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The Leibniz-Clarke Correspondence is a collection of letters exchanged between Gottfried Leibniz and Samuel Clarke between 1715 and 1716, chiefly concerning the nature of space and time. Leibniz expounds his theories of the relativity of space and time, which he defends in his Théodicée (1710), whilst Clarke attempts to rebut these attacks and defend his beliefs in absolute space and time, as put forward by Sir Isaac Newton in his Principia (1687) and Opticks (1704). It was the Princess of Wales at the time, Caroline of Ansbach, who facilitated, co-ordinated and mediated the dispute, and it was through her that all the letters were sent. The Correspondence as we have it today begins with Leibniz's first letter, to which Clarke replied, and from there a further four documents from each man were written, ending only with Leibniz's death in the middle of November of 1716. The full exchange of ten papers was first published in 1717 in French and English, and has been republished more than a dozen times since.
Widely considered the most important work of 18th Century philosophy of physics, it is now seen as a crucial part of the long-running (and arguably continuous to this day) debate about whether space and time should be seen as absolute entities (against which things move) or relative (as mere relationships between objects and events). It inspired and informed the later works of, amongst others, Berkeley, Euler, Voltaire, Maclaurin, Kant, Mach and Einstein. The latter two developed (philosophically and mathematically) a seemingly complete system of space and time that is closer to Leibniz's view than Clarke's. Nonetheless, it would be a mistake to say that Leibniz "won", for there are a number of aspects of current physical theory about space and time that he would have shuddered at. As Alexander notes in his 1956 edition: "If, therefore, one insists on awarding points to Leibniz and Clarke, in the light of modern physics, it is perhaps best to call it a drawn contest."
Background
[edit]Absolute and Relative Space and Time
[edit]Classical ideas
[edit]The first absolute/relative debate began more than two thousand years before either Leibniz or Clarke had even been born. In Ancient Greece, at the very dawn of philosophy itself, a group who are now called the Atomists (particularly Leucippus (active c.450 BCE) and Democritus (active c.400 BCE) postulated that all matter was formed of "atoms", which were small, hard and indestructible. They taught that the atoms moved in a void, and that it was in the eternal fallings and collisions of them that creates everything in the world. By postulating this void that all atoms "fell" with relation to, they were perhaps the first explicit absolutists in history[1].
Aristotle (384 BCE–322 BCE), however, found a fatal flaw in their arguments[2]. If particles always "fell", then that suggested that they were going down. But "down" is only defined with reference to the surface of the Earth. And according to the Atomists, the Earth was created by falling and colliding particles; as such, there had to be direction implicit in the void. But, by definition, the void could not have this feature; it was literally nothing. As such, Aristotle abandoned their ideas, instead insisting that the Universe was made up of multiple layers, and was entirely filled with a plenum. Thus, all motion was relative to other matter, in a well-defined heavenly order[3].
The Copernican Revolution and Galileo
[edit]
The next important developments were made in the field of astronomy. Whilst there were undoubtedly exceptions[4], the received wisdom of the vast majority of the educated classes was that the Earth was stationary in the universe, and the Sun and other planets rotated around it. The crowning glory of this system was Ptolemy's geocentric system, as laid out in his Almagest[5], written in about 150, and which was considered the standard text of astronomy for roughly 1400 years[6]. For reasons that are not entirely clear, and probably will never be known for sure, this view also became the official orthodoxy of the Roman Catholic Church.
