GADROYS, CLAUDE (1642–78). One of the earliest and more avid followers of Descartes. His chief claim to fame rests on his attempt to extend Cartesian principles to astrology in Discours sur les influences des astres selon les principes de M. Descartes (1671). This may seem an odd endeavor, but Descartes does invite his followers to use his account of magnetic phenomena as a model to explain “all the most admirable effects on earth”: “the particles composed of the first element in the pores of terrestrial bodies can not only be the cause of various attractions, such as those in the magnet and in amber, but also of innumerable other most admirable effects” (Principles IV, art. 187). In the French version of this article, Descartes elaborates on the “wholly rare and marvelous effects” that can be explained: “how the wounds of a dead man can be made to bleed when his murderer approaches; how to excite the imagination of those asleep, or even of those awake, and impart to them thoughts that warn them of things to come at a distance, by having them feel the great pains or great joys of a close friend, the evil intents of an assassin, and similar things.” Gadroys conceives of similar explanations for astrologic influences, for the occult actions of the stars on human inclinations, passions, temperament, illnesses, and fate.
In his second work, Le Système du monde selon les trois hypothèses (1675), Gadroys discusses the three main cosmological hypotheses, Ptolemaic, Copernican, and Tychonic. He rejects the Ptolemaic as the least simple of them, with its excess of eccentrics and epicycles, and as completely contrary to the appearances, given the phases of Venus and Mercury (pp. 124–25). He grants that the Tychonic does not have the difficulties of the Ptolemaic, but rejects it anyway, following Descartes, for the reason that “although Tycho invented his system simply to attribute no motion to the earth, still, he attributes more motion to it than does Copernicus” (p. 129; cf. Descartes, Principles III, art. 15–19). Gadroys accepts the Copernican hypothesis and argues for it, in the remainder of his work, by demonstrating its compatibility with Cartesian cosmology, upon which he expounds in great detail.
GALILEI, GALILEO (1564–1642). Italian natural philosopher and mathematician, one of the most important contributors to early modern science. His early education was probably in music, under the tutelage of his father Vincenzo (1520–91), a professional musician and noted musical theorist. Galileo began his formal education in the Faculty of Arts at the University of Pisa in the autumn of 1580. Relatively little is known about the details of his university education, but it is evident that he was exposed to the Aristotelian natural philosophy as interpreted by 16th-century scholastics. By the time he left Pisa in 1585 (without taking a degree), Galileo had developed an antipathy toward the Aristotelian-scholastic natural philosophy and a skill in mathematics that would characterize much of his later scientific career.
Galileo’s first original work was a small 1586 treatise on the hydrostatic balance entitled La bilancetta, which circulated in manuscript. At approximately the same time he showed the extent of his mathematical sophistication by circulating a sequence of theorems on the centers of gravity for various solids of revolution, demonstrated in accordance with the Archimedean method of exhaustion. By the late 1580s Galileo had discovered the isochronous properties of the pendulum, a phenomenon he connected to the harmonic properties of strings: just as the tone of a plucked string remains constant even as the amplitude of the vibrations decreases, so the period of a pendulum remains constant as the amplitude of its excursions from perpendicular decreases. Although he lacked a geometrical demonstration of the property of isochronism, his investigations into the relationship of frequency and tone seem to have convinced him that a mathematical analysis of natural motions, backed by experimental evidence, would form the basis for a new natural philosophy.
In 1589 Galileo retuned to the University of Pisa to assume the chair of mathematics, a position he retained until 1592. During this period he undertook the attempt to reformulate the accepted Aristotelian account of natural motion, as evidenced by a manuscript De motu in which he began to work out the principles that became fundamental to his mechanics. In opposition to the Aristotelian notion that bodies descend with a speed proportional to their weight, Galileo proposed in De motu that in free fall bodies descend with a characteristic uniform speed proportional to their specific gravity. Experiments disconfirmed this theory, and over the next two decades he refined his experiments and reformulated his theories. In the end he arrived at the famous law of free fall which states that (in a vacuum) all bodies are uniformly accelerated at the same rate, and that the distance fallen is proportional to the square of the elapsed time. A key tool employed by Galileo in his research on free fall was the inclined plane, which allowed him to study the speed acquired by a descending ball. Observing that a ball moved spontaneously only when it rolled down an incline, and that given an impulse to move up the plane it would spontaneously decelerate, Galileo inferred that a ball placed on a horizontal plane would be indifferent to motion and rest—an insight which led him to formulate an early version of the law of inertia.
