Pro Cl Us Physics Final b

8/11/2019 Pro Cl Us Physics Final b

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Epistemological aspects of ProclusElements of Physics

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In the train of the renewed academic interest in neoplatonic natural philosophy, Proclus moretechnical scientific works such as theHypotyposis Astronomicarum Positionumand theParaphrasisPtolemaei Tetrabiblou, are beginning to receive some attention, for the first time since the beginning of

printing. The Elements of Physics has been the subject of three significant studies in English by ikulin,!utash and "psomer.. #cholarly $erman translations with $reek and %atin te&ts having been published in'()( *+itenfeld- and '(/ *0oese- respectively.

The aim of this paper is to e&amine theElements of Physics, mainly from an epistemologicalperspective. I will begin by noticing the Platonic, Euclidean and 1ristotelian aspects of the work. The workis distinctive in that it is almost entirely composed of direct paraphrases from thePhysics2I and 2III andDe CaeloI of 1ristotle with no additional commentary and is presented in the format of a te&tbook in thestyle of EuclidsElements, which is a kind of logical structure that is a familiar part of Proclusphilosophical repertoire. In reference to thePhysics, "wen conjectures that3

These arguments and theories in which came to be called the e&act sciences are drawnprincipally from thePosterior Analytics, Topics,Physics,De CaeloandDe Generatione,works that are generally accepted as early and of which the first four at least probably date

substantially from 1ristotles years in the 1cademy or soon after. The influence of the1cademy is strong on them. They are marked by a large respect for mathematics andparticularly for the techni4ues and effects of a&iomatiing that subject, but they do notpretend to any mathematical discoveries, and in this they are close in spirit to Platoswritings. Even the preoccupations with physical change, its varieties and regularities andcauses, and the use of dialectic in analying these, is a position to which Plato had beenapproaching in his later years. 1ristotle, the meticulous empiricist, amassing biological dataor compiling the constitutions of '5/ $reek states, is not yet in evidence. *"wen, 6ethod'7-

#o 1ristotlesPhysicsand EuclidsElementsshare a common background linked to themathematical work of Platos academy, notably with the mathematicians Theudius and 8ermotimus *8eath''7-, and hence have structural similarities. The propositions in the books of Euclid are preceded bydefinitions, postulates, and common notions. 1ristotle e&plains the term element, as a definition,demonstration or proof used in geometrical propositions *Topics2III, ', ')9b:9-, which correlates wellwith the term in Euclid *8eath ''7-. ;urthermore, the basic definitions from book one of EuclidsElementsare akin to the geometric principles that 1ristotle adopts for his physical project, denoting the concept of theindivisibility of points.


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4uestion of how 1ristotle considered this process from a scientific perspective and what value thesee&planations had.'8ussey further notes3

In e&ploring the common structure of one=dimensional continua, 1ristotle, it seems ise&tending the scope of $reek mathematics, for we know of no previous e&ploration of thiskind. 8e considers not only spatially e&tended continua *bodies and their bounding surfaces,lines and points-, but temporal ones *time=stretches, changes- and other physical 4uantitiesneither spatial nor temporal. In treating time=stretches as wholly analogous to lines 1ristotle

is formally


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In proposition 7 *


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fifteen propositions are taken from Dhapters ' through @ ofDe CaeloI in se4uential order, with onlypropositions *


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unusual either. #implicius notes how sometimes 0ook 2 was grouped with the first four books, whereasbook 2II was often considered of lesser importance. +eale reasonably sees the propositions in four mainthematic groupings3 a- circular movement *'=7-> b- problems of finite and infinite motion *@='5-> c-movement and eternity *'7='/-> metaphysical aspects of motion *'(=:'- *5)-.