Nicolaus Copernicus (1473–1543), a Polish scholar, was the one to ultimately upset this dogma. Taking observations of the sky himself, and using the observations of others, he gradually became convinced that the Earth was not the center of the universe[7], and, spurred on by his friend Georg Joachim Rheticus, he finally decided to publish his masterwork, De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres).[8] It is said that he held the first copy of his great work on his deathbed.[9]
Galileo Galilei (1564–1642), a central figure in the Scientific revolution of the 17th century, became an enthusiastic defender of Copernicanism. Before the end of the 16th Century, Galileo has begun experimenting with inclined planes and pendula[10], and had come up with some remarkable results, including that all objects "fall" (or roll down the inclined plane) at the same rate, regardless of their mass or the steepness of the slope. This experimental approach was in direct contradiction to the Aristotelian view, that all scientific knowledge should be acquired by reason alone. At this time, Galileo also came to believe in the truth of the Copernican heliocentric hypothesis[11]. Around ten years later, Galileo heard about, acquired and substantially upgraded the then-new invention of the telescope. Pointing it at the night sky, Galileo made a series of extraordinary discoveries about the universe, including seeing the satellites of Jupiter for the first time. In 1610, he published Sidereus Nuncius (The Starry Messenger), proudly announcing to the world this discovery. As a result of these and other observations[12], Galileo became a firm and overt Copernican.
In 1613, Galileo wrote to his student Benedetto Castelli about some of the problems he saw in reconciling Copernicanism with some parts of the Bible[13]. Galileo was prescient, for in February 1616, the Sacred Congregation of the Index (a special Congregation set up to determine which books were contrary to Catholic doctrine) declared the Copernican system to be heretical, and placed De revolutionibus orbium coelestium on the Index Librorum Prohibitorum (list of prohibited books). Galileo, however, did not stop promoting the heliocentric theory, and so in 1616, Cardinal Robert Bellarmine, at an official audience in The Vatican, told him not to teach or defend Copernicus' ideas. This seems to have been something of a shock to him, as he spent the next few years concentrating on observations and developing an (ultimately erroneous[1]) theory of tides[10]. Whilst investigating tides, Galileo also waded into the absolute-relative debate. He said, with reference to the Law of the excluded middle, that either the Earth moved, or it did not. He believed that it did, and the compelling evidence for this was provided by the tides. His theory was wrong, but his conclusion (that the Earth moved) was correct. He was also probably the first person to unambiguously use the phrase "absolute motion" in a Newtonian sense[1]. His theory of tides, and the Principle of Relativity that flowered from his work, are undoubtedly relativistic in their analysis of motion; however, it is equally clear that he was working from an absolutist mindset throughout his work[1]. This was not the first, and would not be the last, time that philosophers of space and time had mistakenly used these incompatible ideas without realising it.
Galileo, emboldened by the election of his friend as Pope Urban VIII, decided to publish more Copernican advocacy, and in 1632 he released Dialogue Concerning the Two Chief World Systems - Ptolemic and Copernican[14]. The results were disastrous. In September 1632, he was summoned to Rome, arriving in January 1633. He was charged and convicted of heresy in June 1633, and forced to publicly renounce his beliefs in Copernicanism. News of his condemnation spread through the European intellectual classes like wildfire. His sentence was commuted to house arrest, but a broken Galileo never really got over this terrible shock. He spent the rest of his life at home, publishing only one more work[15] before his death in 1642.
Descartes
[edit]René Descartes (1596–1650) was the first person after the Copernican and Galilean affairs to attempt to construct a system of dynamics to make sense of the recent discoveries. His first effort, which was to be published in his work Le Monde (The World) in 1633[16], postulated a Copernican heliocentric Universe, and contained the first unambiguous formulation of the Law of Inertia, namely that bodies will continue in a straight line at a uniform speed unless acted on by some other body (it was not until Newton that this interaction was associated with a "force"). By postulating this Law, Descartes was intuitively and probably unconsciously accepting a form of absolute space.[1]
In 1633, when Descartes was about to publish, he heard of the Church's condemnation of Galileo for his support of Copernicanism. Fearful that the same thing may happen to him, and being the loyal Catholic that he was (as such accepting the Church's authority on these matters), he suppressed publication of Le Monde. Writing to his friend, the respected mathematician Marin Mersenne, in November 1633, he says:
I was so astonished that I almost decided to burn all of my papers or at least to let no one see them. For I could not imagine that he—an Italian and, as I understand, in the good graces of the Pope—could have been made a criminal for any other reason than that he tried, as he no doubt did, to establish that the earth moves.[17]
Descartes then spent the next ten years attempting to reconcile his natural philosophy with his faith. The result was Principia Philosophiae[18], published in 1644, and which Descartes thought struck the perfect balance between his religion and his philosophical inquiries. He defines motion formally as relative, to be compared only to the immediately contiguous bodies surrounding the object, and these bodies are themselves considered to be at rest. According to his theory, the Earth and the planets are carried around the Sun in a fluid[19], relative to which the Earth is at rest[1]; this brought Descartes into line with the Church's doctrines. Unfortunately, he also includes and re-affirms his beliefs in his earlier, absolutist, Laws of motion.
