservable. The Earthand all the objects on it naturally move in circles around theEarth’s axis once a day, but since human observers share thismotion, it cannot be detected. We only notice departures from sharedrotation, such as bodies falling or rising. Consequently, “allexperiments practicable upon the Earth are insufficientmeasures” for proving its stability or its mobility,“since they are indifferently adaptable to an Earth in motion orat rest” (Galilei 1967, 6). This blunted standard objections toCopernicanism on the grounds that there is no evidence of terrestrialmotion.

Having dispelled these arguments against the Copernican system,Galileo then dramatically argues in its favor. In Day Three of theDialogue. Salviati, Galileo’s avatar, has Simplicio,the ever-astounded Aristotelian, make use of astronomicalobservations, especially the facts that Venus has phases and thatVenus and Mercury are never far from the sun, to construct a diagramof the planetary positions. The resulting diagram neatly correspondsto the Copernican model. Then in Day Four, Galileo offers a supposedproof of Copernican theory on the basis of the tides, asserting thatthey result from the combination of the Earth’s diurnal rotationand its annual motion around the sun.

In the Dialogue, things are more complicated than wehave just sketched. Galileo, as noted, argues for circular naturalmotion. Yet he also introduces, in places, an intrinsic tendency forrectilinear motion. For example, Galileo recognizes that a stonewhirled circularly in a sling would fly off along the rectilineartangent if released (Galilei 1967, 189–94; see Hooper 1998).Further, in Day Four, when he is giving his mechanical explanation ofthe tides, he nuances his matter theory by attributing to water anadditional power of retaining an impetus for motion such that it cangenerate a reciprocal movement once it is sloshed against a side of abasin. This was not Galileo’s first dealing with water. We sawit first in the De Motu around 1590, where Galileodiscusses submerged and floating bodies, but he learned much more inhis dispute over floating bodies (which produced the Discourse onFloating Bodies in 1612). In fact, a large part of that debateturned on the exact nature of water as matter, and what kind ofmathematical proportionality could be used to correctly describe itand bodies moving in it (see Palmieri 1998; 2004).

The final chapter of Galileo’s scientific story came in 1638,with the publication of the Two New Sciences. The secondscience, discussed in the last two Days, deals with the principles oflocal motion and has been much commented upon in the Galileanliterature. But the first science, discussed in the first two Days,has been misunderstood and infrequently discussed. It has misleadinglybeen called the science of the strength of materials, and so seems tohave found a place in history of engineering, since such a course isstill taught today. However, this science is not about the strength ofmaterials per se. It is Galileo’s attempt toprovide a mathematical science of his unified matter (see Machamer1998a; Biener 2004; Machamer and Hepburn 2004). Galileo realizes that,before he can work out a science of the motion of matter, he must havesome way of showing that the nature of matter may be mathematicallycharacterized. Both the mathematical nature of matter and themathematical principles of motion he believes belong to the science of“mechanics,” which is the name he gives for this new wayof philosophizing.

So it is in Day One that Galileo begins to discuss how to describemathematically (or geometrically) the causes of the breaking of beams.But this requires a way to reconcile mathematical description with thephysical constitution of material bodies. In this vein, Galileorejects using finite atoms as a basis for physical discussion, sincethey are not representable by continuously divisible mathematicalmagnitudes. Instead, he treats matter as composed of infinitely manyindivisible—which is to say, mathematical—points. Thisallows him to give mathematical accounts for various properties ofmatter. Among these are the density of matter, its coherence inmaterial bodies, and the properties of the resisting media in whichbodies move. The Second Day lays out the mathematical principlesconcerning how bodies break. Galileo does all this by reducing theproblems of matter to problems of how a lever and a balance function,which renders them mathematically tractable via the law of the lever.He had begun this back in 1590, though this time he believes he isgetting it right, showing mathematically how bits of matter solidifyand stick together, and how they break into bits.

