Australasian Journal of Philosophy Volume 80 Issue 3 2002 [Doi 10.1080%2F713659466] Baltzly, D. -- What Goes Up- Proclus Against Aristotle on the Fifth Element

7/22/2019 Australasian Journal of Philosophy Volume 80 Issue 3 2002 [Doi 10.1080%2F713659466] Baltzly, D. -- What Goes

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Australasian Journal of PhilosophyVol. 80, No. 3, pp. 261287; September 2002

WHAT GOES UP:

PROCLUS AGAINST ARISTOTLE ON THE FIFTH ELEMENT

Dirk Baltzly

The Athenian neoplatonist Proclus (c. 410485) is not regarded by most analytically

inclined philosophers as one of antiquitys better minds.1 After all, the work of Proclus

with which most people are acquainted is the Elements of Theology.2 While one might

admire its attempt at rigour in the 211 numbered propositions and their proofs, most

contemporary philosophers will find the premises in these proofs pretty unlikely.Moreover, the resulting metaphysical edificewith its various levels of entities from

transcendent One to unqualified matteris fairly alien to our more naturalist ontologies.

I barrack for the St Kilda Football Club, so it should come as no surprise that I like to

see the rehabilitation of the downtrodden and underappreciated. In what follows, Ill argue

that some of Proclus arguments are at least as worthy of our attention as one of

Aristotles most celebrated arguments in natural philosophy. Part of what we admire about

Aristotle is the methodology and cleverness. He proceeds in a way we approve of, first

identifying the problems that arise when we survey the platitudes about a topic and then

clearing away many of these by drawing distinctions among the various senses of words.He typically offers a theory and tries to justify it by showing that it is better than its

competitors at saving the appearances. Even when Aristotle gets to the wrong conclusion,

we still find that he does things that we regard as methodologically virtuous in the

process.

261

1 There are, of course, exceptions to this general rule. A number of analytically inclined

philosophers, who are also first-rate historians, have done a great deal to rehabilitate neoplatonistphilosophy generally and to show that it is not all mystical mumbo-jumbo. These include

A.C. Lloyd (whose book, Anatomy of Neoplatonism, provided exactly thata look at the logical

principles that are consistently applied to generate neoplatonist metaphysics) and Richard Sorabji

(whose many books on ancient science extracted and explained some of the very best in the naturalphilosophy of the neoplatonists). This paper is a small contribution to this ongoing project.

2 In part this is because ET provides an overview of the structure of neoplatonic metaphysics. It is

also one of the four works of Proclus for which there is a reliable English translation (Dodds

(1963)). The others are Proclus commentary on the Platonic (?) First Alcibiades (ONeill (1965)),

the commentary on Book I of Euclids Elements (Morrow (1970)) and, most importantly, the

Commentary on the Parmenides of Plato (Morrow and Dillon (1987)). Proclus other survivingPlato commentaries have been translated into French: in Timaeum (Festugire (19668)); in Rem

Publicam (Festugire (1970)). Likewise for the massive Platonic Theology (Saffrey and Westerink(1968)), and the shorter essays Ten Doubts on Providence (Isaac (1977)), On Fate (Isaac (1979))

and On the Existence of Evil (Isaac (1982)). The only English versions of these works are the not

entirely reliable translations of the 18th19th century Platonist Thomas Taylor. Taylors English is

pretty literal and thus a bit hard to follow unless you have a very good idea of the context. More

importantly, he was working from a corrupt text of Proclus Greek. A new English translation ofthe Timaeus commentary is currently in preparation through an ARC funded project involving

Harold Tarrant, David Runia, Rick Benitez, John Bigelow and me.


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In this paper, I consider Proclus arguments against Aristotle on the composition of the

heavens from the fifth element, the aether. Proclus argues for the Platonic view (Timaeus

40a) that the heavenly bodies are composed of all four elements, with fire predominating.

I think that his discussion exhibits all the methodological features that we find admirablein Aristotles largely a priori proto-science. Proclus treatment of the question in his

commentary on Platos Timaeus also provides the fullest statement of a neoplatonic

alternative to the Aristotelian theory of the elements. As such, it forms a significant part of

a still largely underappreciated neoplatonic legacy to the history of science.3

I. Context: the harmony of Plato and Aristotle

according to the neoplatonist schools

The neoplatonist schools of Athens and Alexandria in late antiquity had a strict linearphilosophical curriculum. The works of Aristotle were regarded as an introduction to the

higher mysteries of Platos dialogues.4 Of the latter, the Timaeus and the Parmenides were

regarded as the most advanced lessons. The neoplatonists taught that Plato and Aristotle

were in agreement about most things, though there were divergent opinions among them

about the exact extent of this agreement.5 The story of these hermeneutic twists and turns

has been told by others.6 In what follows I am interested in a topic on which even the

neoplatonists saw that it was impossible to reconcile Aristotle and Plato completely. In

the Timaeus, Plato says that heavens are composed of all the elements, but with a prepon-

derance of fire. Aristotle, by contrast, claims that the heavens are composed of a fifthelement: the aether.