In 1592 Galileo accepted the chair of mathematics at the University of Padua, where his research into the laws of motion continued. By the mid-1590s he had become convinced of the plausibility of Copernican astronomy, whose doctrine of a moving earth required further refinement of the concept of motion while also encouraging the search for more accurate astronomical data. In 1609, upon hearing of a device invented in the Netherlands that could make distant objects appear nearer, Galileo set to work replicating and improving it; the result was a telescope with which he made detailed observations of the moon, the satellites of Jupiter, and the phases of Venus. His Siderius Nuncius (Siderial Messenger) of 1610 related his observations and argued against the Aristotelian doctrine of a fundamental distinction between the incorruptible celestial realm and the terrestrial world of change and decay. He proposed that the laws of motion and principles of material things were the same for the Earth and the heavens, and suggested that the observational evidence favored the Copernican system. The challenge to traditional natural philosophy posed by these discoveries led Christopher Clavius and other astronomers to question the reliability of telescopic observations, but by the end of 1610 Clavius and other mathematicians of the Collegio Romano had confirmed the existence of the satellites of Jupiter and had seen the phases of Venus. In April 1611, during Galileo’s visit to Rome, Clavius certified the phenomena revealed by the telescope as genuine.
Galileo was appointed principal mathematician at the University of Pisa and accorded the title of philosopher and mathematician to the Grand Duke of Tuscany (Cosimo II de’Medici, who was duly impressed by Galileo’s naming of the satellites of Jupiter for the house of Medici). His astronomical observations continued, resulting in the discovery of sunspots in 1611. A dispute with the Jesuit Christoph Scheiner (1573–1650) on the nature of sunspots resulted in the 1613 publication of his Letters on Sunspots. Public controversy with a member of the Society of Jesus and his support of theologically controversial Copernican astronomy did not help Galileo’s reputation with conservative forces in the Catholic Church, and in 1615 he was denounced to the Holy Office. This prompted Galileo to summarize his views on the relationship between theology and natural philosophy in a Letter to Grand Duchess Christina, which was circulated widely at the time but was first published (in the Netherlands) in 1636. One recipient of the circulating letter was Robert Cardinal Bellarmine (1542–1621), an influential Jesuit member of the Holy Office. He replied that Copernicanism was an acceptable hypothesis but admonished Galileo against interpreting it in a manner contrary to Scripture or received theology. Copernican teachings were formally condemned in March 1616, and Galileo ceased his advocacy for the new astronomical system.
In the autumn of 1618 the appearance of three comets led to a debate over the nature of comets between Galileo and the Jesuit Orazio Grassi (1592–1654), professor of mathematics at the Collegio Romano, who attempted to account for them without using Copernican assumptions. Galileo’s 1623 Il Saggiatore (The Assayer) was the resulting polemical piece, which he dedicated to his friend Maffeo Cardinal Barberini (1568–1644) who had recently been elected pope and taken the name Urban VIII. The work was well received in Rome, and Galileo held out hope that the Church would modify its condemnation of Copernican astronomy.
Through the late 1620s Galileo was revising an earlier unpublished treatise on the tides, adding a wealth of astronomical and mechanical material. He cast it in the form of a dialogue, initially intending to publish it under the title Dialogue on the Ebb and Flow of the Tides, but later changing the title to Dialogue on the Two Chief World Systems, Ptolemaic and Copernican. It was published in early 1632. To Galileo’s surprise, the Dialogue was condemned as heretical; early in 1633 Galileo was found guilty of vehement suspicion of heresy, forced to recant, and sentenced to imprisonment at the pleasure of the Inquisition. Late in that year Galileo was allowed to retire to his villa in Arcetri near Florence, where he would remain under house arrest for the remainder of his life. Although plagued by health problems in his final years, Galileo continued his research in mathematics and natural philosophy. The principal result of these final years was his Discourses on Two New Sciences, published in the Netherlands in 1638 and containing a sequence of dialogues that set out the most systematic and complete statement of Galileo’s mechanics.
It is largely through the agency of Marin Mersenne that Galileo’s work became known outside Italy. In 1634 Mersenne published a French translation of Galileo’s 1602 lectures on mechanics under the title Les Méchaniques de Galilée, and in 1639 he published a translation of Galileo’s Discourse. Descartes was familiar with Galileo’s contributions, in large part because of Mersenne’s efforts, but he found much to criticize. While praising him for his emphasis on mathematics and his commitment to mechanistic explanations of natural phenomena, Descartes criticized Galileo’s attention to particular cases and the digressions that intrude in his dialogues. In a letter to Mersenne from October 11, 1638, Descartes complained that Galileo “continually makes digressions and does not stop to explain any single matter, which shows that he has not examined things in order and that he has only sought the explanations of certain particular effects without having considered the first causes of nature, and thus that he has built without a foundation” (AT, vol. II, p. 380).
The condemnation of Galileo had a significant influence on Descartes. When he found out about it in November of 1633, he withdrew The World from publication, explaining to Mersenne that the motion of the Earth was demonstrated so evidently that “if it is false, all the foundations of my philosophy are likewise false,” with the result that Copernicanism “is so connected to all the parts of my treatise, that I don’t know how to remove it without making all the rest defective” (AT, vol. I, p. 271). By the time his natural philosophy was made public in the Principles of Philosophy, Descartes formulated his astronomical doctrines against a background of a relativistic definition of motion as “the transference of one part of matter or of one body from the neighborhood of those bodies that immediately touch it and are regarded as being at rest, and into the neighborhood of others” (AT, vol. VIIIa, p. 53). This removed the difficulty of a moving Earth, since the definition permits it to be regarded as at rest when considered with respect to immediately surrounding bodies.