"verall, one could assume that 0ook one deals with the time and space factors that correlate tomotion whereas 0ook Two is s4uarely focused on circular motion in a more three dimensional perspectiveof moving bodies in all directions of space. The arguments use general descriptive concepts of circular

motion that gradually works their way upward to consider the prime mover as cause of primary circularmotion. "n the one hand, Proclus adaptation is a very streamlined, technical presentation, focusing on thebasic concepts that underlie the necessary conditions for e&plaining local motion specifically and thegeometrical demonstrations that justify them logically. Principles of magnitude and the nature of bodies andplace are given central consideration, making the work an e&planation on the nature of physical motion in apractical perspective that integrates astronomical perspectives.

espite the numerous but relatively minor modifications, I think that Proclus accepts the1ristotelian e&planation of physical motion to a large e&tent. 8e seems intent on arranging a more practicalformulation of principles of motion with a clearer demarcation of the scope of the field, with a sharperseparation from the more general physical concepts of change. 8owever, there is a certain boldness andfreedom in Proclus adaptation, especially in book II. 8is merging of 0ook I ofDe Caelowith book 2III ofthePhysicshas the effect of making circular motion the main focus thus changing the perspective of

1ristotles argument structure noticeably. The argument for the e&istence of the Prime 6over is lessdeductive as it proceeds from the notion of circular motion rather than from the more abstract and deductivestrategy of positing the need for the e&istence of eternal motion. 6oreover, unlike 1ristotle, he is notconcerned with e&plicitly proving the unmoved nature of the Prime 6over but is content to simply posit itsindivisible nature.')

"ne of the more curious aspects of the work is that, as ikulin has observed3

the ape& of 0ook I, its last Proposition I 9', parallels the ape& of 0ook II, Proposition II :'3the crescendo of each book is reached at the very end, wherein the completion of a series oftheorems finally occurs. The former proposition proves the immovability of the 4uantitativelyindivisible, and the latter proves the indivisibility of the prime mover, from which itimmediately follows *although Proclus does not make this step, leaving it to the reader- that

the prime mover is itself immovable. *ikulin '/@-Indeed, by ju&taposing the proposition


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Pythagorean, Platonic, 1ristotelian, and #toic sources. Influenced by Pythagoreanism, he outlines ametaphysical system based on mathematical and geometric=based concepts, presented as binary and ternaryconcepts, the highest being the notions of the limit and unlimited *peiras, apeiron- *based on PlatosPhilebus'7cff and :9cff.-3 hence 1ristotle says that bodycomes to completion with the number three. *(/-

The 4ualities of %imit, nlimited and 6i&ed are attributed to geometric lines and these aspectsapply to motion as well3 for every line, he says, either straight, or circular, or a mi&ture ofthe two. ;or this reason there are three species of motion=motion in a straight line, motion in a circle, andmi&ed motion *')5-. The images of the straight line and the circle are further related to cosmologicalfunctions, the line being related to the soul and the circle to the intellect and are also related to thefundamental ontological eo=platonic dynamic of procession, related to the line, and reversion, related tothe circle3


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enmattered. "wing to its affinity with the principles, the unit is simpler than the point, for thepoint, by having position, goes beyond the unit. 1nd additional determinants in the bodilessconcepts effect a lessening of being in the things that accept them. *(7-

Proclus responds by positing that the Pythagorean concept of place has multi=modal ontologicalmeanings, therefore the place on the point did not refer to a material plane of reality.'5In the same work, hedefends the Platonist conception of the ontological status of mathematical concepts, objecting to 1ristotlesabstractionist theory. 8e argues that *'- there is no precision in sense objects> *:- universal concepts are

better than particulars> *9- matter is not more honourable than the soul. Therefore the soul is not a blanktablet, mathematical principles are present in the soul.'7

6oreover, Proclus wrote a work titled"nesti#ation of the -bections by Aristotle to PlatosTimaeus, passages surviving in works by #implicius and Philoponus. 1ccording to #iorvanes3

