##eal stem cell transplants ” ( jurkunas, 2011 ). sharon kleyne notes that, no physiologic variable correlates exactly with dry eye symptoms, although most measurable variables correlate to some degree. instead, she explains, physicians look for a series of symptoms. the presence of one or more symptom could indicate a dry eye condition ( korb, 2000 ). the most common dry eye symptoms include eye irritation, a feeling of dryness in the eyes ; itching, burning and grainy or scratchy eyes ; increased eye allergies, and blurred vision ( especially late in the day ). symptoms such as fatigue, headache, muscle aches and an elevated stress level may not even directly involve the eyes ( mathers, 2005 ). this symptom - based definition works reasonably well, according to mrs. kleyne. the degree and duration of symptoms are critical since a large percentage of the adult population complains of at least mild dry eye symptoms at any given time. this includes 50 % of adult females and a significant percentage of computer users and contact lens patients ( mathers, 2005 ). in addition to symptoms, most ( but not all ) dry eye patients have at least one physiologic parameter outside the range of normal. typically, tear production has decreased, tear film volume is low, tear film evaporation is high, and / or tear film osmolarity is elevated ( mathers, 2004 ). in addition, tears produced in dry eyes contain elevated levels of substances ( metalloproteases and other proteinaceous compounds ) that increase surface inflammation ( barton, 1995 ). © 2012 bio - logic aqua research for the original version on prweb visit : http : / / www. prweb. com / releases / prweb2012 / 4 / prweb9381612. htm


a canticle ( from the latin canticulum, a diminutive of canticum, song ) is a hymn ( strictly excluding the psalms ) taken from the bible. the term is often expanded to include ancient non - biblical hymns such as the te deum and certain psalms used liturgically. these three canticles are sometimes referred to as the " evangelical canticles ", as they are taken from the gospel of st luke. they are sung every day ( unlike those from the old testament which, as is, shown above, are only of weekly occurrence ). they are placed not amongst the psalms ( as are the seven from the old testament ), but separated from them by the chapter, the hymn, the versicle and response, and thus come immediately before the prayer ( or before the preces, if these are to be said ). they are thus given an importance and distinction elevating them into great prominence, which is further heightened by the rubric which requires the singers and congregations to stand while they are being sung ( in honour of the mystery of the incarnation, to which they refer ). further, while the " magnificat " is being sung at solemn vespers, the altar is incensed as at solemn mass. all three canticles are in use in the greek and anglican churches. in the breviary the above - named ten canticles are provided with antiphons and are sung in the same eight psalm - tones and in the same alternating manner as the psalms. to make the seven taken from the old testament suitable for this manner of singing, nos. 2 - 7 sometimes divide a verse of the bible into two verses, thus increasing the number of breviary verses. no. 1, however, goes much farther than this. it uses only a portion of the long canticle in daniel, and condenses, expands, omits, and interverts verses and portions of verses. in the breviary the canticle begins with verse 57, and ends with verse 56 ( dan., iii ) ; and the penultimate verse is clearly an interpolation, " benedicamus patrem, et filium... ". in addition to their breviary use some of the canticles are used in other connections in the liturgy ; e. g. the " nunc dimittis " as a tract at the mass of the feast of the purification ( when 2 february comes after septuagesima ) ;


of the canticles are used in other connections in the liturgy ; e. g. the " nunc dimittis " as a tract at the mass of the feast of the purification ( when 2 february comes after septuagesima ) ; the " benedictus " in the burial of the dead and in various processions. the use of the " benedictus " and the " benedicite " at the old gallican mass is interestingly described by duchene ( christian worship : its origin and evolution, london, 1903, 191 - 196 ). in the office of the greek church the canticles numbered 1, 3, 5, 6, 7, 8, 9 are used at lauds, but are not assigned to the same days as in the roman breviary. two others ( isaiah 26 : 9 - 20, and jonah 2 : 2 - 9 ) are added for friday and saturday respectively. the ten canticles so far mentioned do not exhaust the portions of sacred scripture which are styled " canticles ". there are, so example, those of deborah and barac, judith, the " canticle of canticles " ; and many psalms ( e. g. xvii, 1, " this canticle " ; xxxviii, 1, " canticle of david " ; xliv, 1, " canticle for the beloved " ; and the first verse of pss. 1xiv, 1xv, 1xvi, 1xvii, etc ). in the first verse of some psalms the phrase psalmus cantici ( the psalm of a canticle ) is found, and in others the phrase canticum psalmi ( a canticle of a psalm ). cardinal bona thinks that psalmus cantici indicated that the voice was to precede the instrumental accompaniment, while canticum psalmi indicated an instrumental prelude to the voice. this distinction follows from his view of a canticle as an unaccompanied vocal song, and of a psalm as an accompanied vocal song. it is not easy to distinguish satisfactorily the meanings of psalm, hymn, canticle, as referred to by st. paul in two places. canticum appears to be generic - a song, whether sacred or secular ; and there is reason to think that his admonition did not contemplate religious assemblies of the christians, but their social gatherings. in these the christians were to


. canticum appears to be generic - a song, whether sacred or secular ; and there is reason to think that his admonition did not contemplate religious assemblies of the christians, but their social gatherings. in these the christians were to sing " spiritual songs ", and not the profane or lascivious songs common amongst the pagans. these spiritual songs were not exactly psalms or hymns. the hymn may then be defined as a metrical or rhythmical praise of god ; and the psalm, accompanied sacred song or canticle, either taken from the psalms or from some less authoritative source ( st. augustine declaring that a canticle may be without a psalm but not a psalm without a canticle ). in addition to the ten canticles enumerated above the roman breviary places in its index, under the heading " cantica ", the " te deum " ( at the end of matins for sundays and festivals, but there styled " hymnus ss. ambrosii et augustini " ) and the : " quicumque vult salvus esse " ( sundays at prime, but there styled " symbolum s. athanasii ", the " creed of st. athanasius " ). to these are sometimes added by writers the " gloria in excelsis ", the " trisagion ", and the " gloria patri " ( the lesser doxology ). in the " psalter and canticles pointed for chanting " ( philadelphia, 1901 ), for the use of the evangelical lutheran congregations, occurs a " table of canticles " embracing nos. 1, 3, 8, 9, 10, besides certain psalms, and the " te deum " and " venite " ( ps. xicv, used at the beginning of matins in the roman breviary ). the word canticles is thus seen to be somewhat elastic in its comprehension. on the one hand, while it is used in the common parlance in the church of england to cover several of the enumerated canticles, the prayer book applies it only to the " benedicite ", while in its calendar the word canticles is applied to what is commonly known as the " song of solomon " ( the catholic " canticle of canticles ", vulgate, " canticum canticorum " ). the nine canticles are as follows : originally, these cantic


when a child who has been hospitalized with a serious infection is sent home to complete a prolonged course of antibiotics, they can receive their medicine in two ways — by mouth, or intravenously, via a peripherally inserted central catheter ( picc ) line. though picc lines can be scary for pediatric patients, and require caregivers to be trained in their use and care, many doctors often prefer them to oral medicines for long - term antibiotic treatments. one chop researcher, ron keren, md, mph, director of the center for pediatric clinical effectiveness, was recently awarded nearly two million dollars from the patient - centered outcomes research institute ( pcori ) to lead a study examining whether oral antibiotics are as effective at treating infection over an extended period as picc lines. “ these two antibiotic treatment options have major implications for the overall experience of the child, families and caregivers, but there is a lack of real - world evidence on their benefits and drawbacks to help clinicians and patient families make an informed choice, ” said dr. keren. a type of intravenous ( iv ) catheter, a picc line is a long, flexible tube that is inserted in a peripheral vein, often in the arm or neck, and advanced until its tip rests near the heart. because they tap directly into the circulatory system, picc lines offer maximum drug delivery. unlike regular iv catheters, picc lines can stay in the body for weeks to months, but they require regular maintenance. picc lines must be flushed daily, their dressings have to be inspected and changed, and patients with picc lines must avoid getting them wet or dirty — a tall order for some active pediatric patients. in addition, a variety of equipment is required to use and maintain picc lines, including infusion pumps and portable iv poles. picc lines do have some risks. they can clot, break, or become dislodged. and because they sit in large blood vessels directly above the heart, any bacteria that are inadvertently introduced into the catheter go directly to the heart and are pumped throughout the body, which can lead to a dangerous infection called sepsis. oral antibiotics, on the other hand, are much easier for patients to take and caregivers to manage. however, because oral medications must pass through the digestive system, to have the same efficacy as iv medications oral antibiotics must have high “ bioavailability ” — the percentage of the drug that reaches the blood.