This blatant contradiction was ruthlessly exposed by Newton. In about 1670[20], he wrote a document now called De Gravitatione (after the first two words in Latin)[21] that very explicitly aimed at savaging Descartes. After explaining Descartes' doctrine in his own words, Newton writes "Now, just how confused and discordant with reason this doctrine is, not only the absurd consequences convince, but also Descartes himself, by contradicting himself, seems to acknowledge." He then proceeds to provide a number of examples that show the absurd and counter-factual nature of Descartes' system. Much of what he has to say, without most of the polemic venom, is repeated in the later, more famous exposition of Newtonian absolutism that is found in the Scholium in Newton's Principia.
The History of The Correspondence
[edit]The Newton-Leibniz Controversy
[edit]Newton: The Principia
[edit]Leibniz: The Théodicée
[edit]The Protagonists
[edit]Caroline
[edit]
Caroline of Ansbach (1683–1737) was born the Princess of Brandenburg-Ansbach, and spent her youth in Dresden and Berlin. She was often to be found in these years at the court of the Prussian Queen Charlotte.[22]. In 1704, she met Leibniz, who was a frequent visitor at the court, and they quickly developed a close and lasting friendship. They wrote frequently to one another, Leibniz often teaching Caroline his newest works, or bouncing ideas off of her for his next project. Caroline, a women of considerable intelligence, had a great interest in philosophy, and questioned Leibniz on some of the subtleties of his theories.
In 1701, the English Parliament had passed the Act of Settlement, which made Sophia of Hanover the heir to the throne, and that the English crown would thus pass into the House of Hanover. In September 1705, Caroline married Georg August, Sophia's grandson, and the electoral prince of Hanover. In 1714, when Queen Anne died (Sophia having died two months earlier), and Georg's father became King George I of Great Britain. The court of Hanover was immediately moved to London, and in October 1714, Caroline, who was now Princess of Wales, joined them. Leibniz, who had worked for the Hanoverians for forty years[23], was not relocated, and this was a cause of intense frustration for him.
Caroline met Samuel Clarke at the court in London, where he was commonly found[24] mixing with the other great minds of the day who gathered there. They became friendly—Clarke somewhat taking over the role that Leibniz had played as philosophical mentor—[24]and Caroline wrote to Leibniz in November 1715, saying that she was going to ask him to translate Leibniz's Théodicée into English. Leibniz, seemingly seeing Caroline fall into the hands of his intellectual enemies, the Newtonians, wrote a stinging reply, condemning the English philosophers. Caroline, sensing that this might be the chance to engage two of the finest minds in Europe in a dialogue, showed the letter to Clarke, who drafted a reply; these two papers are now the first two in the Correspondence. From then on, all letters were sent through Caroline, who carefully preserved all the responses, so that after Leibniz's death they could be assembled into what we now call The Leibniz-Clarke Correspondence.