GASSENDI, PIERRE (1592–1655). Gassendi was a Catholic priest who, in humanistic tradition, attempted a revival of the philosophy of the atomist Epicurus. He began his publishing career in 1624 with an ambitious denunciation of scholasticism, Exercitationes paradoxicae adversus Aristoteleos, which he intended to consist of seven books. However, prodded by Marin Mersenne to abandon this initial project, he published only the first book, though he also completed the second, and started his Christian rehabilitation of Epicurus (circa 1626). Gassendi’s work on Epicurus appeared as De vita et moribus Epicuri (1647), Animadversiones in decimum librum Diogenis Laertii (1649), and Syntagma philosophicum, published posthumously in his Opera omnia (1658). He wrote the Fifth Set of Objections to Descartes’s Meditations and published it with Descartes’s replies and his additional lengthy rebuttals as Disquisitio metaphysica (1644). Late in life he was appointed to the chair of mathematics at the Collège Royal.
There were many aspects of Epicurean philosophy that were inconsistent with Christianity, not the least of which was the claim that atoms, the components of the physical universe, are eternal and uncreated. Gassendi amended this seemingly heretical doctrine, claiming the “correction” to be similar to those necessitated by Aristotle’s own view of matter. Instead, atoms are created substances each endowed with their own motion at creation. The motion is sustained with the concurrence of God. Unlike the divisible, composite bodies formed by atoms, atoms themselves are completely solid and, therefore, their integrity cannot naturally be compromised. Further, atoms do not have forms or qualities other than size, shape, and weight or motion, but provide explanation for all physical change as products of these essential qualities. Rarefaction, for example, is explained as a relation between void and atoms: a body becomes less dense as the void space is increased within its internal dimensions. The particular types of atoms present (that is, their size, shape, weight, and quantity of motion) explain the natural processes of any given composite body. With the exception of the human soul, atoms required no immaterial principle to describe secondary causes. Like Descartes, Gassendi epitomized the trend of emphasizing material and efficient causes, tending to eliminate formal and final causes, reducing the latter to the former (in the realm of bodies). In this way Descartes and Gassendi had “mechanistic” understandings of science, though they differed significantly in regard to their conceptions of body, motion, space, and void as well as their epistemological commitments to science.
The debate between Descartes and Gassendi was long and contentious. After the first exchange in the Fifth Set of Objections and Replies, Descartes requested that some his friends boil down Gassendi’s objections from the Disquisitio Metaphysica to a manageable few. Descartes then answered those in a letter he published with the French translation of the Meditations (1647). Gassendi had objected to the First Meditation that Descartes was asking something impossible in wanting people to give up all preconceived opinions, that in doing so, we would be adopting even more harmful opinions, and that the method of universal doubt cannot help us discover any truths. He had objected to the Second Meditation that the cogito presupposes the major premise “Whatever thinks exists” and what thought is, both of which are preconceived opinions. Gassendi also argued that thought cannot exist without an object and that we do not know whether thought is corporeal rather than immaterial. Even though we might not find any extension in our thought, it does not follow that our thought is not extended; even though we might distinguish in thought between thought and body, the distinction might be false. Gassendi objected to the Third Meditation that Descartes’s proofs for the existence of God were not convincing. Not everyone is aware of the idea of God within himself and if someone did have that idea, he should comprehend it. It does not follow that God exists from the fact that we know ourselves to be imperfect. Gassendi also objected to the other Meditations that Descartes was guilty of circularity in proving the existence of God by means of notions in us but in saying afterwards that we cannot be certain of anything without prior knowledge that God exists. He further argued that knowledge of God’s existence does not help us in acquiring knowledge of the truth of mathematics and that God may be a deceiver.
GENEROSITY (GÉNÉROSITÉ, MAGNANIMITÉ). Generosity, which is the term Descartes prefers to the older “magnanimity,” is not strictly speaking a passion but a virtue or habit; it is also the key to all other virtues. It is best described as legitimate self-esteem and composed of three elements: 1) the knowledge that the only thing that really belongs to us is our freedom; 2) the realization that the only thing for which we can be blamed or praised is the use we make of that freedom; 3) our firm resolution to use it well, that is, to do whatever we judge to be the best. Generosity is produced by adding esteem to admiration, which is also the reason why it is related to pride (from which it differs only by its object) and opposed to humility and baseness. A generous person is naturally inclined to do great things, without, for that matter, undertaking anything impossible. Since, on the other hand, his highest aim is to do good to other people, he is courteous, polite, and helpful. Finally, he is not given to jealousy and envy, hatred and anger.
Although generosity and virtuous humility (with which it is perfectly compatible) are habits rather than passions, the fact that their vicious counterparts, pride and baseness, are passions, makes it possible for generosity to be reinforced by the same movement and agitation of the animal spirits that characterizes pride. Given the fact, however, that it is a habit, it is not accompanied by much fluctuation in the spirits. Its best foundation is a good family (bonne naissance) because nothing contributes more to legitimate self-esteem than that; but it can also be acquired, by reflecting on our free will and on the advantages of being resolute in one’s actions. Generosity is a particularly effective remedy against excessive anger because a generous person will realize that his freedom, which he esteems more than anything else, is at risk if he cannot shrug off the offenses of others. A point of particular interest in the recent literature is that generosity is a form of immediate self-awareness, which as such is comparable to the cogito. The only difference would be that, whereas the cogito informs us of ourselves as a thinking spirit, generosity makes us aware of ourselves as a free agent.