The First Day also contains Galileo’s account of theacceleration of falling bodies, and the argument that they fallequally fast in a vacuum, whatever their weight. This discussioncontains the famous thought experiment refuting the Aristoteliantheory of fall, according to which the speed of a body’s fall isproportional to its weight. In this “short and conclusive”argument, Galileo supposes that two bodies, one heavier than theother, are suddenly conjoined in the midst of falling. On the onehand, if Aristotle is correct, the faster fall of the heavier bodywill be retarded by the slower motion of the lighter body, so that theconjoined body will fall slower than the original heavy body. And yet,the conjoined body is heavier than either original body, so it shouldalso fall faster. Hence, there is a contradiction in the Aristotelianposition (Gendler 1998; Palmieri 2005; Brown and Fehige 2019).

Galileo’s second new science, in Days Three and Four of the TwoNew Sciences, deals with the mathematical description of local motionand the laws governing it. This is now the motion of all matter, notjust sublunary stuff, and the treatment takes the categories of timeand acceleration as basic. Here is where Galileo enunciates his law offree fall, the parabolic path of projectiles, and other physical“discoveries” that would lay the foundation for modernphysics (Drake 1999, v. 2).

In the projected Fifth Day, Galileo would have treated the power ofmoving matter to act by impact, which he calls the force ofpercussion. Ultimately, Galileo was unable to give mathematicalprinciples of this kind of interaction, but this problem subsequentlybecame an important locus of interest. René Descartes, probablyfollowing Isaac Beeckman, would eventually convert the problem intothe task of finding equilibrium between the forces conserved bycolliding bodies. Descartes’s own mathematical treatment wasmistaken, but correct principles were given in 1668–9 byChristiaan Huygens, John Wallis, and Christopher Wren.

The sketch above provides the basis for understanding Galileo’scareer. He offered a new science of matter, a new physicalcosmography, and a new science of local motion. In all these, he useda mathematical mode of description based upon, though somewhat changedfrom, the proportional geometry of Book VI of Euclid’sElements and of Archimedes (for details on the changes, seePalmieri 2001).

It is in this way that Galileo developed the categories of themechanical new science, the science of matter and motion. His newcategories utilized some of the basic principles of traditionalmechanics, to which he added the category of time and so emphasizedacceleration. But throughout, he was working out the details about thenature of matter so that it could be understood as uniform anduniversal, and treated in a way that allowed for coherent discussionof the principles of motion. It was due to Galileo that a unifiedmatter became accepted and its nature became one of the problems forthe new science that followed. After him, matter really mattered.

4. Galileo and the Church

No account of Galileo’s importance to philosophy can be completeif it does not discuss the Galileo Affair—the sequence ofinteractions with the Church that resulted in Galileo’scondemnation. The end of the affair is simply stated. In late 1632, inthe aftermath of the publication of the Dialogue Concerning theTwo Chief World Systems, Galileo was ordered to appear in Rome tobe examined by the Congregation of the Holy Office; i.e., theInquisition. In January 1633, a very ill Galileo made an arduousjourney to Rome. From April, Galileo was called four times tohearings; the last was on June 21. The next day, June 22, 1633,Galileo was taken to the church of Santa Maria sopra Minerva, andordered to kneel while his condemnation was read. He was declaredguilty of “vehement suspicion of heresy,” and made torecite and sign a formal abjuration:

I have been judged vehemently suspect of heresy, that is, of havingheld and believed that the sun in the center of the universe andimmoveable, and that the Earth is not at the center of same, and thatit does move. Wishing however, to remove from the minds of yourEminences 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 2003, 194)

Tradition, but not historical fact, holds that, after abjuring,Galileo mumbled, “Eppur si muove (and yet itmoves).” He was sentenced to “formal imprisonment atthe pleasure of the Inquisition,” but this was commuted to housearrest, first in the residence of the Archbishop of Siena, and then,from December 1633, at his villa in Arcetri. When he later finishedhis last book, the Two New Sciences (which does not mentionCopernicanism at all), it had to be printed in Holland, and Galileoprofessed amazement at how it could have been published.