when the last oil well runs dry just as certain as death and taxes is the knowledge that we shall one day be forced to learn to live without oil. exactly when that day will dawn nobody knows, but people in middle age today can probably expect to be here for it. long before it arrives we shall have had to commit ourselves to one or more of several possible energy futures. and the momentous decisions we take in the next few years will determine whether our heirs thank or curse us for the energy choices we bequeath to them. there will always be some oil somewhere, but it may soon cost too much to extract and burn it. it may be too technically difficult, too expensive compared with other fuels, or too polluting. an article in scientific american in march 1998 by dr colin campbell and jean laherrere concluded : " the world is not running out of oil - at least not yet. " what our society does face, and soon, is the end of the abundant and cheap oil on which all industrial nations depend. " they suggested there were perhaps 1, 000 billion barrels of conventional oil still to be produced, though the us geological survey ' s world petroleum assessment 2000 put the figure at about 3, 000 billion barrels. too good to burn the world is now producing about 75 million barrels per day ( bpd ). conservative ( for which read pessimistic ) analysts say global oil production from all possible sources, including shale, bitumen and deep - water wells, will peak at around 2015 at about 90 million bpd, allowing a fairly modest increase in consumption. peaking is at hand, not years away... if i ' m right, the unforeseen consequences are devastating matthew simmons, former us government adviser on campbell and laherrere ' s downbeat estimate, that should last about 30 years at 90 million bpd, so drastic change could be necessary soon after 2030. and it would be drastic : 90 % of the world ' s transport depends on oil, for a start. most of the chemical and plastic trappings of life which we scarcely notice - furniture, pharmaceuticals, communications - need oil as a feedstock. the real pessimists want us to stop using oil for transport immediately and keep it for irreplaceable purposes like these. in may 2003 the association for the study of peak oil and gas ( aspo ), founded by colin campbell, held a workshop on oil depletion in paris. one of the speakers was an investment banker, matthew simmons


##able purposes like these. in may 2003 the association for the study of peak oil and gas ( aspo ), founded by colin campbell, held a workshop on oil depletion in paris. one of the speakers was an investment banker, matthew simmons, a former adviser to president bush ' s administration. from the wilderness publications reported him as saying : " any serious analysis now shows solid evidence that the non - fsu [ former soviet union ], non - opec [ organisation of petroleum exporting countries ] oil has certainly petered out and has probably peaked... no cheap oil, no cheap food " i think basically that peaking of oil will never be accurately predicted until after the fact. but the event will occur, and my analysis is... that peaking is at hand, not years away. " if i ' m right, the unforeseen consequences are devastating... if the world ' s oil supply does peak, the world ' s issues start to look very different. " there really aren ' t any good energy solutions for bridges, to buy some time, from oil and gas to the alternatives. the only alternative right now is to shrink our economies. " planning pays off aspo suggests the key date is not when the oil runs out, but when production peaks, meaning supplies decline. it believes the peak may come by about 2010. fundamental change may be closing on us fast. and even if the oil is there, we may do better to leave it untouched. many scientists are arguing for cuts in emissions of the main greenhouse gas we produce, carbon dioxide, by at least 60 % by mid - century, to try to avoid runaway climate change. that would mean burning far less oil than today, not looking for more. there are other forms of energy, and many are falling fast in price and will soon compete with oil on cost, if not for convenience. so there is every reason to plan for the post - oil age. does it have to be devastating? different, yes - but our forebears lived without oil and thought themselves none the worse. we shall have to do the same, so we might as well make the best of it. and the best might even be an improvement on today. who holds the world ' s oil - and how long will it last? at a glance link :


water and sediment testing epa is currently collecting and analyzing water and sediment samples to help states and other federal agencies understand the immediate and long - term impacts of oil contamination along the gulf coast. the results and the interpretation of all data collected by epa will be posted to www. epa. gov / bpspill. water and sediment samples are being taken prior to oil reaching the area to determine water quality and sediment conditions that are typical of selected bays and beaches in louisiana, mississippi, alabama, and the florida panhandle. this data will be used to supplement existing data generated from previous water quality surveys conducted by states, epa, and others. water sampling will continue once the oil reaches the shore ; periodic samples will be collected to document water quality changes. epa will make data publicly available as quickly as possible. other state and federal agencies make beach closure and seafood harvesting and consumption determinations, but the data generated by epa will assist in their evaluations. why is epa sampling and monitoring the water? epa is tracking the prevalence of potentially harmful chemicals in the water as a result of this spill to determine the level of risk posed to fish and other wildlife. while these chemicals can impact ecosystems, drinking water supplies are not expected to be affected. the oil itself can cause direct effects on fish and wildlife, for example when it coats the feathers of waterfowl and other types of birds. in addition, other chemical compounds can have detrimental effects. monitoring information allows epa to estimate the amount of these compounds that may reach ecological systems. when combined with available information on the toxicity of these compounds, epa scientists can estimate the likely magnitude of effects on fish, wildlife, and human health. to learn more :


all - metal hip implants can damage soft tissue : fda ( reuters ) - metal - on - metal hip implants can cause soft - tissue damage and pain, which could lead to further surgery to replace the implant, the u. s. health regulator said, following several recalls of the artificial hip parts. all - metal hip implants were developed to be more durable than traditional implants but have become a major cause of concern following several safety issues and user discomforts. the traditional implants combine a ceramic or metal ball with a plastic socket. the u. s. food and drug administration said all - metal implants can shed metal where two components connect, such as the ball and the cup that slide against each other during walking or running. such release of metal will cause wear and tear of the implant and can damage bone and soft tissue surrounding the implant. the agency said surgeons should select a metal - on - metal hip implant for their patient only after determining that its benefits outweigh that of an alternative hip system. johnson & johnson, the biggest manufacturer of all - metal devices, recalled its asr hip implant in 2010 following safety problems. smith & nephew withdrew a component of one of its all - metal artificial hip systems last june, following higher level of patient problems with the device. stryker corp begun recalling some components of its implant in july due to risks associated with corrosion. other hip implant makers include zimmer holdings inc and wright medical group. the regulator, however, added that it does not have enough data to specify the concentration of metal ions in a patient ' s body or blood necessary to produce adverse effects. the reaction seemed to be specific to individual patients, the fda said on its website. ( reporting by esha dey in bangalore ; editing by don sebastian ) - tweet this - share this - digg this


last friday, the hill ’ s congress blog highlighted the innovative ways governments, ngo ’ s and the private sector are using to aid for global health. programs like the global alliance for vaccines and immunization ( gavi ) and the global fund to fight aids, tb and malaria are not only ensuring that health interventions are getting to the people that need them most, they are helping to promote market growth and drive down prices. here ’ s an excerpt on public - private partnerships from the blog : “ millions of lives are saved today in developing countries because of bold, innovative financing arrangements over last 10 years. these financing mechanisms are good examples of private sector partnership with public sector for common good. these financing initiatives have pooled large public sector funding with private sector resources, thus allowing tax payers funds to have much larger impact than would otherwise be possible. some of the examples are given below. ” usaid ’ s neglected tropical disease ( ntd ) program is one such collaboration. in a press statement released last fall, dr. ariel pablos - mendez, assistant administrator for usaid ’ s global health bureau, states : “ to date, usaid ’ s ntd program is the largest public - private partnership collaboration in our 50 year history. over the past six years, usaid has leveraged over $ 3 billion in donated medicines reflecting one of the most cost effective public health programs. because of this support, we are beginning to document control and elimination of these diseases in our focus countries and we are on track to meet the 2020 goals. ” you can also read about how sabin in helping countries create sustainable access to immunization financing here.


stat : of all infertile women, an estimated 15 percent are infertile because of pid. what is it exactly? " pelvic inflammatory disease " is shorthand for any serious, non - specific bacterial infection of the reproductive organs that are housed in the pelvis : the uterus, uterine lining, fallopian tubes, and / or ovaries. these infections usually start in the vagina and, when left untreated, can progressively infect other reproductive organs. 20 % of pid cases are found in teens, who often are afraid or unable to get reproductive health care. pid can result in permanent infertility and chronic pain. about how many people have it? about one million cases of pid are reported in the united states annually. how is it spread? in most cases, other sexually transmitted diseases and infections such as gonorrhea and chlamydia are at the root of pid, especially when they are left untreated. some cases of pid are due to infections with more than one type of bacteria. what are its symptoms? • painful periods that may last longer than previous cycles • unusual vaginal discharge • spotting or cramping between periods • pain or cramping curing urination, or blood in the urine • lower back or abdominal pain • nausea or vomiting • pain during vaginal intercourse how is it diagnosed? pid is often difficult to diagnose, and it is widely thought that millions of cases each year go undiagnosed. to diagnose pid, you will need a pelvic exam which includes a pap smear, and a possible laparoscopy ( a diagnostic microsurgical procedure that can usually be done in an office visit ) in order for your doctor or clinician to take a close look at your reproductive system. it is also imperative that you tell your doctor or clinician if you have been sexually active with a partner and what your sexual history has been. is it treatable? in some cases, antibiotics, bed rest, and sexual celibacy are prescribed. in other cases, surgery may be required, including the possible removal of some reproductive organs. is it curable? in some cases, but it can recur even once treated if the person becomes reinfected. can it effect fertility? pid can lead to permanent sterility or ectopic pregnancy. can it cause death? almost any bacterial infection, if it becomes serious enough or affects enough of the body