In his commentary on Platos Timaeus, Proclus argues against Aristotles view of the

elements generally and against the fifth element in particular. He does this by criticising

Ocellus book On Nature. Ocellus was a Pythagorean who actually pre-dated Aristotle (if

he existed at all, that is). The work On Nature, however, is a forgery of the Hellenistic

period which presents Peripatetic views as Pythagorean natural philosophy.7 It is unclear

262 What goes up: Proclus against Aristotle on the fifth element

3 Many of Proclus contributions to natural philosophy are surveyed in Siorvanes (1996). The present

paper adds to what Sirovanes has done by specifically addressing some striking methodologicalparallels between Proclus and Aristotle.

4 Westerink (1962), ch. 26. Proclus was a particularly apt pupil. He received education in

mathematics and Aristotelian logic in the neoplatonist school at Alexandria. At the age of 19, he

came to Athens where Syrianus was head of the Academy. He was regarded as so gifted thatthe retired head, Plutarch, took him on as a special pupil. Cf. Marinus, Life of Proclus, ch. 10

(K.S. Guthrie and Fideler (1986)) and Diller (1957).5 The views found among the neoplatonists are summarised in Sorabji (1990), 3. No doubt this

strikes most of us as a very strange thing to think. After all, it is clear to us that Plato and Aristotle

are in sharp disagreement about a number of matters, particularly in the area of metaphysics. The

neoplatonists, however, read both authors through the filter of a complex hermeneutic theory whichminimised or eliminated what we regard as difference of opinion. For example, Aristotles

Categories was not thought to be a work about ontology, but rather about simple significant wordsin as much as they signify things (Porphyry, On Aristotles Categories 58, 58). As such, it did not

present a view about the primacy of particulars over universals that would be incompatible with

Platonism.6 In addition to the essays in Sorabji (1990), see also Blumenthal (1996); Coulter (1976); Lamberton

(1986); Ppin and Saffrey (1987); Sheppard (1980).7 See Thesleff (1961) and Beutler (1936). The Greek text of Occelus is available in Thesleff and an

English translation can be found in K.S. Guthrie (1987).


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whether Proclus knew that the work was a forgery. Proclus rejects the Aristotelian

arguments for the composition of the heavens by aether and replies to criticisms of the

Platonic view. He concludes by offering a way of showing that the apparent difference

of opinion between Plato and Aristotle on this question can be seen as a mere matter ofterminology.

II. Aristotle on the composition of the heavens

Aristotles central argument for his view on the composition of the heavens is intertwined

with his theory of the elements and natural place. On the Heavens I.2 begins with a

division of local motion into simple and compound kinds. There are alleged to be only

three kinds of simple motion: motion upward, motion downward and motion in a circle.

Other forms of motion, he claims, are a composite of these three basic kinds. The reason

that motion upward, motion downward and circular motion are the only simple kinds is

because there are only two kinds of simple magnitude: the straight line and the circle

(Cael. 268b1720).

These simple motions are then correlated with the simple bodies. The latter are bodies

which have an innate or natural origin of motion. Though the Physics would include living

things among the class of objects that have such an internal principle of motion, in On the

Heavens Aristotle confines his attention to inanimate natural bodies and specifically the

elements. The structure of Aristotles argument is open to dispute. I take it to be best

thought of as an existence proof, followed by an inference to the best explanation.

1. There are simple bodies.

2. These simple bodies possess natural motions.

3. The natural motions of simple bodies are themselves simple.

4. A simple body has only one natural motion.

5. For every simple motion, m, there is at least one simple body whose naturalmotion is m.

6. Circular motion and motion in a straight line are the only kinds of simple motion.

7. There are two simple bodies whose natural motions are upwardfire and air.

8. There are two simple bodies whose natural motions are downwardearth and

water.

9. So there exists a simple body whose natural motion is circulara fifth element in

addition to earth, air, fire and water.