Leibniz
[edit]Clarke and Newton
[edit]The Correspondence
[edit]Initial contact and the first papers
[edit]The Correspondence beings in earnest: the second papers
[edit]Leibniz goes on the attack: the third papers
[edit]Clarke rebuts, with examples: the fourth papers
[edit]The parting shots, and no clear winner:the fifth papers
[edit]Overview: The Leibniz-Clarke Correspondence
[edit]| Paper | Date | Length | Outline of content |
| Leibniz’s first paper | 1715 | 1 | A |
| Clarke’s first reply | 1715 | 2 | B |
| Leibniz’s second paper | 1715 | 3 | C |
| Clarke’s second reply | 1715 | 4 | D |
| Leibniz’s third paper | 1715 | 5 | E |
| Clarke’s third reply | 1716 | 6 | F |
| Leibniz’s fourth paper | 1716 | 7 | G |
| Clarke’s fourth reply | 1716 | 8 | H |
| Leibniz’s fifth paper | 1716 | 9 | I |
| Clarke’s fifth reply | 1716 | 10 | J |
Notes
[edit]- ^ a b c d e f Barbour, J.B. (1989). Absolute or Relative Motion? Volume 1: The Discovery of Dynamics. Cambridge University Press. ISBN 052132467X.
- ^ See Aristotle's Physics Books I-IV (which can be found in full, translated by R.P. Hardie and R.K. Gaye, here) and De Caelo (On the Heavens, which can be found in full, translated by J.L. Stocks, here; both URLs accessed on 28 April 2006)
- ^ Capek, M. (1976). The Concepts of Space and Time. Reidel. ISBN 9027703558.
- ^ See Nicolaus Copernicus#The Copernican heliocentric system for a discussion of pre-Copernican heliocentric theories of astronomy
- ^ Toomer, G.J. (1998). Ptolemy's Almagest. Princeton University Press. ISBN 0691002606.
- ^ "Ptolemy biography". Retrieved 2006-05-20.
- ^ Some time between 1509 and 1512, Copernicus wrote a short essay now known as the Commentariolus (which can be found in full here), in which he can be seen to be beginning to formulate what would later become his heliocentric theory. He moves away from a geocentric picture, but does not provide any mathematical or observational data for his hypotheses
- ^ Scanned images of every page of De revolutionibus orbium coelestium, in Latin, can be found here. It can also be found, in full, translated into English by Edward Rosen, here
- ^ Sheila Rabin. "Nicolaus Copernicus". Retrieved 2006-05-20.
- ^ a b "Galileo biography". Retrieved 2006-05-20.
- ^ Galileo admitted his "accepting of the Copernican position several years ago", in a letter to Kepler of 1697. The relevant section of the letter can be found here
- ^ "Galileo Galilei". Retrieved 2006-05-20.
- ^ The entire text of Galileo's letter to Castelli can be found, translated into English, here
- ^ The text of Dialogue Concerning the Two Chief World Systems - Ptolemic and Copernican can be found, in full, translated by Stillman Drake, here
- ^ The one last book Galileo wrote was Dialogues Concerning the Two New Sciences, which mostly describes and mathematically formalises his earlier experimental results. It can be found, in full, translated by Henry Crew and Alfonso de Salvo, here
- ^ It was eventually published posthumously, in 1644
- ^ Stoothoff, Robert (1991). The Philosophical Writings of Descartes: The Correspondence. Cambridge University Press. ISBN 0521423503.
- ^ The sections of Principia Philosophiae that are relevant to the Cartesian system of motion can be found here (URL accessed on 20 May, 2006)
- ^ The Cartesian system did not contain the notion of a vacuum. Descartes defined place to be identical to extension of matter, and as such the very concept of "a place with nothing in it" is a logical impossibility
- ^ The exact dating of De Gravitatione is difficult to determine, and is a matter of considerable scholarly debate. For more information, see the discussion in A.R.Hall & M.B. Hall (1962). Unpublished Scientific Papers of Isaac Newton. Cambridge University Press. ISBN 0521294363.
- ^ The full text of De Gravitatione, translated by W.B. Allen, can be found here
- ^ Carr, H.W. (1926). Leibniz (1960 ed.). Dover.
- ^ "Biography of Caroline of Ansbach". Retrieved 2006-04-27.
- ^ a b Alexander, H.G. (1956). The Leibniz-Clarke Correspondence. Manchester University Press. ISBN 0719006694.