ever wonder what would happen if every single adult in the u. s. took a few hours each month to support a program that supports the well - being of children? perhaps you would choose to advocate for a child in an unstable environment ; or a child in poor health ; or one who is struggling with their academics ; or one who facing a bully? what kind of impact would that make on the future of our country? i recently came across some information about national make a difference in children month ; a grassroots call to action sponsored by long - time child advocate, kim ratz. the intention of this annual observance is to bring awareness on how our actions can make a positive difference to a child. ms. ratz outlines 4 key actions we can take to have a direct impact on the life of a child on her website : 1. pick one ( or more ) event or activity to do with a child … that will make some kind of positive difference or impact on that child. need ideas? read 100 + ways to make a difference to children. 2. support an organization that serves children … it could be your local community ed. or schools, ymca, boy or girl scouts, place of worship, park and recreation or any other organization that serves kids. 3. tell your policy makers to support initiatives that are good for kids … like your school board, city council, county commissioners, state legislators & congressional delegation ; summer is generally a more relaxed time to communicate with them. share your own story about making a difference to children … and why it ’ s important to support programs for children … 4. tell other people about this campaign … like your neighbors, relatives, friends, people at work, worship, school or play. here are some more ideas from early childhood news and resources on how you can make a difference to a child this month : - volunteer at a local center that helps teen or single mothers ( or fathers ) - volunteer with your local elementary school - help at a soup kitchen for needy families - help at church with sunday school, vbs or another faith - based program - locate a service in your area that assists homeless children with school supplies, medical care or social - emotional development - volunteer to read for kids at your local library - teach classes at a local rec center or community center : arts, crafts, reading, sports, asl, music, etc. - offer your time at the foundation for the blind ( they often run children ’ s classes ) - find a local farm that hosts classes for special needs kiddos


please read how you can help keep the encyclopedia free absolute and relational theories of space and motion since antiquity, natural philosophers have struggled to comprehend the nature of three tightly interconnected concepts : space, time, and motion. a proper understanding of motion, in particular, has been seen to be crucial for deciding questions about the natures of space and time, and their interconnections. since the time of newton and leibniz, philosophers ’ struggles to comprehend these concepts have often appeared to take the form of a dispute between absolute conceptions of space, time and motion, and relational conceptions. this article guides the reader through some of the history of these philosophical struggles. rather than taking sides in the ( alleged ) ongoing debates, or reproducing the standard dialectic recounted in most introductory texts, we have chosen to scrutinize carefully the history of the thinking of the canonical participants in these debates — principally descartes, newton, leibniz, mach and einstein. readers interested in following up either the historical questions or current debates about the natures of space, time and motion will find ample links and references scattered through the discussion and in the other internet resources section below. - 1. introduction - 2. aristotle - 3. descartes - 4. newton - 5. absolute space in the twentieth century - 6. leibniz - 7. ‘ not - newton ’ versus ‘ be - leibniz ’ - 8. mach and later machians - 9. relativity and motion - 10. conclusion - other internet resources - related entries things change. a platitude perhaps, but still a crucial feature of the world, and one which causes many philosophical perplexities — see for instance the entry on zeno ' s paradoxes. for aristotle, motion ( he would have called it ‘ locomotion ’ ) was just one kind of change, like generation, growth, decay, fabrication and so on. the atomists held on the contrary that all change was in reality the motion of atoms into new configurations, an idea that was not to begin to realize its full potential until the seventeenth century, particularly in the work of descartes. ( of course, modern physics seems to show that the physical state of a system goes well beyond the geometrical configuration of bodies. fields, while determined by the states of bodies, are not themselves configurations of bodies if interpreted literally, and in quantum mechanics bodies have ‘ internal states ' such as particle spin. ) while not all changes seem to be merely the ( loco )


bodies. fields, while determined by the states of bodies, are not themselves configurations of bodies if interpreted literally, and in quantum mechanics bodies have ‘ internal states ' such as particle spin. ) while not all changes seem to be merely the ( loco ) motions of bodies in physical space. yet since antiquity, in the western tradition, this kind of motion has been absolutely central to the understanding of change. and since motion is a crucial concept in physical theories, one is forced to address the question of what exactly it is. the question might seem trivial, for surely what is usually meant by saying that something is moving is to say that it is moving relative to something, often tacitly understood between speakers. for instance : the car is moving at 60mph ( relative to the road and things along it ), the plane is flying ( relative ) to london, the rocket is lifting off ( the ground ), or the passenger is moving ( to the front of the speeding train ). typically the relative reference body is either the surroundings of the speakers, or the earth, but this is not always the case. for instance, it seems to make sense to ask whether the earth rotates about its axis west - east diurnally or whether it is instead the heavens that rotate east - west ; but if all motions are to be reckoned relative to the earth, then its rotation seems impossible. but if the earth does not offer a unique frame of reference for the description of motion, then we may wonder whether any arbitrary object can be used for the definition of motions : are all such motions on a par, none privileged over any other? it is unclear whether anyone has really, consistently espoused this view : aristotle, perhaps, in the metaphysics ; descartes and leibniz are often thought to have but, as we ' ll see, those claims are suspect ; possibly huygens, though his remarks remain cryptic ; mach at some moments perhaps. if this view were correct, then the question of whether the earth or heavens rotate would be meaningless, merely different but equivalent expressions of the facts. but suppose, like aristotle, you take ordinary language accurately to reflect the structure of the world, then you could recognize systematic everyday uses of ‘ up ’ and ‘ down ’ that require some privileged standards — uses that treat things closer to a point at the center of the earth as more ‘ down ’ and motions towards that point as ‘ downwards '. of course we would likely explain this usage in terms of the fact that we and our language evolved


standards — uses that treat things closer to a point at the center of the earth as more ‘ down ’ and motions towards that point as ‘ downwards '. of course we would likely explain this usage in terms of the fact that we and our language evolved in a very noticeable gravitational field directed towards the center of the earth, but for aristotle, as we shall see, this usage helped identify an important structural feature of the universe, which itself was required for the explanation of weight. now a further question arises : how should a structure, such as a preferred point in the universe, which privileges certain motions, be understood? what makes that point privileged? one might expect that aristotle simply identified it with the center of the earth, and so relative to that particular body ; but in fact he did not adopt that tacit convention as fundamental, for he thought it possible for the earth to move from the ‘ down ’ point. thus the question arises ( although aristotle does not address it explicitly ) of whether the preferred point is somewhere picked out in some other way by the bodies in the universe — the center of the heavens perhaps? or is it picked out quite independently of the arrangements of matter? the issues that arise in this simple theory help frame the debates between later physicists and philosophers concerning the nature of motion ; in particular, we will focus on the theories of descartes, newton, leibniz, mach and einstein, and their interpretations. but similar issues circulate through the different contexts : is there any kind of privileged sense of motion, a sense in which things can be said to move or not, not just relative to this or that reference body, but ‘ truly ’? if so, can this true motion be analyzed in terms of motions relative to other bodies — to some special body, or to the entire universe perhaps? ( and in relativity, in which distances, times and measures of relative motion are frame - dependent, what relations are relevant? ) if not, then how is the privileged kind of motion to be understood, as relative to space itself — something physical but non - material — perhaps? or can some kinds of motion be best understood as not being spatial changes — changes of relative location or of place — at all? to see that the problem of the interpretation of spatiotemporal quantities as absolute or relative is endemic to almost any kind of mechanics one can imagine, we can look to one of the simplest theories — aristotle ' s account of natural motion ( e. g., on the heavens i. 2 ). according


center of the stars. it would be to push aristotle ' s writings too hard to suggest that he was consciously wrestling with the issue of whether mechanics required absolute or relative quantities of motion, but what is clear is that these questions arise in his physics and his remarks impinge on them. his theory also gives a simple model of how these questions arise : a physical theory of motion will say that ‘ under such - and - such circumstances, motion of so - and - so a kind will occur ’ — and the question of whether that kind of motion makes sense in terms of the relations between bodies alone arises automatically. aristotle may not have recognized the question explicitly, but we see it as one issue in the background of his discussion of the center. the issues are, however, far more explicit in descartes ' physics ; and since the form of his theory is different the ‘ kinds of motion ’ in question are quite different — as they change with all the different theories that we discuss. for descartes argued in his 1644 principles of philosophy ( see book ii ) that the essence of matter was extension ( i. e., size and shape ) because any other attribute of bodies could be imagined away without imagining away matter itself. but he also held that extension constitutes the nature of space, hence he concluded that space and matter were one and the same thing. an immediate consequence of the identification is the impossibility of the vacuum ; if every region of space is a region of matter, then there can be no space without matter. thus descartes ' universe is ‘ hydrodynamical ’ — completely full of mobile matter of in different sized pieces in motion, rather like a bucket full of water and lumps of ice of different sizes, which has been stirred around. since fundamentally the pieces of matter are nothing but extension, the universe is in fact nothing but a system of geometric bodies in motion without any gaps. ( descartes held that all other properties arise from the configurations and motions of such bodies — from geometric complexes. see garber 1992 for a comprehensive study. ) the identification of space and matter poses a puzzle about motion : if the space that a body occupies literally is the matter of the body, then when the body — i. e., the matter — moves, so does the space that it occupies. thus it doesn ' t change place, which is should be to say that it doesn ' t move after all! descartes resolved this difficulty by taking all motion to be the motion of bodies relative to one another,


the space that it occupies. thus it doesn ' t change place, which is should be to say that it doesn ' t move after all! descartes resolved this difficulty by taking all motion to be the motion of bodies relative to one another, not a literal change of space. now, a body has as many relative motions as there are bodies but it does not follow that all are equally significant. indeed, descartes uses several different concepts of relational motion. first there is ‘ change of place ’, which is nothing but motion relative to this or that arbitrary reference body ( ii. 13 ). in this sense no motion of a body is privileged, since the speed, direction, and even curve of a trajectory depends on the reference body, and none is singled out. next, he discusses motion in ‘ the ordinary sense ’ ( ii. 24 ). this is often conflated with mere change of arbitrary place, but it in fact differs because according to the rules of ordinary speech one properly attributes motion only to bodies whose motion is caused by some action, not to any relative motion. ( for instance, a person sitting on a speeding boat is ordinarily said to be at rest, since ‘ he feels no action in himself ’. ) finally, he defined motion ‘ properly speaking ’ ( ii. 25 ) to be a body ' s motion relative to the matter contiguously surrounding it, which the impossibility of a vacuum guarantees to exist. ( descartes ’ definition is complicated by the fact that he modifies this technical concept to make it conform more closely to the pre - theoretical sense of ‘ motion ’ ; however, in our discussion transference is all that matters, so we will ignore those complications. ) since a body can only be touching one set of surroundings, descartes ( dubiously ) argued that this standard of motion was unique. what we see here is that descartes, despite holding motion to be the motion of bodies relative to one another, also held there to be a privileged sense of motion ; in a terminology sometimes employed by writers of the period, he held there to be a sense of ‘ true motion ’, over and above the merely relative motions. equivalently, we can say that descartes took motion ( ‘ properly speaking ’ ) to be a complete predicate : that is, moves - properly - speaking is a one - place predicate. ( in contrast, moves - relative - to is a two - place predicate. ) and note that the predicate is complete