The details and interpretations of these proceedings have long beendebated, and it seems that each year we learn more about what actuallyhappened. One point of controversy is the legitimacy of the chargesagainst Galileo, both in terms of their content and the judicialprocedure. Galileo was charged with teaching and defending theCopernican doctrine that holds the sun is at the center of theuniverse and the Earth moves. The status of this doctrine was cloudy.In 1616, an internal commission of the Inquisition had determined thatit was heretical, but this was not publicly proclaimed. Instead,Copernicus’s book had been placed on the Index of ProhibitedBooks—the list of books Catholics were forbidden to readwithout special permission—with the status “suspendeduntil corrected.” Even more confusingly, therequisite corrections had appeared in 1620, but the booknevertheless remained on the Index until 1835. In fact, theChurch’s first public pronouncement that Copernicanismis a heresy appears in Galileo’s condemnation.

Galileo’s own status was also problematic. In 1616, at the sametime that the Inquisition was evaluating Copernicanism, they were alsoinvestigating Galileo personally—a separate proceeding of whichGalileo himself was not likely aware. The outcome wasBellarmine’s admonition not to “defend or hold” theCopernican doctrine. This “charitable admonition” may (ormay not) have been followed by a “formal injunction”“not to hold, teach, or defend it in any way whatever, eitherorally or in writing.” When the records of this disposition ofthe 1616 case were discovered in 1633, it made Galileo appear guiltyof recidivism, having violated the Inquisition’s injunction bypublishing the Dialogue.

To confound issues further, the case against Galileo transpired in afraught political context. Galileo was a creature of the powerfulMedici and a personal friend of Pope Urban VIII, connections thatsignificantly modulated developments (Biagioli 1993). There were alsopressures stemming from the Counter Reformation, the Thirty Years War,and resulting tensions within Urban’s papacy (McMullin 2005;Miller 2008). It has even been argued (Redondi 1983), that the chargeof Copernicanism was the effect of a plea bargain meant to cover upGalileo’s genuinely heretical atomism, though this latterhypothesis has not found much support.

The legitimacy of the underlying condemnation of Copernicus ontheological and rational grounds is even more problematic. Galileo hadaddressed this problem in 1615, when he wrote his Letter toCastelli and then the Letter to the Grand DuchessChristina. In these texts, Galileo argues that there are twotruths: one derived from Scripture, the other from the created naturalworld. Since both are expressions of the divine will, they cannotcontradict one another. However, Scripture and Creation both requireinterpretation in order to glean the truths theycontain—Scripture because it is a historical document writtenfor common people, and thus accommodated to their understanding so asto lead them towards true religion; Creation because the divine actmust be distilled from sense experience through scientific enquiry.While the truths are necessarily compatible, biblical and naturalinterpretations can go awry, and are subject to correction.

Much philosophical controversy, before and after Galileo’s time,revolves around this doctrine of the two truths and their seemingincompatibility. Which of course, leads us immediately to suchquestions as: “What is truth?” and “How is truthknown or shown?”

Cardinal Bellarmine was willing to countenance scientific truth if itcould be proven or demonstrated (McMullin 1998). But Bellarmine heldthat the planetary theories of Ptolemy and Copernicus (and presumablyTycho Brahe) are only mathematical hypotheses; since they are justcalculating devices, they are not susceptible to physical proof. Thisis a sort of instrumentalist, anti-realist position (Machamer 1976;Duhem 1985). There are any number of ways to argue for some sort ofinstrumentalism. Duhem (1985) himself argued that science is notmetaphysics, and so only deals with useful conjectures that enable usto systematize phenomena. Subtler versions of this position, withoutan Aquinian metaphysical bias, have been argued subsequently and morefully by Van Fraassen (1980) and others. Less sweepingly, it canreasonably be argued that both Ptolemy and Copernicus’s theorieswere primarily mathematical, and that Galileo was defending notCopernicus’s theory per se, but the physicalrealization of it. In fact, it might be better to say the Copernicantheory that Galileo was constructing was a physical realization of asimplified version of Copernicus’s theory, which dispensed withmany of the technical details (eccentrics, epicycles, Tusi couples andthe like). Galileo would be led to such a view by his concern withmatter theory, which minimized the kinds of motion ascribed uniformlyto all bodies. Of course, when put this way, we are faced with thequestion of what constitutes identity conditions for a theory. Six dots pdf free download. Still,there is clearly a way in which Galileo’s Copernicanism is notCopernicus’s.