10. The heavens move with a natural circular motion.

So, probably, the heavens are composed of another simple body different from the four

elementsthis body is aether.

Dirk Baltzly 263


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This, at least, is the barest form of the argument. Aristotle attempts to buttress it in

various ways. He argues against the possibility that the heavens are moved with a forced

motion contrary to the natural motion of the simple body from which it is composed. No

force could prevail continuously and eternally against a simple bodys natural motion(269b6; 286a20). Nor can the heavens be a composite body with a composite motion that

happens to be circular. First, the motions of composite bodies are determined by their

constituent simple bodies (269a28). Moreover, though such a composite motion is not

contrary to a things natural motion (para\ fu/sin), it is nonetheless not according to its

nature (ou) kata\ fu/sin). But that a thing should be moved in a circular fashion continu-ously and eternally and yet that this should fail to be according to its nature is also

absurd.8

There is more that can be said about the details of this particular argument and its

supporting arguments. In the next section, however, I want to consider some of the general

methodological features of Aristotles treatment of the topic that make it worth our

attention. I think that there are four kinds of things that Aristotle does in his discussion of

the composition of the heavens that make it a fine example of ancient Greek natural

philosophy, even if we think that his conclusion is wrong.

A. The extension from established science

Aristotles argument connects simple magnitudes with simple motions. Simple motions, in

turn, are connected with simple bodies. The De Caelo 268b18 passage is the only place in

the corpus where Aristotle talks about simple magnitudes (mege/qh a(pla=). There are,however, some suggestions that the circle and straight line occupy a special place in the

mathematics of Aristotles day. Aristotle tells us that the Pythagoreans distinguished the

straight and the curved (Metaph. 986a25, cf. Republic X, 602c). Apart from this, however,

we have no independent reasons offered for the claim that the straight line and the circle

are the only two simple magnitudes.

Aristotle does attempt to connect the associated premise about three simple motions

with his earlier discussion about the mathematical principles of body generally. In the first

chapter ofOn the Heavens, Aristotle argues that the study of nature is concerned primarily

with bodies and their motions. Moreover, it is concerned with continuous bodiesthat is,three-dimensional solids that can be divided in respect of any of these dimensions. So the

study of nature has a subject matter distinct from the line (which is magnitude that can be

divided in one way only) or the plane (which is two-dimensional magnitude divisible in

two directions). He even invokes the Pythagorean claim that the whole world and

everything in it is summed up in the number three. All this is done in support of the first

premise in the argument abovethat there are three kinds of simple motion.

Now revolution about the centre is circular motion, while the upward motion and

downward movements are in a straight line, upward meaning motion from the centreand downward motion towards it. All simple motion then is motion either away from


8 I take it that this is the sort of argument that Aristotle ought to be mounting at 269a33. It is not

so clear that he doesnt tangle up contrary to nature with not according to nature. See

W.K.C. Guthrie (1971), ad loc.


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or towards or about the centre. This seems to be in exact accord (h)kolouqhke/naikata\ lo/gon) with what we said above: as body found its completion in threedimensions, so its movement completes itself in three forms (268b2026, trans.

Stocks).9

Now, we may think that the mathematical theory with which Aristotle tries to connect

his account of simple motion is flawed. But even so, we can see that Aristotles method -

ological instincts are sound. One good way of arguing for a new theory in one domain is

to show that it is consistent with established theories in other, related domains. Indeed, if

one can show the new theory is not merely consistent with, but just what one would expect

given the older, more established theory, then so much the better.

B. Extending the role of entities or principles within ones own theory

The same relationship obtains between Aristotles argument for the fifth element here in

De Caelo and his theory of natural place generally. The idea of natural place is one that

does other work for Aristotle. For example, it allows him to explain the characteristic

motions of different compound bodies (Gen et Cor II.8) and allows him to declare void

explanatorily superfluous since natural place accounts for motion (Phys. IV.8, 214b14).

Thus, when he invokes the doctrine of simple motions to the natural places of the

elements in his argument about the composition of the heavenly bodies, he is extending

what he has reason to regard as a successful theoretical posit to a new application. By

doing this he promotes theoretical virtues such as simplicity and generality.

C. Criticising competing theories

Aristotle also argues for his own view about the composition of the heavens by attacking

competing views. One view is that it is not only the stars and planets that are composed of

fire, but also that in which they are situated. In On the Heavens II.7 Aristotle argues

against this view by claiming that the phenomena do not uniquely support the view that

the stars and planets are made of firethe heat and light of the sun and stars does not

necessitate that they are composed of fire. Thus the generalization to the case of what theyare situated in is not warranted either. Ill discuss Aristotles alternative explanation of

this heat and light below.