) to be a complete predicate : that is, moves - properly - speaking is a one - place predicate. ( in contrast, moves - relative - to is a two - place predicate. ) and note that the predicate is complete despite the fact that it is analyzed in terms of relative motion. ( formally, let contiguous - surroundings be a function from bodies to their contiguous surroundings, then x moves - properly - speaking is analyzed as x moves - relative - to contiguous - surroundings ( x ). ) this example illustrates why it is crucial to keep two questions distinct : on the one hand, is motion to be understood in terms of relations between bodies or by invoking something additional, something absolute ; on the other hand, are all relative motions equally significant, or is there some ‘ true ’, privileged notion of motion? descartes ' views show that eschewing absolute motion is logically compatible with accepting true motion ; which is of course not to say that his definitions of motion are themselves tenable. there is an interpretational tradition which holds that descartes only took the first, ‘ ordinary ’ sense of motion seriously, and introduced the second notion to avoid conflict with the catholic church. such conflict was a real concern, since the censure of galileo ' s copernicanism took place only 11 years before publication of the principles, and had in fact dissuaded descartes from publishing an earlier work, the world. indeed, in the principles ( iii. 28 ) he is at pains to explain how ‘ properly speaking ’ the earth does not move, because it is swept around the sun in a giant vortex of matter — the earth does not move relative to its surroundings in the vortex. the difficulty with the reading, aside from the imputation of cowardice to the old soldier, is that it makes nonsense of descartes ' mechanics, a theory of collisions. for instance, according to his laws of collision if two equal bodies strike each other at equal and opposite velocities then they will bounce off at equal and opposite velocities ( rule i ). on the other hand, if the very same bodies approach each other with the very same relative speed, but at different speeds then they will move off together in the direction of the faster one ( rule iii ). but if the operative meaning of motion in the rules is the ordinary sense, then these two situations are just the same situation, differing only in the choice of reference frame, and so could not have different outcomes — bouncing


faster one ( rule iii ). but if the operative meaning of motion in the rules is the ordinary sense, then these two situations are just the same situation, differing only in the choice of reference frame, and so could not have different outcomes — bouncing apart versus moving off together. it seems inconceivable that descartes could have been confused in such a trivial way. ( additionally, as pooley 2002 points out, just after he claims that the earth is at rest ‘ properly speaking ’, descartes argues that the earth is stationary in the ordinary sense, because common practice is to determine the positions of the stars relative to the earth. descartes simply didn ' t need motion properly speaking to avoid religious conflict, which again suggests that it has some other significance in his system of thought. ) thus garber ( 1992, chapter 6 - 8 ) proposes that descartes actually took the unequivocal notion of motion properly speaking to be the correct sense of motion in mechanics. then rule i covers the case in which the two bodies have equal and opposite motions relative to their contiguous surroundings, while rule vi covers the case in which the bodies have different motions relative to those surroundings — one is perhaps at rest in its surroundings. that is, exactly what is needed to make the rules consistent is the kind of privileged, true, sense of motion provided by descartes ' second definition. insurmountable problems with the rules remain, but rejecting the traditional interpretation and taking motion properly speaking seriously in descartes ' philosophy clearly gives a more charitable reading. in an unpublished essay — de gravitatione ( newton, 2004 ) — and in a scholium to the definitions given in his 1687 mathematical principles of natural philosophy ( see newton, 1999 for an up - to - date translation ), newton attacked both of descartes ' notions of motion as candidates for the operative notion in mechanics. ( see stein 1967and rynasiewicz 1995 for important, and differing, views on the issue. ) ( this critique is studied in more detail in the entry newton ' s views on space, time, and motion. ) the most famous argument invokes the so - called ‘ newton ' s bucket ’ experiment. stripped to its basic elements one compares : - a bucket of water hanging from a cord as the bucket is set spinning about the cord ' s axis, with - the same bucket and water when they are rotating at the same rate about the cord ' s axis. as is familiar from any rotating system,


bucket of water hanging from a cord as the bucket is set spinning about the cord ' s axis, with - the same bucket and water when they are rotating at the same rate about the cord ' s axis. as is familiar from any rotating system, there will be a tendency for the water to recede from the axis of rotation in the latter case : in ( i ) the surface of the water will be flat ( because of the earth ' s gravitational field ) while in ( ii ) it will be concave. the analysis of such ‘ inertial effects ' due to rotation was a major topic of enquiry of ‘ natural philosophers ' of the time, including descartes and his followers, and they would certainly have agreed with newton that the concave surface of the water in the second case demonstrated that the water was moving in a mechanically significant sense. there is thus an immediate problem for the claim that proper motion is the correct mechanical sense of motion : in ( i ) and ( ii ) proper motion is anti - correlated with the mechanically significant motion revealed by the surface of the water. that is, the water is flat in ( i ) when it is in motion relative to its immediate surroundings — the inner sides of the bucket — but curved in ( ii ) when it is at rest relative to its immediate surroundings. thus the mechanically relevant meaning of rotation is not that of proper motion. ( you may have noticed a small lacuna in newton ' s argument : in ( i ) the water is at rest and in ( ii ) in motion relative to that part of its surroundings constituted by the air above it. it ' s not hard to imagine small modifications to the example to fill this gap. ) newton also points out that the height that the water climbs up the inside of the bucket provides a measure of the rate of rotation of bucket and water : the higher the water rises up the sides, the greater the tendency to recede must be, and so the faster the water must be rotating in the mechanically significant sense. but supposing, very plausibly, that the measure is unique, that any particular height indicates a particular rate of rotation. then the unique height that the water reaches at any moment implies a unique rate of rotation in a mechanically significant sense. and thus motion in the sense of motion relative to an arbitrary reference body, is not the mechanical sense, since that kind of rotation is not unique at all, but depends on the motion of the reference body. and so descartes ’ change of place ( and for


the sense of motion relative to an arbitrary reference body, is not the mechanical sense, since that kind of rotation is not unique at all, but depends on the motion of the reference body. and so descartes ’ change of place ( and for similar reasons, motion in the ordinary sense ) is not the mechanically significant sense of motion. in our discussion of descartes we called the sense of motion operative in the science of mechanics ‘ true motion ’, and the phrase is used in this way by newton in the scholium. thus newton ' s bucket shows that true ( rotational ) motion is anti - correlated with, and so not identical with, proper motion ( as descartes proposed according to the garber reading ) ; and newton further argues that the rate of true ( rotational ) motion is unique, and so not identical with change of place, which is multiple. newton proposed instead that true motion is motion relative to a temporally enduring, rigid, 3 - dimensional euclidean space, which he dubbed ‘ absolute space ’. of course, descartes also defined motion as relative to an enduring 3 - dimensional euclidean space ; the difference is that descartes space was divided into parts ( his space was identical with a plenum of corpuscles ) in motion, not a rigid structure in which ( mobile ) material bodies are embedded. so according to newton, the rate of true rotation of the bucket ( and water ) is the rate at which it rotates relative to absolute space. or put another way, newton effectively defines the complete predicate x moves - absolutely as x moves - relative - to absolute space ; both newton and descartes offer the competing complete predicates as analyses of x moves - truly. newton ' s proposal for understanding motion solves the problems that he posed for descartes, and provides an interpretation of the concepts of constant motion and acceleration that appear in his laws of motion. however, it suffers from two notable interpretational problems, both of which were pressed forcefully by leibniz ( in the leibniz - clarke correspondence, 1715 – 1716 ) — which is not to say that leibniz himself offered a superior account of motion ( see below ). ( of course, there are other features of newton ' s proposal that turned out to be empirically inadequate, and are rejected by relativity : newton ' s account violates the relativity of simultaneity and postulates a non - dynamical spacetime structure. ) first, according to this account, absolute velocity is a well - defined