The other aspect of all this that has been hotly debated is whatconstitutes proof or demonstration of a scientific claim. Galileobelieved he had a proof of terrestrial motion. This argumentconcerning the cause of the tides is contained in On the Ebb andFlow of the Tides, a manuscript he composed in 1616 whileCopernicanism was under the Inquisition’s scrutiny, and the mainthrust of which appears in Day Four of the Dialogue Concerning theTwo Chief World Systems.

In the first place, Galileo restricts the possible class of causes ofthe tides to mechanical interactions, and so rules out Kepler’sattribution of the cause to the moon. How could the moon cause thetides to ebb and flow without any connection to the seas? Such anexplanation would be an invocation of magic or occult powers. Thus,for Galileo, the only conceivable (or maybe plausible) physical causefor the regular reciprocation of the tides is the combination of thediurnal and annual motions of the Earth. Briefly, as the Earth rotatesaround its axis, some parts of its surface are moving along with theannual revolution around the sun and some parts are moving in thecontrary direction. (In the same way that a point near the top of acar’s wheel is rotating in the same direction as the car ismoving, while a point near the ground is rotating toward the rear.) Inthe frame of the fixed stars, this creates accelerations andretardations of the Earth’s surface, and since the terrestrialwaters are not attached to the surface, they slosh back and forth astheir basins speed up and slow down. Hence the tides. Moreover, sincethe Earth’s diurnal and annual rotations are regular, so are thetidal periods. Local differences in tidal flows are due to thedifferences in the physical conformations of the basins in which theyoccur (for background and more detail, see Palmieri 1998). Albeitmistaken, 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, andtherefore for Copernicanism.

Yet one can also see why Bellarmine and the instrumentalists would nothave been impressed. First, they did not accept Galileo’srestriction of possible causes to mechanically intelligible causes.Second, Galileo’s explanation is not precise; it does notaccount for many details of tidal motion. Most significantly, themotion of the Earth’s surface varies over twelve hours, not thesix-hour cycle of the tides. Third, the argument does not touch uponthe central position of the sun or arrangement of the planets ascalculated by Copernicus. So at best, Galileo’s argument is aninference to the best partial explanation from a limited set offeatures of Copernicus’s theory. Meanwhile, there werecompelling considerations about the size of celestial bodies thatweighed against the Copernican cosmology, stemming from a lack ofunderstanding of the telescope’s optics (Graney 2015).

Nevertheless, when the tidal argument is added to the earliertelescopic observations that show the improbabilities of the oldercelestial picture—the fact that Venus has phases like the moonand so must revolve around the sun; the principle of the relativity ofperceived motion which neutralizes the physical arguments against amoving Earth; and so on—it was enough for Galileo to believethat he had the necessary proof to convince the doubters.Unfortunately, it was not until after Galileo’s death and theacceptance of a unified material cosmology, utilizing thepresuppositions about matter and motion that were published inthe Two New Sciences, that people were ready forsuch proofs. But this could occur only after Galileo had changed theacceptable parameters for gaining knowledge and theorizing about theworld.