GEOMETRY. Classically, geometry (literally “earth measurement”) was regarded as the abstract science whose object is continuous spatial magnitudes and whose method proceeds by deduction from clearly grasped and transparently true first principles such as common notions and definitions. This classification distinguishes geometry from arithmetic on the basis of its object—where geometry considers continuous magnitudes, arithmetic is the deductively organized study of discrete multitudes or numbers. The principal geometers of Greek antiquity, Euclid, Apollonius, and Archimedes, left behind an immense body of geometric results whose level of sophistication was not revisited until the 17th century. In Descartes’s day, one of the principal activities of geometric authors was the preparation of editions and commentaries on classical authors, as well as the speculative “restoration” of lost treatises. One consequence of the success of Descartes’s program in the Geometry was that the classical division between arithmetic and geometry was undermined; Cartesian analytic geometry uses algebraic methods that apply to any quantity, and are not confined to the specific domain of continuous magnitudes. Further, his success in solving and generalizing problems taken from classical geometry meant that future geometric research departed from the tradition of commentary on ancient authors.
Geometry occupies a central position in Descartes’s system, not least because he took the geometric method as a model for all knowledge. As he remarked in the Discourse, “those long chains of completely simple and easy reasoning that geometers commonly use to arrive at their most difficult demonstrations gave me occasion to imagine that all things that can fall within the scope of human knowledge are interconnected in the same way” (AT, vol. VI, p. 19). Aside from his fundamental contributions to the development of geometry, Descartes also made geometry fundamental to his physics by insisting that the geometric concept of extension was the essence of body, with the result that all of natural philosophy became a branch of applied geometry. As he put it: “I recognize no matter in corporeal things that which the geometers call quantity and take as the object of their demonstrations, i.e. quantity that is in every way capable of being divided, shaped, and moved” (Principles II, art. 64; AT, vol. VIIA, pp. 78–79).
GEOMETRY (GÉOMÉTRIE, GEOMETRIA). When Descartes arrived in the Netherlands in 1628 he took with him what Isaac Beeckman called an “Algebra” (Journal III, pp. 94–95), which is no doubt an early version of the Géométrie, published eventually in 1637 as one of the essays illustrating the method of the Discourse. But it is only in 1632, after his work on the problem of Pappus, that the text seems to have reached a definitive stage—Descartes’s claim that “it was composed while the Meteors were already being printed” and that part of it was invented only then (AT, vol. I, p. 458) is presumably an exaggeration, even if the idea of adding the Geometry came in the very last stage of the project of the Discourse. Descartes knew that his Geometry would have few readers; indeed, Descartes meant it to be difficult and left it to his readers to find out the exact details. It is for the few friends that could understand it that he ordered six separate copies to be printed. Its difficulty was the reason not only why a friend of Descartes, Godefroot van Haestrecht (1592/93–59), wrote an introduction (“Calcul de M. Descartes,” AT, vol. X, pp. 659–80), but also why Frans van Schooten, when he prepared a Latin translation (plans of which were made as early as 1639), added notes and commentaries by himself and by Florimond Debeaune. By the time the Latin edition was published (August 1649), however, Descartes had lost interest in it: Van Schooten’s Latin was not elegant enough and Descartes had not been able to revise the text before it was printed. Still, the portrait of Descartes, which the book contains (engraved by Van Schooten), is the only one of him published during his lifetime. According to Descartes it was, apart from the beard and the cloths, a good likeness. The Latin version was reprinted in two volumes in 1659 and 1661 (the delay of the second volume being caused presumably by the death of van Schooten) and enlarged with commentaries and additional pieces by Johannes Hudde (1628–1704), Henricus van Heuraet (1633–60), and Erasmus Bartholinus (1625–98).
The Geometry is divided into three books, the first of which sets out the foundations of his approach and considers problems solvable by the construction of lines and circles. The second book considers the general nature of curves and the solution problems involving curves, most notably the locus problem propounded by Pappus. The third book is a study in the theory of equations, showing how to determine the number of roots in an equation and how to apply these algebraic results to the classification of curves and the solution of geometric problems.
The fundamental insight in Descartes’s Geometry is contained in its first sentence: “Any problem in geometry can easily be reduced to such terms that a knowledge of the lengths of certain straight lines is sufficient for its construction” (AT, vol. VI, p. 370), Descartes interprets arithmetical operations (addition, subtraction, multiplication, division, and the extraction of roots) as geometric constructions on straight lines that yield other straight lines. Classical authors had interpreted the product of two lines as a surface and the product of three as a solid, with the result that algebraic equations beyond the third degree had no geometrical interpretation. Descartes overcame this limitation by taking all arithmetical or algebraic operations on line segments to yield other line segments. This criterion of “dimensional homogeneity” permits equations of arbitrary degree to be employed in the study of geometric curves. Furthermore, by interpreting a curve as an equation in two unknowns that form the axes of a coordinate system, curves can be represented in a two-dimensional plane and the nature of the curve is expressed as an algebraic relation among geometric magnitudes.