When we turn to the less well-known Meteorologica Aristotle argues directly against

the view that the heavens generally are made of fire. He says that if the intervals

[between the various heavenly bodies?] were full of fire and the bodies [i.e. the stars and

planets] also consisted of fire, every one of the other elements would long ago have

vanished (Meteo. I.3, 340a1). All that fire would have destroyed everything down here.

His next target seems to be a two-element view according to which the stars and

planets themselves are composed of fire, but the intervals between them are filled with air.

This view is unacceptable for similar reasons. The amount of earth and the water down

here in the sublunary sphere would be tiny in comparison with the amount of air necessary

Dirk Baltzly 265

9 Unless otherwise noted, translations from Aristotle and Plato are taken from Barnes (1984) and

Cooper (1997).


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to fill the vast spaces between the stars. But when an element like water is transmuted into

air, it is not the case that an enormous amount of the latter is produced from a small

amount of the former. So if there were so much air in the intervals between the stars, the

elements would not be in proportion to one another. Aristotle thinks that this argument canbe made to work even if one denies that the elements can be transmuted into one another.

It is sufficient, he thinks, if some quantity of element A is equal in power to some quantity

of element B.10

It is a bit unclear whether either of these arguments counts against Platos position in

the Timaeus because it is so unclear what that position actually is. At 39e40a Timaeus

says that the Demiurge tried to reproduce the forms that are contained within the paradigm

from which He is workingthe Living Being itself. In pursuit of this aim, He makes the

heavenly race of gods; winged things that dwell in the air; things that live in the water;

and things that live on dry land. Timaeus then says:

The gods He made mostly out of fire, to be the brightest and fairest to the eye (40a24,

trans. Zeyl).

It turns out that Timaeus is primarily discussing the fixed stars, though perhaps also the

planets (40b). It is less clear that he has anything at all to say about the composition of the

celestial regions in which these bodies are situated. It must be full of something, since the

Timaeus denies that there is void (58a).

Even if Platos view on this matter is unclear, Proclus and the neoplatonists take him to

hold the view that the heavens as a wholeand not merely the fixed stars and planets

are composed primarily of fire.11 So, from their point of view, Aristotles objection ought

to seem like a serious one. Given the size of the sphere of the stars, if it is mostly fire up

there, then it is a bit of mystery why we arent all burned to a crisp.

D. Meeting obvious objections to your own theory

There is an obvious problem for Aristotles view that the heavens are composed of

aetheran element wholly unlike the other four. Surely we have very good empirical

evidence for the claim that at least one of the heavenly bodies is composed of fire, for how

else can we explain the suns heat?

Aristotle was aware of this problem and addressed it both in On the Heavens II.7 and

also in the less well-known Meterologica I.3. His solution is that the motions of the

heavenly bodies generate friction in a layer of fire-like material located below the inner

boundary of the aether. The atmosphere up to the level of the moon is not actually a

simple layer-cake of pure air and then pure fire. The place of pure fire, or even its

existence, in the Meteorologica is a bit hard to pin down.


10 Aristotle also discusses the question of the proportion of the elements in Gen et Corr. II.6. There

are some interpretive issues about the details of the argument here in the Meteorologica. These

need not concern us here, but see the discussions of Alexander Aphrodisias and John Philoponus in

their respective commentaries.11 in Tim. II. 47,15, a passage that I will discuss in more detail below.


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Immediately around earth and water are air and what we are accustomed to call fire

(o dia\ sunh/qeian kalou=men pu=r), though it is not really fire; for fire is an excessof heat and a kind of boiling (zesij). But we must understand that of what we call air,

the part which immediately surrounds the earth is moist and hot because it is vaporousand contains exhalations from the earth, but the part above that is hot and dry (Meteo.

I.3, 340b224, trans. Lee).

This hot and dry exhalationthe u(pe/kkauma or fire sphereis highly inflammableand the motion of the sun is able to ignite it. When it does this, we get a flame (flo/c)

which is really a boiling of dry air (pneu/matoj chrou= ze/sij, Meteo. I.4, 341b23). Thesun is able to do this because its motion is both rapid and relatively close to the layer of

flammable stuff. The moon, of course, is closer but moves too slowly to spark it off. The

stars are wheeling around at a tremendous rate, but they are too far away (Meteo. I.3,341a1932). Aristotle supposes that the general idea that rapid motion produces heat gains

empirical support from the (purported) fact that lead balls are heated and sometimes even

melted when they are fired as missiles.12

III. Options for criticising Aristotles view

In this section I want to consider some possible avenues for rejecting Aristotles view on

the composition of the heavens. Some of these will not be open to a neoplatonist like

Proclus, because they involve calling into question aspects of Aristotles philosophy withwhich the neoplatonists agree. Reviewing some of the criticisms made by Aristotles

successors also allows us to see Proclus critique in its proper historical context.

