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Gassendi and the Void ISIH Conference April 18, 2007 Ann Orlando Slide 1 Hello; I am Ann Orlando from Weston Jesuit School of Theology in Cambridge, Massachusetts. It is my pleasure to be here this afternoon. Today we take the reality of voids for granted, we talk easily about the vast regions of empty space. But until the seventeenth century most natural philosophers believed that no such thing existed. After all, if it was nothing, then how could it exist. Pierre Gassendi, one of the leading figures of the scientific revolution, more than anyone else challenged this, and argued convincingly that in fact vacuums are found in nature and are integral to the way in which nature ‘works.’ His arguments were based not only on new physical observations but also on the Christian tradition, a tradition which had through the previous centuries, denied the existence of a void. 1

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Gassendi and the VoidISIH ConferenceApril 18, 2007Ann Orlando

Slide 1

Hello; I am Ann Orlando from Weston Jesuit School of Theology in Cambridge,

Massachusetts. It is my pleasure to be here this afternoon.

Today we take the reality of voids for granted, we talk easily about the vast

regions of empty space. But until the seventeenth century most natural philosophers

believed that no such thing existed. After all, if it was nothing, then how could it exist.

Pierre Gassendi, one of the leading figures of the scientific revolution, more than anyone

else challenged this, and argued convincingly that in fact vacuums are found in nature

and are integral to the way in which nature ‘works.’ His arguments were based not only

on new physical observations but also on the Christian tradition, a tradition which had

through the previous centuries, denied the existence of a void.

To elucidate these arguments, I will begin by describing Gassendi’s overall

intellectual model and systematic philosophy.

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Slide 2 Background on Pierre Gassendi

Pierre Gassendi was born in Champtercier, France in 1592; he died in Paris in

1655. During his life Gassendi had three parallel careers: ecclesial, academic and

intellectual.

By far the most important of these was his career among the intellectual elite of

France. He was a member of several correspondence groups of European intellectuals

whose members included Mersenne, Galileo, Descartes, Hobbes and Pascal. Along with

Gassendi, they debated new scientific theories and experiments. Although these early

modern philosophers and physicists often differed with each other, they were unified in

rejection of Aristotelian physics; in its place they were developing the mechanical

universe model of physics.

Gassendi himself made critical contributions to this development. He was

recognized in his own time as a brilliant experimental physicist in astronomy, dynamics,

optics and atomic theory. However there were three abiding beliefs that Gassendi held

which placed him out of step with most of the natural philosophers in the his own day

and succeeding generations. First, he believed that the book of nature could best be

described by words, not mathematics. Second, he believed that those words were best

developed considering all past words spoken on any subject. Third, he believed that

physics and religion were part of one unified whole. That is, he tried to reconcile the

book of nature and the book of faith.

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Slide 3 Intellectual Model

To effect that reconciliation, he relied on the techniques of both the empiricists

and the humanists. But he did so from the perspective that human knowledge is

uncertain; he advocated for a probabilistic epistemology that always left room for new

explanations as additional data (whether empirical or humanist) became available.

His physics was first and foremost based on observation and inference to the most

probable result. Gassendi believed the mind was a tabula rasa on which data from the

senses was projected, combined and analyzed to form understanding. But he was not a

naïve empiricist. He recognized that observations and initial premises could be faulty or

incomplete. Richard Popkin, for instance, has analyzed the importance of skepticism in

Gassendi’s epistemology.1 For Gassendi, we can never know perfectly and must

continually rely on new information from our senses to advance knowledge. Through

physics and the study of nature we can at least know things approximately, or probably.

Therefore, according to Gassendi, the goal of physics is “if not to pursue the truth of

things, at least (to pursue) the true likeness of things.”2

Also important in Gassendi’s epistemology is the relationship between

mathematics and physics. David Sepkoski observed, “Gassendi’s nominalism and

mathematical constructivism thus departed from Cartesian and Galilean philosophy of

mathematics by denying that mathematical objects (and similar abstractions) were

ontologically real.”3 Rather, to the extent that mathematics was useful at all, it could at

1 Richard Popkin, The History of Skepticism from Erasmus to Spinoza (New York: Harper Row, 1965).2 Gassendi, 1:132. “…nisi rerum veritatem, saltem versilmilitudinem assequi…” All references to Gassendi are from the Opera Omnia unless otherwise noted.3 David Sepkoski, “Nominalism and constructivism in seventeenth-century mathematical philosophy,” Historia Mathematica 32 (2005): 41.