Descartes proposed that a general method of solution for geometric problems could be found by reasoning in a sort of analysis that begins by supposing the problem solved and uncovering the algebraic equations that determine this solution. In Descartes’s words: “If, then, we wish to solve any problem, we first suppose the solution already to have been effected, and give names to all the lines that seem needful for its construction—those that are unknown as well as those that are known. Then, making no distinction between known and unknown lines, we must unravel the difficulty in any way that shows most naturally the relations between these lines, until we find it possible to express a single quantity in two ways. This will constitute an equation . . . and we must find as many such equations as we have supposed lines which are unknown” (AT, vol. VI, pp. 372–73). Exploiting this approach led Descartes to the solution of previously unsolved problems and permitted him to generalize results that had previously been stated only for special cases.
Classical geometry distinguished between “plane” problems whose solutions required only compass and rule constructions, “solid” problems relying on curves (such as conic sections) generated by the intersection of solids and planes, and “linear” solutions which employed more complex curves (such as the spiral) generated by compound motions. Classical authors did not consider curves more complex than conic sections to be properly geometric, but Descartes held that this criterion was too restrictive. He held that any curve that could be given a “precise and exact” measure was properly geometrical (as opposed to mechanical), and identified such curves with those that could be described by a regular motion or series of motions (AT, vol. VI, p. 390). Descartes even introduced a complex proportional compass (known as the “mesolabe”) that generalizes the traditional compass and produces complex curves that satisfy his criterion for geometric constructability. Descartes further assumed that every geometrical curve could be expressed in terms of an equation, and a principal result of the Geometry is the classification of curves into types or genres on the basis of their equations. In view of its many contributions, it is no exaggeration to say that the publication of the Geometry fundamentally changed the study of mathematics.
GEULINCX, ARNOLD (1624–69). Geulincx was born in Antwerp. He studied theology and humanities in Louvain, where he became a professor of philosophy in 1646, first as associate, then, in 1652, as primarius. At the beginning of 1658, however, for reasons that have as yet to be clarified, he was dismissed from all his academic functions. He fled to Leiden, where he embraced the Calvinist faith and became a protégé of the Leiden professor of theology Abraham Heidanus (1597–1678), a Cartesian. Thanks to his influence, presumably, Geulincx was appointed reader (1662) and then professor (1665) of philosophy in Leiden. Meanwhile he graduated in medicine. He died from the plague in 1669. Apart from “Miscellaneous Questions” (Quaestiones quodlibeticae, 1650), a treatise on logic (Logica suis fundamentis restituta, 1662) and the first part of a work on moral philosophy (Tractatus ethicus, 1665) most of his works were published posthumously. His Ethics in particular enjoyed great popularity and was reprinted several times until 1709. Although modem commentators value his contribution to logic, Geulincx is still a much-neglected philosopher who deserves more attention than he usually gets.
Geulincx became familiar with Cartesian philosophy in Louvain through his teacher Willem Philippi (ca. 1600–65). What he retains from it is the reform of logic and method and the dualism of body and mind, which he interprets in an occasionalist way. The foundation of Geulincx’s occasionalism is the principle that one cannot do what one does not know how to do. Accordingly, since we do not know how our body works, we are not the real subjects of bodily actions; inversely, it is impossible for a body to act on our minds or on other bodies because it would not know how to do this. Still, Geulincx believes that there is a harmony between what happens in the outside world and what is willed or perceived by our minds. The agent responsible for this is God, who also imposed on the material world a certain number of laws. Geulincx is original in completing Cartesianism with an ethical theory, despite the fact that, as he puts it, “I am a spectator on this scene, not an actor” (Tractatus Ethicus I, ii, 11). According to Geulincx the object of ethics is virtue, that is, love of God and of right reason. Of the four cardinal virtues, diligence, obedience, justice, and humility, which are the immediate expressions of virtue as such, humility, which is the contempt of oneself out of love for God, is the most important one. It entails a certain number of obligations, which are actually formulated as divine commands. We must be ready to die if God calls us; we should not end our life voluntarily; we should take care of our body, etc. Although Geulincx’s views bear some resemblance to Baruch Spinoza’s, especially as regards his tendency to reduce the substantiality of individual bodies and his interest in practical philosophy, this should not be exaggerated. Apart from the fact that Geulincx has a different conception of moral philosophy and of the relation of mind and body, his God is the Christian God.