To read many of the documents of Galileo’s trial, seeFinocchiaro 1989; Mayer 2012. To understand the long, tortuous, andfascinating aftermath of the Galileo affair see Finocchiaro2005; and for Pope John Paul II’s 1992 rehabilitation ofGalileo, see Coyne 2005.

Bibliography

Primary Sources: Galileo’s Works

The main body of Galileo’s work is collected in:

  • Favaro, Antonio (ed.), 1890–1909, Le Opere diGalileo Galilei, Edizione Nazionale, 20 vols., Florence: Barbera;reprinted 1929–1939 and 1964–1966. [available online]

English translations:

  • 1586, The Little Balance (LaBilancetta)
    • Fermi, Laura, and Bernardini, Gilberto (trans.) in Fermi, Laura,and Bernardini, Gilberto, 1961, Galileo and theScientific Revolution, New York: Basic Books; reprinted 1965, NewYork: Fawcett; and 2003 and 2013, Mineola, NY: Dover.
  • ca. 1590, On Motion (De Motu)
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    • Drake, Stillman (trans.), 1978, Operations of theGeometric and Military Compass, Washington, D.C.: SmithsonianInstitution.
  • 1610, The Starry Messenger (Sidereus Nuncius,Venice: Thomas Baglioni.)
    • Van Helden, Albert (trans.), 1989, Sidereus Nuncius, orThe Sidereal Messenger, Chicago: University of ChicagoPress; 2nd edition, 2016; reprinted, with facsimile of Library ofCongress’s first edition and expository essays, in De Simone,Daniel, and John W. Hessler (eds.), 2013, The StarryMessenger: From Doubt to Astonishment, Washington, D.C.: Libraryof Congress/Levenger Press.
    • Barker, Peter (trans.), 2004, SidereusNuncius, Oklahoma City: Byzantium Press.
    • Shea, William R. (trans.), 2009, Galileo’s SidereusNuncius, or A Sidereal Message, Sagamore Beach, MA:Science History Publications; 2nd revised printing, 2012.
  • 1612, Discourse on FloatingBodies (Discorso intorno alle Cose che Stanno in sul’Acqua, Florence: Cosimo Giunti.)
    • Drake, Stillman (trans.) in Drake, Stillman, 1984, Cause,Experiment, and Science, Chicago: Chicago University Press.
  • 1613, Letters on the Sunspots (Istoria eDimostrazioni intorno alle Macchie Solari, Rome: GiacomoMascardi.)
    • Reeves, Eileen, and Van Helden, Albert (trans.) in Galilei,Galileo, and Scheiner, Christoph 2010, OnSunspots, Chicago: University of Chicago Press.
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Collections of primary sources in English:

  • Drake, Stillman (ed.), 1957, The Discoveries and Opinionsof Galileo, New York: Anchor Books.
  • Finocchiaro, Maurice A. (ed.), 1989, The GalileoAffair: A Documentary History, Berkeley: University ofCalifornia Press.
  • Finocchiaro, Maurice A. (ed.), 2008, The EssentialGalileo, Indianapolis: Hackett.
  • Shea, William R., and Davie, Mark (ed.),2012, Galileo: Selected Writings, Oxford:Oxford University Press.

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Enhanced bibliography for this entryat PhilPapers, with links to its database.

Other Internet Resources

  • Galileo Galilei’s Notes on Motion, Joint project of the Biblioteca Nazionale Centrale,Florence; Museo Galileo, Florence; Max Planck Institute for theHistory of Science, Berlin.
  • The Galileo Project, maintained by Albert Van Helden; contains Dava Sobel’stranslations of all 124 letters from Suor Maria Celeste to Galileo inthe sequence in which they were written.
  • Museo Galileo, The Institute and Museum of the History of Science, Florence,Italy.

Related Entries

Copernicus, Nicolaus natural philosophy: in the Renaissance religion: and science

Acknowledgments

Thanks to Zvi Biener and Paolo Palmieri for commenting on earlierdrafts of this entry.

Galileo's Daughter Book

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