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best provide a description or label for empirical observations. For Gassendi, mathematics

could not ‘prove’ or demonstrate anything about nature. “When a mathematician proves

some proposition you had not known, he accomplishes no more than a man who discloses

the contents of a casket by writing out a label for it by opening it up.”4

In place of mathematics, Gassendi thought words were the best descriptors of

nature; all words previously written on any subject in natural philosophy should be

evaluated for their validity using the techniques developed by the Renaissance humanists.

Lynn Sumida Joy has analyzed in detail Gassendi’s intellectual development as a

humanist.5 His acceptance of revelation and the truths taught by religion are based on his

willingness to accept the truth of accounts from others whom he considers authoritative.

“What is accepted by all or most knowledgeable persons and by those who are all for the

most part persons of distinction and status has the least grounds for being disbelieved.”6

For Gassendi the most authoritative source of knowledge was the Bible:

“Consequently, Divine Faith which we have from God is the firmest since we have a

preconception that God is certainly absolutely truthful.”7 He observes that although

divine faith “does not possess the evidence which science acquires through

demonstration, it nevertheless acquires its evidence from divine authority, which gives it

a certainty equal to itself.”8 The certainty of faith depends on the authority of the speaker,

and since God’s authority is absolute, faith (and only faith) can be known with certainty.

However, even authoritative human opinion can only have degrees of certainty. For

Gassendi, the humanists’ methods could suggest the degree of certainty that should be

4 Ibid., 3: 208, trans. Brush, 106 5 Lynn Sumida Joy, Gassendi the Atomist (Cambridge: Cambridge University Press, 1987).6 Gassendi, Institutio; trans. Howard Jones (Assen: Van Gorcum, 1981), 119.7 Gassendi, 1:120. “Ex quo efficitur, ut Fides Divina, seu quam Deo habemus, firmissima sit, quia praeconcepimus Deum sic certo certuis esse veracem.” 8 Ibid., 1:121; trans. Jones, 149.

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credited to human authors, just as repeated experiments could determine the degree of

certainty to attach to observed data.

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Slide 4 Toward a Systematic Philosophy

Gassendi’s life project was finding the correct philosophical framework within

which to organize both empirical and humanist data to create the most probable

understanding on any topic in natural philosophy. He discovered in Epicurus a system of

logic, physics and ethics that seemed compatible with early seventeenth century empirical

observations. From Epicurus, Aristotle’s near contemporary, Gassendi constructed a

framework which he thought could support both the new experiments and Christian

teaching.

Demonstrating the consistency of Epicureanism with seventeenth-century

Catholic Christianity was quite a challenge for two reasons. First was the basic atheistic

premise of Epicureanism, and the associated beliefs in ethics based on pleasure and the

mortality of the human soul. In antiquity, Epicureanism had been considered the worst of

all philosophical systems by nearly every other ancient philosophy, both pagan and

Christian, because of these tenets. Second, Epicurean physics advocated physical

concepts such as the eternity of the cosmos, the existence of other worlds in space and

time, the existence of a void, and the atomic structure of all substances which were

sharply opposed to the prevailing Christianized Aristotelian physics.

Little previous research has examined in detail Gassendi’s efforts to reconcile

Epicureanism and Christianity. Analyzing how Gassendi tried to use the Christian

classics in support of his natural philosophy reveals some of the early signs of the fissures

that were developing between science and religion. For instance, Gassendi supported the

Copernican cosmology until the Church’s 1633 condemnation of Galileo. At that point

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he moved to the Tychonian system as an alternative because it was consistent with both

Church teaching and empirical data.

My research interest focuses on how Gassendi tried to create a philosophical

synthesis which combined seemingly irreconcilable methods (empiricism and humanism)

and philosophies (Epicureanism and Christianity).