GIBIEUF, GUILLAUME (ca. 1591–1650). A French theologian who was a member of the Oratory and of the Sorbonne. Descartes courted Gibieuf as someone who could promote his Meditations to other members of the Paris theological faculty. Gibieuf took enough of an interest to correspond with Descartes concerning his work. However, his primary interests were in theological matters, mainly the issue of freedom of the will. His main work is De Liberiate Dei et Hominis (1630), a critique of the Jesuit view that indifference is essential to human freedom. The anti-Jesuit Cornelius Jansenius approved of Gibieuf’s text, as did Descartes, who told Marin Mersenne in 1641 that he has said nothing in the Meditations “that is not in accord with what is said in his book De Libertate” (AT, vol. III, p. 360). However, some of Descartes’s later writings seem to be more sympathetic to the Jesuit position that Gibieuf and other critics of Jesuit theology condemned as a form of heretical Pelagianism.
GILBERT, WILLIAM (1544–1603). English physician and natural philosopher best known for his researches into the phenomenon of magnetism, which culminated in the 1600 publication of the treatise De magnete (“On the Magnet”). Born to a prosperous merchant family in Colchester, Gilbert entered St. John’s College, Cambridge, in 1558, taking the degrees of B.A. in 1561, M.A. in 1564, and M.D. in 1569. He was elected to a fellowship at St. John’s in 1569 and held several college offices. Gilbert established a medical practice in London in the early 1570s, becoming a member of the Royal College of Physicians, to whose presidency he was elected in 1600.
Gilbert employed a wide variety of experiments in De magnete to test hypotheses about the nature of magnetism, and he was emphatic in his rejection of Aristotelian accounts of magnetic attraction. He was the first to distinguish clearly between magnetism and static electricity, and he organized De magnete in the form of a comprehensive review of what was known about magnetic attraction. A key component in Gilbert’s theorizing was the construction of laboratory models of the Earth from lathe-turned lodestones. He performed experiments on these models and then argued by analogy to draw conclusions about the phenomenon of magnetic attraction in the Earth itself. Gilbert’s theory of magnetism was strongly influenced by Neoplatonic doctrines. In his animistic scheme of things, magnetism is literally the soul of the Earth, and a perfectly spherical lodestone (if aligned with the Earth’s poles) would spin on its axis, just as the Earth spins on its axis in 24 hours. This endorsement of a rotating Earth was based in part on the doctrines of Nicholaus Copernicus, to which Gilbert added his own arguments from magnetism; he was nevertheless silent on the issue of whether the heliocentric model of the world was to be preferred.
Descartes was certainly familiar with Gilbert’s doctrines, but he had little patience for a theory that postulated a Neoplatonic world soul and characterized magnetism as a ubiquitous immaterial cosmic force. In the Rules for the Direction of the Mind he casually mentions that “someone may ask me what conclusions are to be drawn about the nature of the magnet simply from the experiments Gilbert claims to have performed, whether they be true or false” (AT, vol. X, p. 431), but he obviously set little store by Gilbert’s doctrines. Instead, Descartes sought to explain magnetism mechanically. In the fourth part of the Principles of Philosophy he attempts this by means of a constantly circulating flow of subtle particles from one hemisphere of the Earth to the other (AT, vol. VIIA, pp. 275–314).
GLANVILL, JOSEPH (1636–80). English clergyman and philosopher. Educated at Exeter College and Lincoln College, Oxford, Glanvill was ordained in the Church of England in 1660 and was appointed rector of the Abbey Church at Bath. He had a strong interest in natural philosophy and attacked scholastic philosophy in The Vanity of Dogmatizing (1661). Glanvill conceived the new philosophy as a kind of skepticism, and he popularized among English readers an interpretation of Descartes that characterized his philosophy as an essentially skeptical method for metaphysics and natural philosophy. His emphasis on the incompleteness of our knowledge of nature and the limits of mechanical explanation was congenial to Henry More, and the two became close associates. As was also the case with More, Glanvill’s early enthusiasm for Descartes turned to disenchantment and he eventually came to regard Cartesianism as an exercise in dogmatic metaphysics that overemphasized the explanatory success of mechanism and denied the reality of spirits. His continuing interest in natural philosophy led to his election as a fellow of the Royal Society, and in 1668 he published Plus Ultra, or the Progress and Advancement of Knowledge since the Days of Aristotle where he extolled the world of the Society. He became best known for his investigations into witchcraft and demonic possession, which he conducted with More. His 1666 Philosophical Endeavour towards the Defence of the Being of Witches and Apparitions was reissued in 1681 by More, who appended to it an extended polemic against Descartes.
GOCLENIUS, RUDOLPH (RUDOLPH GÖKEL, 1547–1628). German professor of natural philosophy and mathematics, one of the more influential late scholastics. Born in Corbach in the principality of Waldeck, Goclenius attended the University of Marburg from 1564 to 1568 and continued his studies at the University of Wittenberg, with his principal academic interest in natural philosophy. He took the degree magister artis in 1571 and was appointed to the rectorship of the local school in Corbach. He composed a Latin celebratory poem dedicated to Prince Wilhelm of Hesse, and the success of this venture brought him the post of rector of the school in Kassel in 1575. In 1581 he was appointed to the professorship in physics at the University of Marburg. He remained at the University of Marburg for the rest of his career, serving in various capacities including professor of logic, mathematics, and ethics, as well as rector of the university and dean of the faculty of philosophy.