A. Natural Place

The argument of De Caelo I.2 relies heavily on the idea of the natural motions of the

simple bodies. Aristotle supposes that these motions are explained (in part at least) by the

influence of natural place and one might well have serious reservations about this latter

view. In fact, it was criticised by Aristotles successors in the Lyceum. In some instances,

this criticism was coupled with a rejection of the existence of the fifth element.Aristotle comes close to attributing to place a power to contribute to motion. In the

context of developing aporia about place, he says:

Furthermore, the locomotions of the elementary natural bodiesnamely, fire and earth

and the likeshow not only that place is something, but also that it exerts a certain

influence (tina\ du/namin). Each is carried to its own place, if it is not hindered, theone up, the other down (Phys. IV.1, 208b812, trans. Hardie and Gaye).

When we think about the movement of fire upward or earth downward, it is difficult tosay whether the origin of this motion is an aspect of the nature of fire or earth, or some

Dirk Baltzly 267

12 W.K.C. Guthrie (1971) ad loc notes that this extraordinary notion seems to have been widely held

in antiquity. He cites Lucretius VI, 178; Seneca, Nat. Quest. II.57.2; Ovid, Met. II, 727; XIV, 825;

Virgil, Aen. IX, 588.


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influence that is exerted by the limit or the centre of the cosmos. Within Aristotles own

school Theophrastus (c. 372288) may have rejected the idea that the natural place of the

elements exerts an influence on them. Rather, what fire and earth want in their natural

movements is to be in the right relation to one anothernot in relation to the positions inthe cosmos that we take to be their natural place.

Theophrastus too appears to have had this conception of place in his Physics when he

continues his account in the form of a puzzle and says:

Perhaps place is not an existing thing in its own right (ou)k esti kaq au(to\n ou)sia

tij to/poj), but we speak of it because bodies have an order and position through their

natures and powers. And similarly in the case of plants and animals and in general of

non-homogeneous things, whether animate or inanimate, if they have a nature that

exhibits form. For in these too there is an order and position of parts in relation to the

whole thing (kai ga\r tou/twn ta/cij tij kai qe/sij twn merwn e)sti pro\j th\nolhn ou)sian). And this is why everything is said to be in its own space through

having proper order. For each part of the body would also desire and demand its space

and position (Simplic in Phys 639,1322; trans. after Sorabji (1988)).

The rejection of the causal influence of place on the motion of the elements need not

by itself undermine the argument of De Caelo I.2. One could still insist that the heavens

are not composed of any of the four elements which have a natural rectilinear motion, on

the assumption that the celestial motion is itself natural. However, the rejection of natural

place undermines the idea that there is a place where fire is naturally in a state of rest. On

Theophrastus account, fire ceases its upward motion when it gets into the right relation to

the other elements by getting on top of them. Changes in their position relative to it would

make it conceptually possible for fire to be perpetually in motionjust as the aether

allegedly is. This concession becomes important as the controversy unfolds in antiquity.

Strato of Lampsacus was Theophrastus successor as head of the Lyceum. He

disagreed with Aristotle on at least three points. First, he rejected Aristotles general

conception of the place of an object as the inner boundary of that which contains the

object (cf. Aristotle Phys. IV.4). It seems likely that he was motivated by the puzzles that

Theophrastus raised about Aristotles theory of place.13 Next, he repudiated Aristotles

views on natural motion and accepted an Epicurean view according to which all things

tend downward by virtue of their weight.14 This is equivalent to a rejection of the doctrine

of natural place, even when the latter is understood merely as a way of talking about the

powers of the simple bodies themselves. Finally, he apparently rejected the fifth element

and claimed that the heavens were made of fire.15 None of our evidence indicates the

relation between these three deviations from Aristotles physical theory, but we may

speculate that it results from a wholesale rejection of the doctrine of natural place and the

views associated with it.


13 Reported by Simplicius in his Physics commentary, 645, 5 ff and discussed by Sorabji (1988) and

Sambursky (1962).14 Simplicius, in Cael. 267, 29.15 Reported by Stobaeus, Eclogae (ed. Wachsmuth) I. 200, 212.