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Slide 5 Epicureanism and Modifications

To justify his use of Epicureanism, Gassendi first had to refute the damaging ad

hominem attacks against Epicurus himself that dated to antiquity. Gassendi claims that

the Church Fathers misunderstood and misinterpreted Epicurus, especially his ethics. He

argues that Epicurus’s personal ethics had more in common with Christian ethics than

many other ancient pagan philosophers. Gassendi calls upon Origen in Contra Celsum

and Augustine in the City of God to bear witness that Epicurus was no worse, and

perhaps better, than other pagan philosophers.9

Gassendi sets about “Baptizing Epicurus” (Margret Osler’s phrase)10 by making

God the author of the most objectionable Epicurean tenets. For instance, he asserted that

God created the atoms and gave them their motion and proclivity to combine in order to

form other substances. Similarly, Gassendi argues that God created man to seek pleasure.

Therefore pleasure could be an appropriate basis for Christian ethics.

9 Ibid., 5:200-202.10 Margaret Osler, Divine Will and the Mechanical Philosophy, Gassendi and Descartes on Contingency and Necessity in the Created World (Cambridge: Cambridge University Press, 1994) 22.

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Slide 6 Gassendi and the Christian Classics

Gassendi looks to the Bible and the Church Fathers to validate his systematic

philosophy. Although the Church Fathers were typically not interested in physics per se,

they were deeply concerned about the reconciliation of Scripture with observed natural

phenomena. It was typically in this context that the Fathers wrote about physics,

astronomy and cosmology, often as a commentary on Genesis. Gassendi analyzes

patristic arguments throughout his own development of physics. As Harry Brundell has

observed, one of the key reasons for Gassendi’s use of the early Church Fathers is their

opposition to Aristotle. At the very beginning of Gassendi’s massive Syntagma

Philosophicum, he writes:

The early Church Fathers were particularly opposed to Aristotle and his philosophy, and they displayed extreme animosity against the followers of Aristotle. But when some philosophers were converted to the faith, they began to set aside the more serious errors of Aristotle. What remained of Aristotelian philosophy was then accommodated to religion so successfully that it was no longer suspect and finally became the handmaid ministering to religion. Therefore I say, just as it was possible in the case of Aristotelian philosophy, which is now taught publicly, so it is possible with other philosophies such as the Stoic and Epicurean. All of them have much that is of value and worthy of being learned once the errors are eliminated and refuted in the same way as the very grave errors of Aristotle were refuted.11

This passage encapsulates Gassendi’s approach to Christianizing Epicureanism. The way

to justify Epicureanism is first to reject Aristotle, as the Church Fathers had done, and

then to recognize that later theologians were able to use Aristotle in theology after

correcting his “grave errors.” Just so, Gassendi argues he should be allowed to do the

same for Epicurus’s philosophy.

11 Harry Brundell, Pierre Gassendi, From Aristotelianism to a New Philosophy (Dordrecht: Reidel, 1987), 52. (Gassendi, I:5)

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As an example of his approach, lets consider the way in which Gassendi appealed

to both experimental and humanists ‘data’ to support his arguments for the existence of a

void against the prevailing theory.

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Slide 7 The Problem with a Void

Epicurus had suggested that atoms move in a void with a random swerve that

accounts for the variation and uncertainty observed in nature and men. But the standard

description of nature as taught in the schools of the Middle Ages was based on Ptolemy's

magnum opus, the Alamgest, together with Aristotle's On The Heavens and On Physics.

These were the authoritative cosmological and physical treatises. The fundamental

reasons for the rejection of a void are found in Aristotle’s On the Heavens (I.9.279a.10-

17) in which he states that there is only one world; that voids do not exist; and time is the

number of motion of natural bodies.12

One further point of Aristotelian understanding needs to be explained as it relates

to the void, and that is Aristotle’s definition of velocity found in the Physics.13 Aristotle

argued that speed was inversely proportional to the density of the medium through which

the object moves. Therefore a rock thrown in water will move slower than one thrown in

the air. By this reasoning, a rock thrown in a vacuum would move with infinite velocity,

which is not possible. Two conclusions result: first, a vacuum cannot exist; and second,

natural motion is circular.

The reconciliation of Aristotle's physics and the descriptions found in the Bible

dominated the university discussions from the thirteenth through the seventeenth

centuries. As Edward Grant described in detail, official ecclesial opposition to a void

was codified in 1277 when the bishop of Paris, Etienne Tempier, issued a series of 219

condemnations of heretical views. These condemnations were very influential, especially

12 Aristotle, On the Heavens, trans. Guthrie in Grant, Planets, Stars and Orbs, The Medieval Cosmos, 1200-1687 Cambridge: Cambridge University Press, 1994), 169.13 Aristotle, Physics, trans. Philip Wicksteed, Loeb Classics (Cambridge: Harvard University Press, 1952), 417-425.