Goclenius enjoyed a reputation as a conciliator in controversies among theological and philosophical factions. In keeping with this reputation, his contributions to natural philosophy, mathematics, and logic were eclectic and show a pronounced reluctance to depart from traditional authorities. He upheld the traditional logic of Aristotle against the innovations of Petrus Ramus, and promoted the scholastic-Aristotelian method in physics. His encyclopedic work Physicae completae speculum (“The Mirror of all Physics,” 1604) assembles material from mathematics, geography, astronomy, botany, and medicine, as well as precepts taken from logic, metaphysics, ethics, and theology. His influential Lexicon philosophicum (1613) introduced such terms as “psychology” and “ontology” into the philosophical vocabulary. His posthumously published Mirabilium naturae liber (“Book of the Marvels of Nature,” 1625) contains a detailed investigation into such phenomena as magnetism.
GOD. Descartes characterizes God as “a substance that is infinite, independent, supremely intelligent, supremely powerful, and which created both me and everything else” (AT VII, p. 45). This account is typical of the “God of the philosophers”—the infinitely powerful, all knowing Creator whose essence can be understood by finite minds, although orthodoxy requires that God cannot be fully comprehended by a finite being. (See knowledge of God.) God plays an absolutely indispensable role in Descartes’s philosophy, and specifically in his metaphysics, epistemology, and natural philosophy.
Cartesian metaphysics emphasizes the role of God as creator, not merely of the universe and the finite creatures that inhabit it, but also of the eternal truths such as the common notion that nothing comes from nothing. This aspect of Descartes’s philosophy emphasizes the absolute dependence of things on God, a dependence so complete that even the truths of logic and mathematics require God’s creative act in order to hold true, which means that God could freely have chosen alternatives to such truths. God’s causal power extends to self-creation, and Descartes characterizes God as self-caused, or causa sui, a doctrine that led to some intense exchanges with Antoine Arnauld in the fourth set of Objections and Replies (AT, vol. VII, pp. 235–46). A further aspect of God’s creative power is that divine concurrence is necessary to preserve things in existence. The result is that (as Descartes puts it in Meditation III), there is only a conceptual distinction between creation and preservation, and therefore God’s sustaining of the world is equivalent to his continuous re-creation of it (AT, vol. VII, p. 49).
Descartes held that the demonstration of God’s existence was a matter of the first importance for philosophy (AT, vol. VII, p. 1), and the Meditations pursue two different strategies for demonstrating God’s existence. The first (explored in the Third Meditation) begins with the idea of God and reasons that an idea with so much objective reality cannot have been caused by anything less perfect and powerful than God himself. Thus, since the mind of a finite individual meditating on the idea of God has insufficient power to have produced such a perfect idea, it must arise from some source outside the meditator’s mind; and since such a source cannot have less reality and perfection than God, there must be a God who answers in all respects to the idea of God. (See cosmological argument.) The second strategy (worked out in the Fifth Meditation) argues that existence belongs conceptually to the very essence of God. Since God is by definition the supremely perfect being, and existence is a perfection, it follows that God’s existence is a necessary consequence of his essence. (See ontological argument.) Descartes regarded these demonstrations of God as more certain than those of mathematics, and concluded that an atheist mathematician would find himself in the self-contradictory position of denying a truth that is far more certain than any mathematical theorem (AT, vol. VII, p. 141).
Cartesian epistemology is impossible without a God, since the “truth rule” that clear and distinct perceptions must be true is guaranteed only by the existence of a benevolent, nondeceiving God. If God were to permit us to be mistaken even about those things we seem to grasp most clearly, then there would be no sure way for us to make a judgment and avoid error. But such deceit is inconsistent with the perfection of God. This leads to the conclusion that God’s non-deceiving nature guarantees that those things I clearly and distinctly conceive must be true. As a consequence, I know with certainty that I will not fall into error, provided that I confine my judgments to those things clearly and distinctly perceived.
The place of God in Descartes’s natural philosophy is not only as creator of the world, but also as the ultimate source of the laws of motion that govern the material world. God’s immutability guarantees that the conservation principle holds, and this is the foundation of the laws of motion. In fact, Descartes holds that God is the “first and general” cause of motion (AT, vol. VIIIA, p. 61). This emphasis on God’s causal role makes it difficult for Descartes’s natural philosophy to avoid occasionalism, since the God who creates and sustains the world, continuously re-creating it in accordance with immutable laws of motion, would seem to be the only causal agent.
Pierre-Sylvain Régis and Nicolas Malebranche offered different developments of Descartes’s account of the role of God in natural philosophy. Malebranche was the primary proponent of the occasionalist thesis that God is the only real cause of effects in the material world. Such a thesis is connected to Descartes’s claim in the Principles that God is the primary cause who conserves the total quantity of motion by continuing to create the material world in the same way from moment to moment. However, Descartes himself suggested that God’s causation of motion involves his “concurrence” with the action of bodily causes. In line with this suggestion, Régis claimed that changes in motion derive directly not from God’s action but rather from a created nature that provides the ground for the laws of motion.