Proclus concentrates mainly on the physical reasons why 1ristotles objections are false. 8edoes not appear to be concerned with the a priori part of the objection that derived from themathematics of contiguity. ?Proclus replies are highly systematic. 8e employs one basiccounter=argument to refute in a uniform and coherent manner 1ristotles different kinds ofcriticism. "ne of these core counter=arguments is that the sensible 4ualities arise from acombination of many geometrical properties, not just from one or two, as 1ristotle tried toargue. *:'/='(-

;rom the preceding considerations, one can see that Proclus and 1ristotle are almostdiametrically at odds on the 4uestions of the ontological status of mathematical and geometrical elements.Proclus gives an idealist e&planation for concepts which 1ristotle views in realist terms. onetheless, Idont think that this poses a problem for Proclus tacitly endorsing the parts of the 1ristotelian works that hisElements of Physicsare based on. 1ccording to $erson3 the corporeal x the divisible x themoved. Plausible as these may be in a eoplatonic ontological conte&t, they have no businessin a work like the Elements of Physics if they have not been argued for. *"psomer '(5-

'5onsidering ?ingsle$s pointed criti0ue of the Aristotelian accounts of 7re+Socratic philosophers,theres reason to think that 7roclus 7latonic interpretation of 7$thagorean mathematics ha#e a certaindegree of plausibilit$: since the publication of hernisss work on Aristotle and the 7resocratics in -*there has been a deeper awareness (@! of the fact that Aristotle and his school were fre0uentl$ capableof misinterpreting the 7resocratics at a #er$ fundamental le#el (*!.'7


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8owever, in the original 1ristotelian source, which is the final paragraph of the final book of thePhysics, and is a summary argument for the whole chapter,'/although the notion of the indivisibility of thePrime 6over has not been specifically argued for, the implicit association of incorporealty withindivisibility does seem to be 1ristotles view.

6oreover, as discussed earlier, it actually seems that there is less of a metaphysical focus andconcern with the Prime 6over than in 1ristotlesPhysics. The nature of the Prime 6over became a much=debated metaphysical and theological 4uestion in ancient *and modern- times revolving around its relation

to the unmoved mover in book II of 1ristotles/etaphysicsand 4uestions of creation and the capacity forinfinite power to act on finite continuum *#orabji :5)=/-. Proclus made a significant contribution to thedebate by positing that 1ristotle has argued that the Prime 6over is the final cause but not the efficientcause of the universe *#orabji-. Therefore, it may be than that he is making modest claims about the Prime6over in this work because he wants to keep that issue in a more strictly metaphysical conte&t andattempting a clearer separation between metaphysical and physical fields.

In terms of what degree of eo=Platonic influence can be found in the Elements of Physics, Ithink there are a few things that can be safely assumed. Even though the work is faithfully 1ristotelian incontent, it is plausible that certain eo=Platonic ontological influences are implicit in the way that thepropositions have been arranged. There may be a possible Platonic divisibleCindivisible thematic contrastbetween books I q II as well a contrast between rectilinear and circular motion. There may also be a moreontological orientation in the prevalence of propositions relating to the opposites of finiteClimited and

infiniteCunlimited. There may be a tendency to favour arguments influenced by the dialectical concepts ofPlatosParmenides.'(Aith these considerations in mind, it is probable that this work is not a simple1ristotelian te&tbook, but rather a compilation of 1ristotelian physical a&ioms of motion subtly re=arrangedaccording to eo=Platonic orientations.

IV

In terms of the historical impact and importance of the te&t, we have traces of its survival inmedieval Islamic philosophical circles. The first five propositions of 0ook I are 4uoted by the Dhristianstudent of 1l=;arabi, zahya Ibn 1di in a work on motion *Endress '7(=@'-. #ome short e&tracts are cited inanother te&t, credited to 1ristotle. Doincidently, it appears with passages from ProclusElements ofTheolo#y, of which a shortened, monotheistic adaptation, the0iber de Causis, attributed to 1ristotle, wascomposed in 1rabic *Pines, 1rabic :/@=:(9-.:)TheElements of Physicsseems to have moderately well

circulated in 6edieval Europe, as we have roughly two doen $reek and %atin manuscripts that have comedown to us, compared to the fifty or so surviving manuscripts of theElements of Theolo#y*odds 9-.