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This strategy for criticising Aristotles account of the composition of the heavens is not

one open to a neoplatonist like Proclus. In general, the neoplatonists did not want to reject

Aristotles notion of natural place. In fact, Iamblichus took the doctrine of place even

further than Aristotle himself did. Unlike Aristotle, Iamblichus clearly states that the placeof an object exerts a phyiscal power which holds that object together.16 My particular

place (i/)dioj to/poj) moves with me wherever I go and keeps the matter from which I am

composed from spreading out in an unseemly fashion.17 So, on Iamblichus view, it is not

only the natural places of the elements that exert a causal influence on bodies, but other

places as well.

Proclus follows Iamblichus in making place or space dynamic in this sense. In

particular, he thinks that the place of the whole cosmos is an immaterial body that inter-

penetrates everything.18 He equates it with the super-celestial light of the myth of Er in

Republic Book X. Proclus views on the nature of space are themselves novel and tightly

argued, but they have been discussed at length elsewhere. I raise the issue because of

the role that natural place plays in Aristotles argument concerning the composition of the

heavens. One strategy for rejecting that argument is to reject the whole idea of natural

place. But this is not an option for Proclus or the other neoplatonists since they accept a

version of that doctrine far stronger than Aristotles own conception.

B. Simple natural motion

Criticism within the Lyceum of the doctrine of the aether culminates with the book of

Xenarchus (2nd C. BC) called Against the Fifth Element. Fragments of this work arepreserved in Simplicius commentary on Aristotles De Caelo. Sambursky provides a nice

discussion of most of the fragments, but one in particular is relevant to subsequent

arguments from Proclus.19 Xenarchus attacked the idea that the circular motion of the

heavens required a separate element different from fire.

Rectilinear motion is natural to none of the four elements when they are actual (kata\

fu/sin), but only when they are coming to be so. Something which is coming to bedoes not exist unqualifiedly (ou)k estin a(plwj), but is between being and not being.

. . . For this reason we do not say that the fire which moves upwards is properly called(kuri/wj) fire, but is coming to be fire; and that when it is in its proper place and has

risen above everything else and come to rest, then it will have come to be fire properly.

. . . So in the case of the simple bodies it is just false that there is simple motion . For it

has been shown that the motion is an accident not of that which is, but of that which is

coming to be. Therefore if it is necessary to assign some motion to things when they

are, and if this motion is to be simple, then it is requisite to assign them circular

motion. There are, after all, only two simple motionsrectilinear and circular. But

Dirk Baltzly 269

16 Reported by Simplicius, in Phys. 640,11117 Simplicius connects this further development with Iamblichus (in Cat. 361,7362, 33; in Phys. 629,

812) and also with Proclus successor, Damascius (in Phys. 624,35 ff.).18 Proclus views on space as an incorporeal body have been extensively discussed in the secondary

literature. See Sambursky (1982); Sorabji (1988); Schrenk (1989); Schrenk (1994); Siorvanes

(1996).19 Sambursky (1962), 12232.


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rectilinear motion belongs to the four elements when they are in a state of becoming

(h( de\ e)p eu)qeiaj ginome/nwn e)stin) but not when they are in a state of being(a)ll ou)k ontwn twn tessa/rwn). So, it wouldnt be absurd to assign circular

motion to fire and rest to the remaining three (Simplicius, in Cael. 21, 3522,10).

In this passage Xenarchus rejects a crucial premise in Aristotles argumentthat for

each simple body there is one and only one natural motion. But he also goes further in

suggesting that at different levels of actuality, simple bodies may have different natural

motions. This is a suggestion that will loom large in Proclus treatment of the kind of fire

that composes the heavens. But Proclus does more than simply take this idea on board.

Note that Xenarchus offers no justification for the idea that fire in its fully actual state has

a circular motion, while the natural motion of the other three elements in a state of being

is, rather perversely, a state of rest. It requires a theory of the elements to motivate thisassignment of motions to them. Proclus goes beyond Xenarchus criticism in providing

such a theory.

C. The fire sphere

Aristotles explanation for the suns heat was also criticised from a variety of points of

view prior to Proclus.