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after they received support from Pope John XXI. Two condemnations in particular

denounced the idea of a void: Condemnation 66 argued that God could not move the

heavens in a straight line otherwise there would be a vacuum; and Condemnation 190

argued that empty space did not exist before God created the world.14

14 Edward Grant, Much Ado About Nothing (Cambridge: Cambridge University Press, 1981), 108-110. See also Lolordo, Pierre Gassendi and the Birth of Early Modern Philosophy, 109-110.

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Slide 8 Gassendi’s Empirical and Historical

Evidence for a Void

To refute this standard position, Gassendi invoked both experimental data and the

Christain classics. For experimental support he points to three classes of experiments to

demonstrate the existence of void: chemical, barometric and dynamic. The chemical

experiments suggested by Gassendi were based on dissolving compounds in water. He

reasoned that since salts and other compounds dissolved in water can be reconstituted

from evaporated water that the dissolved particles must reside in void spaces mixed in

with the water.15

Saul Fisher has described the impact of the barometric experiments by Torricelli

and Pascal on Gassendi’s thought.16 In these experiments, a U-shaped tube, sealed at one

end, was filled with mercury. Then the apparatus was carried to a higher altitude, causing

the mercury to partially empty from the tube. The question becomes what, if anything,

fills the gap between the new, lower mercury level and the sealed end of the tube.

Gassendi (and Pascal) argued that only a void could remain in the gap.17 Thus having

established that a void could be artificially created, Gassendi suggested that voids or

vacuums could also appear in nature.18

15 Ibid., 1:195-196.16 Saul Fisher, Pierre Gassendi, 128-132.17 Being the expert empiricist that he was, Gassendi recognized as a valid argument against a void that light could pass through the gap. Relying on his atomism for an explanation, Gassendi allowed that the gap was not completely void, but there still remained some atoms mixed with a void in the gap through which light could ‘flow’. Note that the discounting of an aether or other material required for light to travel through did not occur until the Michelson-Morely Experiment of 1887.18 This description is found in both the Appendix to his Animadversiones (3:iij-xxiij) and the Syntagma (I:203-216).

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Perhaps his most important empirical arguments were those based on motion.

Commenting on Galileo’s Diologo, Gassendi described19 his key experiment that

confirmed Galileo’s theory of dynamics: the famous ship experiment. In this experiment,

he demonstrated that balls dropped from the mast of a moving ship fall at the foot of the

mast, regardless of how fast the ship is moving.20

Paolo Galluzzi describes how this experiment led Gassendi to develop several

important insights into the laws of dynamics. First, that all motion was relative. The

motion of the balls when they are released from the mast ‘includes’ the horizontal motion

of the ship.

Another insight that Gassendi formulated was the law of inertia. He believed that

his experiment demonstrated that only an external force acts on the balls, and further that

unless an external force acts in some way, a body will continue in motion indefinitely.

This led to Gassendi’s succinct statement that a body moving in a vacuum will

perpetually continue in a straight line at a constant speed.21 This was the first written

statement of the law of inertia.

Gassendi also found empirical evidence for empty space in the observed motion

of celestial bodies and the barometric experiments.22 He argued that the motion of

celestial bodies was such that most of the space between them was empty or an

extramundane void, since celestial bodies were not observed to ‘hit’ or encounter any

19 The De Motu Impresso is a collection of three letters written by Gassendi to Pierre Du Puy. These letters were circulated among the Mersenne network as a unit, and Gassendi intended that they be considered as a unit. The De Motu is found in 3: 478-563.20 Paolo Galluzzi, “Gassendi and L’Affaire Galilee of the Laws of Motion,” in Galileo in Context. ed. Jurgen Renn (Cambridge: Cambridge University Press, 2001), 239-276.21 Ibid., 1: 343; trans. Brush, 385.22 Ibid., I:195-196.

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other bodies. Even more controversially, Gassendi suggested that there existed a void in

the sub-lunar region between the moon and the earth.23

His reasoning for a sub-lunar void was based on the barometric experiments.