empirically inadequate, and are rejected by relativity : newton ' s account violates the relativity of simultaneity and postulates a non - dynamical spacetime structure. ) first, according to this account, absolute velocity is a well - defined quantity : more simply, the absolute speed of a body is the rate of change of its position relative to an arbitrary point of absolute space. but the galilean relativity of newton ' s laws mean that the evolution of a closed system is unaffected by constant changes in velocity ; galileo ' s experimenter cannot determine from observations inside his cabin whether the boat is at rest in harbor or sailing smoothly. put another way, according to newtonian mechanics, in principle newton ' s absolute velocity cannot be experimentally determined. so in this regard absolute velocity is quite unlike acceleration ( including rotation ) ; newtonian acceleration is understood in absolute space as the rate of change of absolute velocity, and is, according to newtonian mechanics, in general measurable, for instance by measuring the height that the water ascends the sides of the bucket. ( it is worth noting that newton was well - aware of these facts ; the galilean relativity of his theory is demonstrated in corollary v of the laws of the principia, while corollary vi shows that acceleration is unobservable if all parts of the system accelerate in parallel at the same rate, as they do in a homogeneous gravitational field. ) leibniz argued ( rather inconsistently, as we shall see ) that since differences in absolute velocity were unobservable, they could not be genuine differences at all ; and hence that newton ' s absolute space, whose existence would entail the reality of such differences, must also be a fiction. few contemporary philosophers would immediately reject a quantity as meaningless simply because it was not experimentally determinable, but this fact does justify genuine doubts about the reality of absolute velocity, and hence of absolute space. the second problem concerns the nature of absolute space. newton quite clearly distinguished his account from descartes ' — in particular with regards to absolute space ' s rigidity versus descartes ' ‘ hydrodynamical ’ space, and the possibility of the vacuum in absolute space. thus absolute space is definitely not material. on the other hand, presumably it is supposed to be part of the physical, not mental, realm. in de gravitatione, newton rejected both the standard philosophical categories of substance and attribute as suitable characterizations. absolute space is not a substance for it lacks


hand, presumably it is supposed to be part of the physical, not mental, realm. in de gravitatione, newton rejected both the standard philosophical categories of substance and attribute as suitable characterizations. absolute space is not a substance for it lacks causal powers and does not have a fully independent existence, and yet not an attribute since it would exist even in a vacuum, which by definition is a place where there are no bodies in which it might inhere. newton proposes that space is what we might call a ‘ pseudo - substance ’, more like a substance than property, yet not quite a substance. ( note that samuel clarke, in his correspondence with leibniz, which newton had some role in composing, advocates the property view, and note further that when leibniz objects because of the vacuum problem, clarke suggests that there might be non - material beings in the vacuum in which space might inhere. ) in fact, newton accepted the principle that everything that exists, exists somewhere — i. e., in absolute space. thus he viewed absolute space as a necessary consequence of the existence of anything, and of god ' s existence in particular — hence space ' s ontological dependence. leibniz was presumably unaware of the unpublished de gravitatione in which these particular ideas were developed, but as we shall see, his later works are characterized by a robust rejection of any notion of space as a real thing rather than an ideal, purely mental entity. this is a view that attracts even fewer contemporary adherents, but there is something deeply peculiar about a non - material but physical entity, a worry that has influenced many philosophical opponents of absolute space. after the development of relativity ( which we will take up below ), and its interpretation as a spacetime theory, it was realized that the notion of spacetime had applicability to a range of theories of mechanics, classical as well as relativistic. in particular, there is a spacetime geometry — ‘ galilean ’ or ‘ neo - newtonian ’ spacetime — for newtonian mechanics that solves the problem of absolute velocity ; an idea exploited by a number of philosophers from the late 1960s ( e. g., earman 1970, friedman 1983, sklar 1974 and stein 1968 ). for details the reader is referred to the entry on spacetime : inertial frames, but the general idea is that although a spatial distance is well - defined between any two simultaneous points of this spacetime, only the temporal interval is well - defined between non


the reader is referred to the entry on spacetime : inertial frames, but the general idea is that although a spatial distance is well - defined between any two simultaneous points of this spacetime, only the temporal interval is well - defined between non - simultaneous points. thus things are rather unlike newton ' s absolute space, whose points persist through time and maintain their distances ; in absolute space the distance between p - now and q - then ( where p and q are points ) is just the distance between p - now and q - now. however, galilean spacetime has an ‘ affine connection ’ which effectively specifies for every point of every continuous curve, the rate at which the curve is changing from straightness at that point ; for instance, the straight lines are picked out as those curves whose rate of change from straightness is zero at every point. ( another way of thinking about this space is as possessing — in addition to a distance between any two simultaneous points and a temporal interval between any points — a three - place relation of colinearity, satisfied by three points just in case they lie on a straight line. ) since the trajectories of bodies are curves in spacetime the affine connection determines the rate of change from straightness at every point of every possible trajectory. the straight trajectories thus defined can be interpreted as the trajectories of bodies moving inertially, and the rate of change from straightness of any trajectory can be interpreted as the acceleration of a body following that trajectory. that is, newton ' s second law can be given a geometric formulation as ‘ the rate of change from straightness of a body ' s trajectory is equal to the forces acting on the body divided by its mass ’. the significance of this geometry is that while acceleration is well - defined, velocity is not — in accord with empirically determinability of acceleration but not velocity according to newtonian mechanics. ( a simple analogy helps see how such a thing is possible : betweenness but not ‘ up ’ is a well - defined concept in euclidean space. ) thus galilean spacetime gives a very nice interpretation of the choice that nature makes when it decides that the laws of mechanics should be formulated in terms of accelerations not velocities ( as aristotle and descartes proposed ). put another way, we can define the complete predicate x accelerates as trajectory ( x ) has - non - zero - rate - of - change - from - straightness, where trajectory maps bodies onto


as aristotle and descartes proposed ). put another way, we can define the complete predicate x accelerates as trajectory ( x ) has - non - zero - rate - of - change - from - straightness, where trajectory maps bodies onto their trajectories in galilean spacetime. and this predicate, defined this way, applies to the water in the bucket if and only if it is rotating, according to newtonian mechanics formulated in terms of the geometry of galilean spacetime ; it is the mechanically relevant sense of the word in this theory. but all of this formulation and definition has been given in terms of the geometry of spacetime, not relations between bodies ; acceleration is ‘ absolute ’ in the sense that there is a preferred ( true ) sense of acceleration in mechanics and which is not defined in terms of the motions of bodies relative to one another. ( note that this sense of ‘ absolute ’ is broader than that of motion relative to absolute space, which we defined earlier. in the remainder of this article we will use it in the broader sense. the reader should be aware that the term is used in many ways in the literature, and such equivocation often leads to massive misunderstandings. ) thus if any of this analysis of motion is taken literally then one arrives at a position regarding the ontology of spacetime rather like that of newton ' s regarding space : it is some kind of ‘ substantial ’ ( or maybe pseudo - substantial ) thing with the geometry of galilean spacetime, just as absolute space possessed euclidean geometry. this view regarding the ontology of spacetime is usually called ‘ substantivalism ’ ( sklar, 1974 ). the galilean substantivalist usually sees himself as adopting a more sophisticated geometry than newton but sharing his substantivalism ( though there is room for debate on newton ' s exact ontological views, see disalle, 2002 ). the advantage of the more sophisticated geometry is that although it allows the absolute sense of acceleration apparently required by newtonian mechanics to be defined, it does not allow one to define a similar absolute speed or velocity — x accelerates can be defined as a complete predicate in terms of the geometry of galilean spacetime but not x moves in general — and so the first of leibniz ' s problem is resolved. of course we see that the solution depends on a crucial shift from speed and velocity to acceleration as the relevant senses of ‘ motion ’ : from the rate of change of


in general — and so the first of leibniz ' s problem is resolved. of course we see that the solution depends on a crucial shift from speed and velocity to acceleration as the relevant senses of ‘ motion ’ : from the rate of change of position to the rate of rate of change. while this proposal solves the first kind of problem posed by leibniz, it seems just as vulnerable to the second. while it is true that it involves the rejection of absolute space as newton conceived it, and with it the need to explicate the nature of an enduring space, the postulation of galilean spacetime poses the parallel question of the nature of spacetime. again, it is a physical but non - material something, the points of which may be coincident with material bodies. what kind of thing is it? could we do without it? as we shall see below, some contemporary philosophers believe so. there is a ‘ folk - reading ’ of leibniz that one finds either explicitly or implicitly in the philosophy of physics literature which takes account of only some of his remarks on space and motion. the reading underlies vast swathes of the literature : for instance, the quantities captured by earman ' s ( 1999 ) ‘ leibnizian spacetime ’, do not do justice to leibniz ' s view of motion ( as earman acknowledges ). but it is perhaps most obvious in introductory texts ( e. g., ray 1991, huggett 2000 to mention a couple ). according to this view, the only quantities of motion are relative quantities, relative velocity, acceleration and so on, and all relative motions are equal, so there is no true sense of motion. however, leibniz is explicit that other quantities are also ‘ real ’, and his mechanics implicitly — but obviously — depends on yet others. the length of this section is a measure, not so much the importance of leibniz ' s actual views, but the importance of showing what the prevalent folk view leaves out regarding leibniz ' s views on the metaphysics of motion and interpretation of mechanics. that said, we shall also see that no one has yet discovered a fully satisfactory way of reconciling the numerous conflicting things that leibniz says about motion. some of these tensions can be put down simply to his changing his mind ( see cover and hartz 1988 for an explication of how leibniz ' s views on space developed ). however, we will concentrate on the fairly short period in