Proclus scientific works were some of the first of his to be printed *#egonds 9'(- and theElements was the object of a ;rench translation and commentary by ;rench mathematician Pierre ;orcadelin '575. 1ccording to ikulin3 !/ Cor that which eists inanother and re0uires a substrate can ne#er be self+generati#e, (6& 4-!/ 6#er$ eistent is related to e#er$other either as a whole or as a part or b$ identit$ or b$ di"erence.(6&;;!/ &here is no in5nite hea#inessor lightness. (67 II, ->!/ o sensuall$ percei#able bod$ is in5nite. (67 II, -!/ &he mo#er of eternal motionis eternal. (67 II, -=!/ &he unmo#ed is the leader of things mo#ing and mo#ed. (67 II, -!/ for 5nitepowers ha#e also 5nite energies: for energ$ proceeds from power (67 II, '-! (7ines, Arabic '=3+'*!.


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scientific works did not impact on scientific thinkers of the early modern period. 8is Commentary on theElements of Euclidwas appreciated by Dopernicus *#iorvanes :(/-, !epler:'and possibly ewton.::#ambursky optimistically remarks3


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;rom the preceding, one can see that Proclus held a certain scientific perspectives such as anappreciation for empirical accuracy, an awareness of the principle of "ckhams raor, and a healthy amountof skepticism. %ooking to theElements of Physicsone can appreciate the 4uasi algebraic logico=mathematical a&iomatic efforts, the formal organied concision, the greater clarity in separating the physicalfrom the metaphysical field, and the greater integration of astronomical concerns> elsewhere he notes3!:Hne could also cite his more nuanced #iew of the astronomical circular motion compared to Aristotle: As has been said before, the circle applies solel$ to the spheres of the 5ed stars, but the straight line(eutheia! to the generation, whereas the spiral is to the planets, combining both the cur#e (peripheries!and the straight line/ thus the mo#ements in latitude and depth are the paradigms of and the causesapproimates (prosecheis! to them mo#ements down here, that is the up and down and the sidewa$s(7roclus, In &im, *.=.3+-'! cf. Flo$d '>!


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hisPrincipium 1apientiae.:5In the passage below he gives a basic view pertaining to the motivations ofancient philosophers compared to more a more modern mentality3

It never occurred to the ancient 1tomists that the atomic theory of the ultimate nature ofthings could have any bearing on their further development. 1nd if it had occurred to them,Epicurus, at any rate, saw the pursuit of wealth a misuse of human energy as disastrous as thepursuit of power. "ne reason why the ancient 1tomists took not a single step towards thetechni4ue of modern science was that the practical motive, which has driven science to create

that techni4ue in the centuries since $alileo, was foreign to their minds. This is also thereason why they never tried to ascertain the laws of motion, the dominating concern ofscience in the si&teenth and seventeenth centuries. If you want to control ature, these lawsare the first thing you need to understand. Epicurus was not seeking to control or to e&ploitature> for an accession of power and wealth would only have upset that peace of mindwhich he found in the simplest possible manner of life. If the happiness you desire can bestbe obtained by living on bread and water and wearing a homespun shirt, the sight of steamagitating the lid of a boiling kettle will not impel you to invent the steam=engine, the power=loom, and the tractor. *Dornford '/-:7

In addition, he perceptively e&plores the notion of the role of the interaction between naturalphilosophers and medical practitioners in the development of scientific thought3