Aristotles theory of the comets and shooting stars involves not only the presence of

the fire sphere, but also the claim that it is carried around by the rotation of the aetherial

sphere immediately above it (Meteo. I.7, 344a913). It seems ad hoc to insist that theheavens must be composed of something other than fire on the ground that they move

eternally in a circle if one then posits a form of fire that does exactly that. 20 Even a

dedicated Aristotelian like Alexander of Aphrodisias finds that there is a genuine problem

about the motion of the fire sphere. How shall we regard it? As a natural motion? As a

forced motion, but one that is nonetheless eternal? He writes:

What is the power that comes to be from the movement of the divine body for the body

adjacent to it which is mortal and coming to be? Is this some nature other than the

proper [nature] of each of the natural bodies which we say is a principle of motion and

of rest to that to which it belongs? (Questiones II.3, 47,3048,1, trans. Sharples

(1992).)

Alexanders own answer to this question is not one that can be stated simply. What is

important for our purposes is that the neoplatonists generally did not reject the idea of the

fire sphere itself. As we shall see, they thought that the heavenly bodies were composed of

fire, but denied that their fire had heat as an essential property. Thus they too employ the

mechanism of the fire sphere.21 Their solution to Alexanders problem was to introduce


20 Cf. Xenarchus as reported by Simplicius in Cael. 20, 24 ff.21 Proclus ascribes a view at least consonant with Aristotles fire sphere to Iamblichus ( in Tim. I. 117,

24). The exception, as usual, is Philoponus. Not only does he emphatically reject the fifth element,he supposes that the fire from which the heavens are composed is importantly similar to the fire

down here. This explains the suns heatnot the fire sphere (Philoponus, in Meteo. 49, 2234).

This is a claim that his orthodox, pagan opponent Simplicius clearly rejects (in Cael. 66, 3367, 5;

88, 2834; 90,1318).


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another category of motion. The eternal circular motion of the fire sphere is neither natural

nor unnatural. Rather it is supernaturalas befits its contact with the more divine forms of

elements in the heavens.22

One final point about the controversy over the fire sphere is relevant for our discussionof Proclus. There is confusion among the commentators about whether terrestrial fire or

the hot, dry exhalation of the fire sphere is (or is closer to being) elemental fire. One might

suppose that the fire in the fire sphere is closer to being elemental since Aristotle says that

it is the most inflammable (Meteo. I.4, 341b24). Another reason to suppose that the fire

up there is more elemental is the fact that terrestrial fire needs fuel. This point had

already been used by Theophrastus to call into question its status as an element, for

elements surely ought to be able to exist by themselves. 23

In any event, if we assume that the fire in the fire sphere is more elemental, then there

is a puzzle about why the fire down here is hotter than elemental fire. 24 Recall that the fire

sphere does not boil until it is ignited by the passage of the Sun. So although the portions

of it that are thus ignited may be hotter than the fire in your barbecue, on the whole the hot

and dry exhalation is not hotter than terrestrial flame. In his response to this problem,

Alexander argues that the greater degree of heat possessed by terrestrial fire is to be

explained by the greater degree of mixture with matter.

The idea that the qualities that we associate with the elements as we know them here

result from the admixture of matter turns out to be one that Proclus employs to great

effect. Nor is the idea one that is utterly unmotivated empirically. Alexander uses the

example of red hot iron which is hotter than ordinary flame. Its not that there is more

coldness mixed in with the flame than with the red hot poker. Rather, Alexander says, the

intensification [of heat] in the iron results from the solidity and unyielding [quality] of the

matter (Quaest. II.16, 62, 23, trans. Sharples (1994)). Of course, we moderns would not

describe a hot poker as a case in which fire mixed with the iron. But from the point of

view of ancient science, this seems quite a reasonable thing to say.

Having surveyed some of the objections that were raised against Aristotles doctrine of

the fifth element prior to Proclus, we are now in a position to turn to his account of the

matter and see how innovative it is.

III. Proclus dialectical development of his positive view

Aristotle characteristically develops his own position on a topic by first framing the

puzzles or aporiai that common sense raises about the topic. He then reviews earlier

theories and their shortcomings in addressing these problems. Finally he develops his own

view as one that incorporates such positive insights as have been found in the earlier

theories. Just like Aristotle, Proclus works up to his most explicit statement of his view (in

Tim. II. 42, 9 ff.) by discussing the views of predecessors. He begins by noting that there

are disagreements among them on this question. His account of the history of the questionis oddbut perhaps no odder than some of Aristotles accounts of pre-Socratic

Dirk Baltzly 271

22 Simplicius in Cael. 21, 2325.23 Theophrastus, de Igne 49.24 Alexander Quaestiones II.17, trans. Sharples.


12/27

philosophy.25 The moral Proclus draws is that there are good reasons to try to preserve

both the claim that a) the whole cosmos is composed out of the four elements and yet

b) the heavens have a different substance or essence (ou)si/a). Proclus enumerates the

possibilities and argues by elimination.