. some of these tensions can be put down simply to his changing his mind ( see cover and hartz 1988 for an explication of how leibniz ' s views on space developed ). however, we will concentrate on the fairly short period in the mid 1680 - 90s during which leibniz developed his theory of mechanics, and was most concerned with their interpretation. we will supplement this discussion with the important remarks that he made in his correspondence with samuel clarke around 30 years later ( 1715 – 1716 ) ; this discussion is broadly in line with the earlier period, and the intervening period is one in which he turned to other matters, rather than one in which his views on space were dramatically evolving. arguably, leibniz ' s views concerning space and motion do not have a completely linear logic, starting from some logically sufficient basic premises, but instead form a collection of mutually supporting doctrines if one starts questioning why leibniz held certain views — concerning the ideality of space, for instance — one is apt to be led in a circle. still, exposition requires starting somewhere, and leibniz ' s argument for the ideality of space in the correspondence with clarke is a good place to begin. but bear in mind the caveats made here — this argument was made later than a number of other relevant writings, and its logical relation to leibniz ' s views on motion is complex. leibniz ( lv. 47 — this notation means leibniz ' s fifth letter, section 47, and so on ) says that ( i ) a body comes to have the ‘ same place ’ as another once did, when it comes to stand in the same relations to bodies we ‘ suppose ’ to be unchanged ( more on this later ). ( ii ) that we can define ‘ a place ’ to be that which any such two bodies have in common ( here he claims an analogy with the euclidean / eudoxan definition of a rational number in terms of an identity relation between ratios ). and finally that ( iii ) space is all such places taken together. however, he also holds that properties are particular, incapable of being instantiated by more than one individual, even at different times ; hence it is impossible for the two bodies to be in literally the same relations to the unchanged bodies. thus the thing that we take to be the same for the two bodies — the place — is something added by our minds to the situation, and only ideal. as a result, space, which is after all constructed from these ideal places,


bodies. thus the thing that we take to be the same for the two bodies — the place — is something added by our minds to the situation, and only ideal. as a result, space, which is after all constructed from these ideal places, is itself ideal : ‘ a certain order, wherein the mind conceives the application of relations ’. it ' s worth pausing briefly to contrast this view of space with those of descartes and of newton. both descartes and newton claim that space is a real, mind - independent entity ; for descartes it is matter, and for newton a ‘ pseudo - substance ’, distinct from matter. and of course for both, these views are intimately tied up with their accounts of motion. leibniz simply denies the mind - independent reality of space, and this too is bound up with his views concerning motion. ( note that fundamentally, in the metaphysics of monads that leibniz was developing contemporaneously with his mechanics, everything is in the mind of the monads ; but the point that leibniz is making here is that even within the world that is logically constructed from the contents of the minds of monads, space is ideal. ) so far ( apart from that remark about ‘ unchanged ’ bodies ) we have not seen leibniz introduce anything more than relations of distance between bodies, which is certainly consistent with the folk view of his philosophy. however, leibniz sought to provide a foundation for the cartesian / mechanical philosophy in terms of the aristotelian / scholastic metaphysics of substantial forms ( here we discuss the views laid out in sections 17 - 22 of the 1686 discourse on metaphysics and the 1695 specimen of dynamics, both in garber and ariew 1989 ). in particular, he identifies primary matter with what he calls its ‘ primitive passive force ’ of resistance to changes in motion and to penetration, and the substantial form of a body with its ‘ primitive active force ’. it is important to realize that these forces are not mere properties of matter, but actually constitute it in some sense, and further that they are not themselves quantifiable. however because of the collisions of bodies with one another, these forces ‘ suffer limitation ’, and ‘ derivative ’ passive and active forces result. ( there ' s a real puzzle here. collision presupposes space, but primitive forces constitute matter prior to any spatial concepts — the primitive active and passive forces ground motion and extension respectively. see garber and rauzy


active forces result. ( there ' s a real puzzle here. collision presupposes space, but primitive forces constitute matter prior to any spatial concepts — the primitive active and passive forces ground motion and extension respectively. see garber and rauzy, 2004. ) derivative passive force shows up in the different degrees of resistance to change of different kinds of matter ( of ‘ secondary matter ’ in scholastic terms ), and apparently is measurable. derivative active force however, is considerably more problematic for leibniz. on the one hand, it is fundamental to his account of motion and theory of mechanics — motion fundamentally is possession of force. but on the other hand, leibniz endorses the mechanical philosophy, which precisely sought to abolish aristotelian substantial form, which is what force represents. leibniz ' s goal was to reconcile the two philosophies, by providing an aristotelian metaphysical foundation for modern mechanical science ; as we shall see, it is ultimately an open question exactly how leibniz intended to deal with the inherent tensions in such a view. the texts are sufficiently ambiguous to permit dissent, but arguably leibniz intends that one manifestation of derivative active force is what he calls vis viva — ‘ living force ’. leibniz had a famous argument with the cartesians over the correct definition of this quantity. descartes defined it as size times speed — effectively as the magnitude of the momentum of a body. leibniz gave a brilliant argument ( repeated in a number of places, for instance section 17 of the discourse on metaphysics ) that it was size times speed2 — so ( proportional to ) kinetic energy. if the proposed identification is correct then kinetic energy quantifies derivative active force according to leibniz ; or looked at the other way, the quantity of virtus ( another term used by leibniz for active force ) associated with a body determines its kinetic energy and hence its speed. as far as the authors know, leibniz never explicitly says anything conclusive about the relativity of virtus, but it is certainly consistent to read him ( as roberts 2003 does ) to claim that there is a unique quantity of virtus and hence ‘ true ’ ( as we have been using the term ) speed associated with each body. at the very least, leibniz does say that there is a real difference between possession and non - possession of vis viva ( e. g., in section 18 of the discourse ) and it is a small step


speed associated with each body. at the very least, leibniz does say that there is a real difference between possession and non - possession of vis viva ( e. g., in section 18 of the discourse ) and it is a small step from there to true, privileged speed. indeed, for leibniz, mere change of relative position is not ‘ entirely real ’ ( as we saw for instance in the correspondence ) and only when it has vis viva as its immediate cause is there some reality to it. ( however, just to muddy the waters, leibniz also claims that as a matter of fact, no body ever has zero force, which on the reading proposed means no body is ever at rest, which would be surprising given all the collisions bodies undergo. ) an alternative interpretation to the one suggested here might say that leibniz intends that while there is a difference between motion / virtus and no motion / virtus, there is somehow no difference between any strictly positive values of those quantities. it is important to emphasize two points about the preceding account of motion in leibniz ' s philosophy. first, motion in the everyday sense — motion relative to something else — is not really real. fundamentally motion is possession of virtus, something that is ultimately non - spatial ( modulo its interpretation as primitive force limited by collision ). if this reading is right — and something along these lines seems necessary if we aren ' t simply to ignore important statements by leibniz on motion — then leibniz is offering an interpretation of motion that is radically different from the obvious understanding. one might even say that for leibniz motion is not movement at all! ( we will leave to one side the question of whether his account is ultimately coherent. ) the second point is that however we should understand leibniz, the folk reading simply does not and cannot take account of his clearly and repeatedly stated view that what is real in motion is force not relative motion, for the folk reading allows leibniz only relative motion ( and of course additionally, motion in the sense of force is a variety of true motion, again contrary to the folk reading ). however, from what has been said so far it is still possible that the folk reading is accurate when it comes to leibniz ' s views on the phenomena of motion, the subject of his theory of mechanics. the case for the folk reading is in fact supported by leibniz ' s resolution of the tension that we mentioned earlier, between the fundamental role of force


the states of motion of bodies — some of his statements do suggest that he was confused in this way. for another way of stating the problem for the folk reading is that the claim that relative motions alone suffice for mechanics and that all relative motions are equal is a principle of general relativity, and could leibniz — a mathematical genius — really have failed to notice that his laws hold only in special frames? well, just maybe. on the one hand, when he explicitly articulates the principle of the equivalence of hypotheses ( for instance in specimen of dynamics ) he tends to say only that one cannot assign initial velocities on the basis of the outcome of a collision, which requires only galilean relativity. however, he confusingly also claimed ( on copernicanism and the relativity of motion, also in garber and ariew 1989 ) that the tychonic and copernican hypotheses were equivalent. but if the earth orbits the sun in an inertial frame ( copernicus ), then there is no inertial frame according to which the sun orbits the earth ( tycho brahe ), and vice versa : these hypotheses are simply not galilean equivalent ( something else leibniz could hardly have failed to notice ). so there is some textual support for leibniz endorsing general relativity, as the folk reading maintains. a number of commentators have suggested solutions to the puzzle of the conflicting pronouncements that leibniz makes on the subject, but arguably none is completely successful in reconciling all of them ( stein 1977 argues for general relativity, while roberts 2003 argues the opposite ; see also lodge 2003 ). so the folk reading simply ignores leibniz ' s metaphysics of motion, it commits leibniz to a mathematical howler regarding his laws, and it is arguable whether it is the best rendering of his pronouncements concerning relativity ; it certainly cannot be accepted unquestioningly. however, it is not hard to understand the temptation of the folk reading. in his correspondence with clarke, leibniz says that he believes space to be “ something merely relative, as time is, … an order of coexistences, as time is an order of successions ” ( liii. 4 ), which is naturally taken to mean that space is at base nothing but the distance and temporal relations between bodies. ( though even this passage has its subtleties, because of the ideality of