The clue leading us to the origin of this theory is furnished by the medical writers of the8ippocratic corpus. In particular, the author of the treatise "n 1ncient 6edicine, who mayhave been 8ippocrates himself, was clearly conscious of a profound opposition between thedogmatic method of the natural philosopher and the empirical method of the physician. 8isprotest against the importation of the philosophers procedure into his own art of healing isilluminating. *9'-*?-Ahat now concerns us is the fact that the physician approached the4uestion of the nature of man as it were from below, advancing towards it from what seemedto him the certain facts observed in particular cases. It was at this point that medicine cameinto conflict with natural philosophy, which had reached its theories of mans nature from theopposite 4uarter, descending to it from above. *9/-

Id like to take this observation and posit the general notion of a complementary productivedialogue between natural philosophers and practical scientists. 1t the same time I posit that the philosophers

deductive oriented thinking and the doctor or the astronomers more inductive approach are complementaryfacets that allowed scientific disciplines to develop a coherent field of theoretical knowledge and practicalscientific method. To a certain e&tent these conditions roughly correspond to the re4uirements of thePlatonic and 1ristotelian scientific programs. The most productive situations for scientific progress wouldthen depend on a reasoned balance between theoretical and practical development and a productiveinteraction between the two areas.:@

%ooking at how this notion plays out in the historical situation in 4uestion, compared to1ristotles time, Proclus had the advantage of the more developed state of practical science in the

:51dmittedly, this is a posthumously edited work that seems to have had little academic impact.:7


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8ellenistic period>:/however by Proclus time this period of practical scientific research had beenstagnating for the past two centuries.:(Aith the closing the 1cademy a generation away and the onset of asocial=political decay that would lead to the period of the dark ages with the ne&t few centuries, Proclus wasfaced with the necessity of a conservative stance, which most likely influenced his massive synthesiingproject of organiing aspects of the entire $reek philosophical tradition into a perennialist vision.9)Aith thepossibility of productive interaction with practical scientific research very limited, the large volume ofProclus writings could attest to the idea that, by necessity, the more theoretical side had a predominance

over the practical research prerogatives.9'

onetheless, this conservative stance did not necessarily stifle his$reek tendency for individual, original intellectual activity. ;or e&ample, as 6ueller observes3


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Even though this short work has not been considered to have a significant importance in thehistory of science *ikulin :)9-, however I think it does have interest in terms of the logical andepistemological aspects of theoretical science. "ne can point to the 1ristotelian rational formulation of theisomorphic relation of the time, space and motion continuum is, by=and=large, even in our hyper=speededmodern society, still the way we understand and communicate our perception of spatio=temporal reality.The te&t can be seen to articulate the preliminary fundamental conceptual notions necessary for developinga scientific apprehension of the nature of motion as it e&ists in nature. 6ichael 1ugros recently gave a

lecture at 6IT on the importance of what he terms N is Ktwice ascoldL as M->N. Hr, if we are prone to imagining that natural 0uantities beha#e 1ust like mathematicalones, we might think it self+e#ident that there is no such thing as a greatest speed (Augros -4!.


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Works consulted

1ncient 1uthors

Aristotle. On the Heavens. transl. 9. ?. . )uthrie, transl.. Fondon : Ear#ard Oni#ersit$ 7ress, -*.7rint.

Aristotle. On the Heavens I & II.. transl. S. Feggatt, transl.. 9arminster : Aris P 7hillips, -. 7rint.

Aristotle, Phsics, Qoe Sachs (trans.!, Gutgers O. 7., -.

Aristotle. Phsics I. transl. 7. E. 9icksteed P C.


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lear$, Q. Q., 7roclus 7hilosoph$ of -'!: *=+4-*. 7rint.

6ndress, )erhard. Wah$a Ibn Adis rit0ue of Atomism &hree &reatises on the the Indi#isble 7art,6dited with an Introduction and otes.:eitschri$t $;r Geschichte des rabisch/Islamischen+*-=. 7rint.

ikulin, imitri. Y7h$sica


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7ines, Shlomo. Hmne 0uod mo#etur necesse est ab ali0uot mo#eri: A refutation of )alen b$Aleander of Aphrodisias and the &heor$ of >!. -+;. 7rint.

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