Gassendi repeated those experiments at different altitudes. As the altitudes increased, the

gap in the sealed mercury column increased. Gassendi reasoned that this indicated as one

moved toward the moon, air was becoming thinner and thinner, and that eventually there

would be no air or anything else, only a void.

Gassendi juxtaposes this type of experimental evidence next to evidence from the

history of philosophy and theology.

For historical Christian evidence of a void, Gassendi notes that angels are said to

be in space without being corporeal. Further angels can penetrate corporeal things such

as stone and walls, and yet angels have no corporeal dimension. Edward Grant notes that

Gassendi extends the analogy between angels and a void by turning to Nemesius who

suggested that grace and space were made incorporeal per se.24

Nemesius, fourth century bishop of Emesa, was best known for his On Human

Nature which was well received in antiquity and used in the Middle Ages as an

authoritative Christian source. However, it must be allowed that Nemesius is at best a

secondary figure; it is telling that Gassendi must appeal to him as patristic support for this

important concept.

Gassendi looked for additional theological support for an extramundane void from

Irenaeus. He notes that the second century bishop of Lyons equated the Greek kenoma

with the Latin inane. In a reference to Irenaeus, Gassendi points out that “certain of the

23 Ibid., I:182; trans. Brush, 386.24 Ibid., 1:219. See also Grant, Much Ado About Nothing, 21-22.

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Fathers in order to argue against the Valentinians call it kenoma.”25 He observes that

Irenaeus had separated the notion of void from God in his arguments, implying (in

Gassendi’s view) than an infinite void could exist.26

25 Ibid., 1: 185. “specialeque est aliquorum Patrum, ut dum adversus Valentinios disputant, ‘to kenoma’ vocent.”26 Irenaeus, Against the Heresies II.4, ANF Vol. 1, trans. Coxe (Peabody: Hendrickson, 1995), 362-363.

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Slide 9 Implications of a Void: Nature of

Space and Time

This discussion highlights how several basic concepts in medieval and early

modern physics were inter-related. What one thought about the void effected how one

thought about the nature of space and time, and motion.

Because Gassendi believed in the reality of a void, he also asserted that

dimensionality is not the same thing as a body, which is defined by substance and

accidents. “We conclude that space and time must be considered real things, or actual

entities, for although they are not the same sort of things as substance and accident are

commonly considered, they still actually exist.”27

Among the properties of both space and time are their infinitude and Gassendi

comes very close to asserting that they are eternal. Antonia Lolordo has stressed this line

of reasoning in Gassendi.28 Empty space and time exist independently of God; God

creates corporeal entities in space and time. Gassendi asserts, without giving any

references, that the majority of the Sacred Doctors agree with this.29

Just as space can be measured by extended bodies, but is not the same thing as an

extended body, so time can be measured by the motions of celestial bodies, but time itself

is not the motion of celestial bodies. “Whatever it (time) is, it would appear to be

something incorporeal, like the void.” 30

27 Gassendi, 1:182; trans. Brush 384.28 Antonia Lolordo, Pierre Gassendi and the Birth of Early Modern Philosophy (Cambridge: Cambridge University Press, 2007), 110-127.29 Ibid.30 Ibid., I:, 223; trans. Brush, 393.

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Gassendi directly challenged the scholastic view through a discussion on the

eternity of essences. He argues that it is easier to accept the notion that space is

uncreated and independent of God which is “a concept that appears to be far more

acceptable than another that the doctors commonly admit, namely that the essences of

things are eternal, uncreated and independent of God.”31 Although no specific reference

is given, he seems to be referring to Aquinas, especially his On Being and Essence. If so,

he is overstating Aquinas’s position. It is true that Aquinas believed in the eternity of

essences, but certainly not that they were independent of God.

31 Ibid., I:184; trans. Brush, 389-390.

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Slide 10 Evidence of Space and Time

For patristic support of the distinction of space ant time from corporeal bodies,

Gassendi again turned to Nemesius: “Let what Nemesius has to say stand for them all,

‘Indeed every body is endowed with three dimensions, but not everything endowed with

three dimensions is a body. Of this sort are place and quantity which are incorporeal

entities (entia).” 32

Gassendi begins his discussion of time with Augustine and the Confessions Book

11: “Everybody quite rightly remembers what Saint Augustine said: ‘If no one asks me

what time is, I know the answer; if I wish to explain it to an inquirer, I do not know it.’