an order of successions ” ( liii. 4 ), which is naturally taken to mean that space is at base nothing but the distance and temporal relations between bodies. ( though even this passage has its subtleties, because of the ideality of space discussed above, and because in leibniz ' s conception space determines what sets of relations are possible. ) and if relative distances and times exhaust the spatiotemporal in this way, then shouldn ' t all quantities of motion be defined in terms of those relations? we have seen two ways in which this would be the wrong conclusion to draw : force seems to involve a notion of speed that is not identified with any relative speed, and ( unless the equivalence of hypotheses is after all a principle of general relativity ) the laws pick out a standard of constant motion that need not be any constant relative motion. of course, it is hard to reconcile these quantities with the view of space and time that leibniz proposes — what is speed in size times speed2 or constant speed if not speed relative to some body or to absolute space? given leibniz ' s view that space is literally ideal ( and indeed that even relative motion is not ‘ entirely real ’ ) perhaps the best answer is that he took force and hence motion in its real sense not to be determined by motion in a relative sense at all, but to be primitive monadic quantities. that is, he took x moves to be a complete predicate, but he believed that it could be fully analyzed in terms of strictly monadic predicates : x moves iff x possesses - non - zero - derivative - active - force. and this reading explains just what leibniz took us to be supposing when we ‘ supposed certain bodies to be unchanged ’ in the construction of the idea of space : that they had no force, nothing causing, or making real any motion. it ' s again helpful to compare leibniz with descartes and newton, this time regarding motion. commentators often express frustration at leibniz ' s response to newton ' s arguments for absolute space : “ i find nothing … in the scholium that proves or can prove the reality of space in itself. however, i grant that there is a difference between an absolute true motion of a body and a mere relative change … ” ( lv. 53 ). not only does leibniz apparently fail to take the argument seriously, he then goes on to concede the step in the argument that seems to require absolute space


motion of a body and a mere relative change … ” ( lv. 53 ). not only does leibniz apparently fail to take the argument seriously, he then goes on to concede the step in the argument that seems to require absolute space! but with our understanding of newton and leibniz, we can see that what he says makes perfect sense ( or at least that it is not as disingenuous as it is often taken to be ). newton argues in the scholium that true motion cannot be identified with the kinds of motion that descartes considers ; but both of these are purely relative motions, and leibniz is in complete agreement that merely relative motions are not true ( i. e., ‘ entirely real ’ ). leibniz ' s ‘ concession ’ merely registers his agreement with newton against descartes on the difference between true and relative motion ; he surely understood who and what newton was refuting, and it was a position that he had himself, in different terms, publicly argued against at length. but as we have seen, leibniz had a very different analysis of the difference to newton ' s ; true motion was not, for him, a matter of motion relative to absolute space, but the possession of quantity of force, ontologically prior to any spatiotemporal quantities at all. there is indeed nothing in the scholium explicitly directed against that view, and since it does potentially offer an alternative way of understanding true motion, it is not unreasonable for leibniz to claim that there is no deductive inference from true motion to absolute space. the folk reading which belies leibniz has it that he sought a theory of mechanics formulated in terms only of the relations between bodies. as we ' ll see presently, in the nineteenth century, ernst mach indeed proposed such an approach, but leibniz clearly did not ; though certain similarities between leibniz and mach — especially the rejection of absolute space — surely helps explain the confusion between the two. but not only is leibniz often misunderstood, there are influential misreadings of newton ' s arguments in the scholium, influenced by the idea that he is addressing leibniz in some way. of course the principia was written 30 years before the correspondence, and the arguments of the scholium were not written with leibniz in mind, but clarke himself suggests ( civ. 13 ) that those arguments — specifically those concerning the bucket — are telling against leibniz.


years before the correspondence, and the arguments of the scholium were not written with leibniz in mind, but clarke himself suggests ( civ. 13 ) that those arguments — specifically those concerning the bucket — are telling against leibniz. that argument is indeed devastating to a general principle of relativity — the parity of all relative motions — but we have seen that it is highly questionable whether leibniz ' s equivalence of hypotheses amount to such a view. that said, his statements in the first four letters of the correspondence could understandably mislead clarke on this point — it is in reply to clarke ' s challenge that leibniz explicitly denies the parity of relative motions. but interestingly, clarke does not present a true version of newton ' s argument — despite some involvement of newton in writing the replies. instead of the argument from the uniqueness of the rate of rotation, he argues that systems with different velocities must be different because the effects observed if they were brought to rest would be different. this argument is of course utterly question begging against a view that holds that there is no privileged standard of rest! as we discuss in section 8, mach attributed to newton the fallacious argument that because the surface of the water curved even when it was not in motion relative to the bucket, it must be rotating relative to absolute space. our discussion of newton showed how misleading such a reading is. in the first place he also argues that there must be some privileged sense of rotation, and hence not all relative motions are equal. second, the argument is ad hominem against descartes, in which context a disjunctive syllogism — motion is either proper or ordinary or relative to absolute space — is argumentatively legitimate. on the other hand, mach is quite correct that newton ' s argument in the scholium leaves open the logical possibility that the privileged, true sense of rotation ( and acceleration more generally ) is some species of relative motion ; if not motion properly speaking, then relative to the fixed stars perhaps. ( in fact newton rejects this possibility in de gravitatione ( 1962 ) on the grounds that it would involve an odious action at a distance ; an ironic position given his theory of universal gravity. ) however the kind of folk - reading of newton that underlies much of the contemporary literature replaces mach ' s interpretation with a more charitable one. according to this reading, newton ' s point is that his mechanics — unlike descartes ' — could explain why


the kind of folk - reading of newton that underlies much of the contemporary literature replaces mach ' s interpretation with a more charitable one. according to this reading, newton ' s point is that his mechanics — unlike descartes ' — could explain why the surface of the rotating water is curved, that his explanation involves a privileged sense of rotation, and that absent an alternative hypothesis about its relative nature, we should accept absolute space. but our discussion of newton ' s argument showed that it simply does not have an ‘ abductive ’, ‘ best explanation ’ form, but shows deductively, from cartesian premises, that rotation is neither proper nor ordinary motion. that is not to say that newton had no understanding of how such effects would be explained in his mechanics. for instance, in corollaries 5 and 6 to the definitions of the principles he states in general terms the conditions under which different states of motion are not — and so by implication are — discernible according to his laws of mechanics. nor is it to say that newton ' s contemporaries weren ' t seriously concerned with explaining inertial effects. leibniz, for instance, analyzed a rotating body ( in the specimen ). in short, parts of a rotating system collide with the surrounding matter and are continuously deflected, into a series of linear motions that form a curved path. but the system as leibniz envisions it — comprised of a plenum of elastic particles of matter — is far too complex for him to offer any quantitative model based on this qualitative picture. ( in the context of the proposed ‘ abductive ’ reading of newton, note that this point is telling against a rejection of intrinsic rigidity or forces acting at a distance, not narrow relationism ; it is the complexity of collisions in a plenum that stymies analysis. and since leibniz ' s collision theory requires a standard of inertial motion, even if he had explained inertial effects, he would not have thereby shown that all motions are relative, much less that all are equal. ) although the argument is then not newton ' s, it is still an important response to the kind of relationism proposed by the folk - leibniz, especially when it is extended by bringing in a further example from newton ' s scholium. newton considered a pair of identical spheres, connected by a cord, too far from any bodies to observe any relative motions ; he pointed out that their rate and direction of rotation could still be experimental


in a further example from newton ' s scholium. newton considered a pair of identical spheres, connected by a cord, too far from any bodies to observe any relative motions ; he pointed out that their rate and direction of rotation could still be experimentally determined by measuring the tension in the rod, and by pushing on opposite faces of the two globes to see whether the tension increased or decreased. he intended this simple example to demonstrate that the project he intended in the principia, of determining the absolute accelerations and hence gravitational forces on the planets from their relative motions, was possible. however, if we further specify that the spheres and cord are rigid and that they are the only things in their universe, then the example can be used to point out that there are infinitely many different rates of rotation all of which agree on the relations between bodies. since there are no differences in the relations between bodies in the different situations, it follows that the observable differences between the states of rotation cannot be explained in terms of the relations between bodies. therefore, a theory of the kind attributed to the folk ' s leibniz cannot explain all the phenomena of newtonian mechanics, and again we can argue abductively for absolute space. ( of course, the argument works by showing that, granted the different states of rotation, there are states of rotation that cannot merely be relative rotations of any kind ; for the differences cannot be traced to any relational differences. that is, granted the assumptions of the argument, rotation is not true relative motion of any kind. ) this argument ( neither the premises nor conclusion ) is not newton ' s, and must not be taken as a historically accurate reading, however, that is not to say that the argument is fallacious, and indeed many have found it attractive, particularly as a defense not of newton ' s absolute space, but of galilean spacetime. that is, newtonian mechanics with galilean spacetime can explain the phenomena associated with rotation, while theories of the kind proposed by mach cannot explain the differences between situations allowed by newtonian mechanics, but these explanations rely on the geometric structure of galilean spacetime — particularly its connection, to interpret acceleration. and thus — the argument goes — those explanations commit us to the reality of spacetime — a manifold of points — whose properties include the appropriate geometric ones. this final doctrine, of the reality of spacetime with its component points or regions, distinct from matter, with geometric properties, is what we earlier identified as ‘ substantiv