Descartes was concerned to restrict his claims about God for the most part to what is revealed by reason. He thereby attempted to avoid disputes about theological matters that depend on faith. Even so, his later followers became entangled in theological disputes concerning the relation of human freedom to divine grace and the manner in which God brings about transubstantiation in the mystery of the Eucharist.
GOD, KNOWLEDGE OF. In the Meditations, Descartes claimed that a proof of the existence of a nondeceptive God is needed for stable and certain knowledge. The fact that such a proof seems to require such knowledge gave rise to the famous problem of the Cartesian circle. However, Descartes countered that his clear and distinct perceptions allow him to provide the needed proof. In fact, the Meditations included two arguments for the existence of God that drew on different though complementary explications of God’s nature. (See cosmological argument and ontological argument.) Both arguments suggest that God possesses an unlimited form of the same sort of substantiality or perfections that creatures possess. Descartes did deny that the term substance applies “univocally,” or in the same way, to God and creatures (Principles I, art. 51), but such a denial is consistent with the standard Thomistic view that terms apply to God and creatures “analogically” since God possesses the named perfections primarily and creatures in a derivative way.
However, Descartes’s doctrine of God’s free creation of the eternal truths is in some tension with such a view insofar as it implies that God differs entirely from creatures since they are essentially conditioned by the eternal truths while God is not. Descartes’s disciple Pierre-Sylvain Régis later emphasized this implication of the eternal truths doctrine since God creates all perfections in creatures ex nihilo, the created perfections can bear no relation to God’s perfections. Appealing to a position that Thomas and other scholastics rejected, Régis concluded that names for perfections could apply to God and creatures only “equivocally.” In offering this conclusion, Régis was countering the claim in Nicolas Malebranche that perfections in creatures are present “eminently” in God insofar as God has ideas of these perfections that are not distinct from his own substance.
GOUSSET, JACQUES (1635–1704). A Calvinist minister and a noted Hebrew scholar. Gousset studied at Saumur, and became a minister at Poiters in 1662, but left France in 1685 when the Edict of Nantes was revoked. He settled in the Netherlands and became minister of the Walloons at Dordrecht. Five years later he gave up the position to occupy the chair of Greek and Theology at Groningen, which he held until he died. His principal works concerned the Hebrew language and the interpretation of biblical passages. He also wrote a treatise on whether the Cartesian system of the world should be considered dangerous, Dissertatio philos. ostendens cartesianum mundi systema non esse . . . periculosum (1696), and a defense of Descartes’s view of the activity of secondary causes against Nicolas Malebranche’s system of occasional causes in Causarum primae et secundarum realis operatio (issued posthumously, 1716).
GRAVITY. In Aristotelian natural philosophy, heaviness and lightness are qualities of bodies derived from the elements they are composed of. The elements earth and water are heavy; air and fire are light. Heavy bodies tend to move toward the center of the universe (which is also the center of the Earth); light bodies away from the center. Medieval philosophers, in analyzing the motion of falling bodies, had arrived at a rule equivalent to that still used in elementary physics (s = ½gt2). Galileo Galilei too had presented a derivation of this rule.
In his early collaboration with Isaac Beeckman, Descartes also offers a derivation of the rule based on the assumptions that an equal impulse of motion is given at each instant to the falling body and that quantity of motion is preserved (see inertia). He offered no explanation, however, for the impulse itself. In later work, he argued that the vortex surrounding each planet exerts a pressure on every body on that planet, directed toward the center of the planet and proportional, more or less, to the area of the outward-facing surface of the body (Principles IV, art. 28). Dense bodies, which have relatively few pores or channels, offer more resistance to vortex particles, and are therefore heavier than more rarefied bodies (Principles IV, art. 20).
The explanation of the orbits of the moon around the Earth, and of all the planets around the sun, was quite different. Every planet-sized body is surrounded by a vortex of small particles revolving around it. Their speed is proportional to their distance from the planet. Coarse matter in the midst of these vortices is dragged around with them, and settles into an orbit around them in such a way that it is in equilibrium with the vortex particles around it (Principles III, art. 140–45).
The tides are explained by yet another mechanism. The vortex at whose center is the Earth, and in whose outer layers the Moon revolves, remains constant in diameter. In the region immediately between the Earth and Moon, there is less room for the vortex particles to move. This produces pressure on the atmosphere and oceans of the Earth directly beneath the Moon, and thus a low tide there, and 90 degrees around the Earth’s circumference on either side a high tide (Principles IV, art. 49).
Although the vortex theory of gravity was defended even into the 1740s (by Bernard de Fontenelle), it was decisively rejected by Isaac Newton, Christiaan Huygens, and other physicists well before the end of the 17th century. Explanations based on it were likewise rejected; the Newtonian assumption of a single inverse-square force operating between all parts of matter provided a unified explanation of all the phenomena described above, and yielded—as Descartes’s theory did not—precise quantitative results. Nevertheless Descartes’s theory succeeded in showing how gravity could be accounted for in an isotropic space, thus allowing natural philosophers to abandon the notion that the universe has a center—a special place in which heavy bodies congregate.