”33 Gassendi expands on Augustine:

…whatever it is it would appear to be something incorporeal, like the void… Then in the same way that space was described earlier as an incorporeal and immobile extension in which it is possible to designate length, width and depth so that every object might have its place, so time may be described as an incorporeal fluid extension in which it is possible to designate past, present and future so that every object may have its time.34

The concept of time as distinct from motion allows Gassendi to interpret Joshua’s battle

at which the sun stood still and the day lasted longer than any day before or since (Josh.

10).35 In this interpretation, Josh. 10 does not imply that time stood still, only that time

could no longer be measured by the revolution of the sun.

32 Ibid; 1:182; trans. Brush, 385. Here and elsewhere Brush translates entia as beings; this I think gives a poor connotation of what Gassendi is saying. I have translated it as entities. Gassendi does not in any way mean to imply that empty space is a tangible thing which ‘being’ might connote. 33 Gassendi, 1:220; trans. Brush, 390.34 Ibid.35 Gassendi, 1:225, gives Joshua 10:14 as “non fuisse ullum neque antea neque postea tam longum diem” whereas the Vulgate has “non fuit ante et postea tam longa dies.”

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Gassendi asserted that time, like his concept of space, exists outside of creation.

“Before the creation of the universe a certain time flowed by…a time which flows during

the existence of the universe and will continue to flow when the universe ceases to be.”36

To argue for the eternal existence of time, or at least time independent of creation,

Gassendi turned to Scripture and Pope Gelasius. He finds biblical support of infinite

expanse of time in:

Psalm 101:27-28, They shall be changed. But thou art always the selfsame, and thy years shall not fail. They shall be changed.

Exodus 3:14, I am who am, Who Is sent me to you. Revelation 1:8, Who is and who was and who is to come

Gassendi observed that many of the Church Fathers, including Augustine, Gregory

Nazianzus, and John Damascene did oppose the notion of infinite duration of time.

Gassendi claimed this puts Augustine (and others) at odds with Gelasius’s account of the

Council of Nicea. According to Gassendi, Gelasius defined eternity as infinite time, as

represented by “In the beginning was the Word.” The ‘was’ refers to time before

creation.37 What Gassendi fails to note is that Nicea and Gelasius are arguing against the

Arians, and their notion that the Son was not coeternal with the Father; Gelasius was not

discussing the nature of time.

36 Ibid., 1: 224; trans. Brush, 394.37 Ibid., 1: 228.

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Slide 11 Impact of Gassendi’s Understanding

of Space and Time

Gassendi was perceptive and even revolutionary in his understanding of void, space

and time. His arguments on these concepts form a bridge to his understanding of

incorporeal substances (God, angels, human intellect) and corporeal substances

(composed of atoms). God creates incorporeal and corporeal entities in space and time.

Thus in Gassendi there are three classes of entities (space and time, incorporeal

substances, and corporeal substances) each with its own ‘physics’ that can be investigated

both empirically and historically.

The similarity between space and time, and their independence from corporeal

bodies, is quite modern and informed Newton’s understanding of space. Of particular

importance was Gassendi’s separation of measurement from the thing measured. Thus

space and time could be measured by extended corporeal bodies, without implying that

space and time themselves must be corporeal bodies or the motion of corporeal bodies.

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Slide 12 Conclusions

The vacuum pump was invented shortly before Gassendi’s death, but there is no

indication that he had an opportunity to experiment with one. However, the next

generation of physicists, especially Boyle and Newton, were able to use the vacuum

pump to develop a physical understanding of the properties of a vacuum, much as Galileo

used the telescope to observe the planets. The scholastic objections to a void, like the

objections to a heliocentric solar system, passed into oblivion by the end of the

seventeenth century.

Many of the most prominent philosophers and scientists of the next generation

were deeply influenced by Gassendi. But his influence outstripped his fame and his

works. His intellectual model that embraced both empiricism and Christian humanism

was quickly eclipsed. Although used as a source for Epicureanism, for instance by

Thomas Jefferson, his method of painstaking analysis of ancient authors was quickly left

behind. The style of the Christian humanist was not suitable to the new style of the

scientist as it developed in the eighteenth century. Gassendi’s emphasis on the nuance of

words was replaced by an emphasis on the apparent certainty of mathematics as the best

way to describe nature.

Thank you for your time and attention this morning. Are there any questions or comments?

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