deny any relations between bodies and spacetime itself. like the actual leibniz, they allow absolute quantities of motion, but claim that space and time themselves are nothing but the relations between bodies. of course, such views raise the question of how a motion can be not relative to anything at all, and how we are to understand the privileging of frames ; huggett ( 2006 ) contains a proposal for addressing these problems. ( note that sklar and van fraassen are committed to the idea that in some sense newton ' s laws are capable of explaining all the phenomena without recourse to spacetime geometry ; that the connection and the metrical properties are explanatorily redundant. a similar view is defended in the context of relativity in brown 2005. ) between the time of newton and leibniz and the 20th century, newton ' s mechanics and gravitation theory reigned essentially unchallenged, and with that long period of dominance, absolute space came to be widely accepted. at least, no natural philosopher or physicist offered a serious challenge to newton ' s absolute space, in the sense of offering a rival theory that dispenses with it. but like the action at a distance in newtonian gravity, absolute space continued to provoke metaphysical unease. seeking a replacement for the unobservable newtonian space, neumann ( 1870 ) and lange ( 1885 ) developed more concrete definitions of the reference frames in which newton ' s laws hold. in these and a few other works, the concept of the set of inertial frames was first clearly expressed, though it was implicit in both remarks and procedures to be found in the principia. ( see the entries on space and time : inertial frames and newton ' s views on space, time, and motion ) the most sustained, comprehensive, and influential attack on absolute space was made by ernst mach in his science of mechanics ( 1883 ). in a lengthy discussion of newton ' s scholium on absolute space, mach accuses newton of violating his own methodological precepts by going well beyond what the observational facts teach us concerning motion and acceleration. mach at least partly misinterpreted newton ' s aims in the scholium, and inaugurated a reading of the bucket argument ( and by extension the globes argument ) that has largely persisted in the literature since. mach viewed the argument as directed against a ‘ strict ’ or ‘ general - relativity ’ form of relationism, and as an attempt to establish the existence of absolute


( and by extension the globes argument ) that has largely persisted in the literature since. mach viewed the argument as directed against a ‘ strict ’ or ‘ general - relativity ’ form of relationism, and as an attempt to establish the existence of absolute space. mach points out the obvious gap in the argument when so construed : the experiment only establishes that acceleration ( rotation ) of the water with respect to the earth, or the frame of the fixed stars, produces the tendency to recede from the center ; it does not prove that a strict relationist theory cannot account for the bucket phenomena, much less the existence of absolute space. ( the reader will recall that newton ' s actual aim was simply to show that descartes ' two kinds of motion are not adequate to accounting for rotational phenomena. ) although mach does not mention the globes thought experiment specifically, it is easy to read an implicit response to it in the things he does say : nobody is competent to say what would happen, or what would be possible, in a universe devoid of matter other than two globes. so neither the bucket nor the globes can establish the existence of absolute space. both in mach ' s interpretations of newton ' s arguments and in his replies, one can already see two anti - absolute space viewpoints emerge, though mach himself never fully kept them apart. the first strain, which we may call ‘ mach - lite ’, criticizes newton ' s postulation of absolute space as a metaphysical leap that is neither justified by actual experiments, nor methodologically sound. the remedy offered by mach - lite is simple : we should retain newton ' s mechanics and use it just as we already do, but eliminate the unnecessary posit of absolute space. in its place we need only substitute the frame of the fixed stars, as is the practice in astronomy in any case. if we find the incorporation of a reference to contingent circumstances ( the existence of a single reference frame in which the stars are more or less stationary ) in the fundamental laws of nature problematic ( which mach need not, given his official positivist account of scientific laws ), then mach suggests that we replace the 1st law with an empirically equivalent mathematical rival : mach ' s equation ( 1960, 287 ) the sums in this equation are to be taken over all massive bodies in the universe. since the top sum is weighted by distance, distant masses count much more than near ones. in a world with a ( reasonably ) static distribution of heavy distant bodies, such as we appear to live


to be taken over all massive bodies in the universe. since the top sum is weighted by distance, distant masses count much more than near ones. in a world with a ( reasonably ) static distribution of heavy distant bodies, such as we appear to live in, the equation entails local conservation of linear momentum in ‘ inertial ’ frames. the upshot of this equation is that the frame of the fixed stars plays exactly the role of absolute space in the statement of the 1st law. ( notice that this equation, unlike newton ' s first law, is not vectorial. ) this proposal does not, by itself, offer an alternative to newtonian mechanics, and as mach himself pointed out, the law is not well - behaved in an infinite universe filled with stars ; but the same can perhaps be said of newton ' s law of gravitation ( see malament 1995, and norton 1993 ). but mach did not offer this equation as a proposed law valid in any circumstances ; he avers, “ it is impossible to say whether the new expression would still represent the true condition of things if the stars were to perform rapid movements among one another. ” ( p. 289 ) it is not clear whether mach offered this revised first law as a first step toward a theory that would replace newton ' s mechanics, deriving inertial effects from only relative motions, as leibniz desired. but many other remarks made by mach in his chapter criticizing absolute space point in this direction, and they have given birth to the mach - heavy view, later to be christened “ mach ' s principle ” by albert einstein. the mach - heavy viewpoint calls for a new mechanics that invokes only relative distances and ( perhaps ) their 1st and 2nd time derivatives, and thus ‘ generally relativistic ’ in the sense sometimes read into leibniz ' s remarks about motion. mach wished to eliminate absolute time from physics too, so he would have wanted a proper relationist reduction of these derivatives also. the barbour - bertotti theories, discussed below, provide this. mach - heavy apparently involves the prediction of novel effects due to ‘ merely ’ relative accelerations. mach hints at such effects in his criticism of newton ' s bucket : newton ' s experiment with the rotating vessel of water simply informs us that the relative rotation of the water with respect to the sides of the vessel produces no noticeable centrifugal forces, but that such forces are produced by its relative rotation with respect to the mass of the earth and the other celestial bodies. no


us that the relative rotation of the water with respect to the sides of the vessel produces no noticeable centrifugal forces, but that such forces are produced by its relative rotation with respect to the mass of the earth and the other celestial bodies. no one is competent to say how the experiment would turn out if the sides of the vessel [ were ] increased until they were ultimately several leagues thick. ( 1883, 284. ) the suggestion here seems to be that the relative rotation in stage ( i ) of the experiment might immediately generate an outward force ( before any rotation is communicated to the water ), if the sides of the bucket were massive enough. more generally, mach - heavy involves the view that all inertial effects should be derived from the motions of the body in question relative to all other massive bodies in the universe. the water in newton ' s bucket feels an outward pull due ( mainly ) to the relative rotation of all the fixed stars around it. mach - heavy is a speculation that an effect something like electromagnetic induction should be built into gravity theory. ( such an effect does exist according to the general theory of relativity, and is called ‘ gravitomagnetic induction ’. the recently finished gravity probe b mission was designed to measure the gravitomagnetic induction effect due to the earth ' s rotation. ) its specific form must fall off with distance much more slowly than 1 / r2, if it is to be empirically similar to newtonian physics ; but it will certainly predict experimentally testable novel behaviors. a theory that satisfies all the goals of mach - heavy would appear to be ideal for the vindication of strict relationism and the elimination of absolute quantities of motion from mechanics. direct assault on the problem of satisfying mach - heavy in a classical framework proved unsuccessful, despite the efforts of others besides mach ( e. g., friedlander 1896, fopl 1904, reissner 1914, 1915 ), until the work of barbour and bertotti in the 1970s and 80s. ( between the late 19th century and the 1970s, there was of course one extremely important attempt to satisfy mach - heavy : the work of einstein that led to the general theory of relativity. since einstein ' s efforts took place in a non - classical ( lorentz / einstein / minkowski ) spacetime setting, we discuss them in the next section. ) rather than formulating a revised law of gravity / inertia using relative quantities, barbour and bertotti attacked the problem using the framework of lagrangian


/ minkowski ) spacetime setting, we discuss them in the next section. ) rather than formulating a revised law of gravity / inertia using relative quantities, barbour and bertotti attacked the problem using the framework of lagrangian mechanics, replacing the elements of the action that involve absolute quantities of motion with new terms invoking only relative distances, velocities etc. their first ( 1977 ) theory uses a very simple and elegant action, and satisfies everything one could wish for from a mach - heavy theory : it is relationally pure ( even with respect to time : while simultaneity is absolute, the temporal metric is derived from the field equations ) ; it is nearly empirically equivalent to newton ' s theory in a world such as ours ( with a large - scale uniform, near - stationary matter distribution ) ; yet it does predict novel effects such as the ones mach posited with his thick bucket. among these is an ‘ anisotropy of inertia ’ effect — accelerating a body away from the galactic center requires more force than accelerating it perpendicular to the galactic plane — large enough to be ruled out empirically. barbour and bertotti ' s second attempt ( 1982 ) at a relational lagrangian mechanics was arguably less machian, but more empirically adequate. in it, solutions are sought beginning with two temporally - nearby, instantaneous relational configurations of the bodies in the universe. barbour and bertotti define an ‘ intrinsic difference ’ parameter that measures how different the two configurations are. in the solutions of the theory, this intrinsic difference quantity gets minimized, as well as the ordinary action, and in this way full solutions are derived despite not starting from a privileged inertial - frame description. the theory they end up with turns out to be, in effect, a fragment of newtonian theory : the set of models of newtonian mechanics and gravitation in which there is zero net angular momentum. this result makes perfect sense in terms of strict relationist aims. in a newtonian world in which there is a nonzero net angular momentum ( e. g., a lone rotating island galaxy ), this fact reveals itself in the classic “ tendency to recede from the center ”. since a strict relationist demands that bodies obey the same mechanical laws even in ‘ rotating ’ coordinate systems, there cannot be any such tendency to recede from the center ( other than in a local subsystem ), in any of the relational theory ' s models