For it is necessary that either: (1) The heavens are composed of a fifth element entirely

different from the four elements, as some say, or (2) They are made of [all of] the

four elements, or (3) They are made of some particular one of the four elements, or

(4) They are made from more than one [but not all four]. Further, if they are composed

of the four elements then either (2a) they have the same form as the sub-lunary

elements or (2b) they have a different form.

But if (1) the heavens are composed ofsomething other than the four elements, how isit that Plato says that the entire cosmos is composed from these four (32b48)? And if

(3) it is made from just one of the four, how can he say a bit later (40a2) that the stars

are for the most partfire? And if (4) it is composed of more than one [but not all], how

will it not be imperfect or incomplete by not having all things while even the Earth and

generally the things below the moon do have all the elements? (in Tim. II. 42, 2843, 9.)

Contemporary readers may be somewhat disappointed with the arguments against

options (1) and (3). Surely, it will be said, Proclus is rightly ranked as a second-rate

philosopher because he is so prone to such superficial appeals to Platos authority. But itis important to remember the context of the work before us. Proclus Timaeus

commentary presents lectures to a group of students who have already progressed through

most of the neoplatonic curriculum. They, presumably, have seen enough to find the fact

that Plato says x good evidence for x. In any event, Proclus does in fact provide better

arguments against (1)which is Aristotles viewas well as (3). An argument against the

view that it is composed of only one of the four elements emerges from Proclus further

consideration of (2):

But on the other hand, if (2) it is composed of all of them, how will it be that thecomposite out of these that exists up above is indissoluble while composites of the four

elements here below are subject to dissolution? For it will not be indissoluble because

the four elements in the heavens have equal dominion, since if they had equal

dominion, where would the diversity [seen in the heavens] come from? Moreover, if

there were equal dominion among the elements, how is that Plato says that up there

things are for the most part fire? And if it is composed out of others, how is it that

though it is a composite it is moved with a simple motion? (in Tim. II. 43, 920.)

The argument against the view that there is equal dominion among the four elements inthe heavens can also be turned to an argument against (3)the claim that there is only one


25 See Festugire (196668) ad loc for an account of some of the difficulties with the text. The locus

classicus for criticisms of Aristotle as an expositor of his predecessors views is, of course, the

work of H.F. Cherniss.


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of the four elements up there. The problem is the diversity of appearances in the heavens.

Some parts of the heavenly sphere are clearly transparent. Other parts must be solid since

they cast a shadow, as we see in eclipses. Other parts of the heavens give off light.

Proclus solution is to opt for (2b)all four of the elements are present in the heavens,although in a different manner than they are manifested in the sublunary sphere. I will

quote at length the passage in which he announces this conclusion and the reasons for it.

The nature of the problems being such as this, the better option is to say that the whole

heaven is [composed out of] a preponderance of fire, but it includes in a causal way

(kat ai)ti/an) the powers of the other elementsfor instance, the solidity andstability of earth; the adhesive and unifying quality of water; the tenuousness

and transparency of air. . . . One should consider that the fire there is not the same as

the fire here below the moon . . . The fire down here is genuinely enmattered andgenerated and destructible. . . . But earth is up there in a causal way, being another

form of earth such as would be expected if it is connascent (sumfu/esqai) with thedivine fire, having only abstract solidity (au)to\ mo/non e)/xousa to/ stereo/n), just as

the fire [up above] has luminosity [alone]. And as the [celestial] fire does not burn, so

the earth there is not denseit is the highest kind of each. The fire up there is pure and

really real. Likewise, here below is the really real earth and the wholeness of earth, but

the fire here is enmattered and exists through participation (kata\ me/qecin) just as the

earth is up there in the primary way (prwtw=j). The other one is present in each in an

appropriate waywhere the pinnacle or highest kind of earth is, there is the sedimentof fire. The moon is also an indication, having a solid and dark quality, and blocking

out the light (for it is in earths nature alone to occlude things in this way); likewise for

the stars which stand in the way of our attempts to see beyond, as if making a shadow

above themselves.

And it is clear that as these two are there on highfire and earththe things that are

intermediate between them must also be there: the primarily (prwtw=j) transparent

(that is, air, like the brightest kind down here) and water (like the lightest of vapours or

something still more pure) in order that all things should be in all, but each in anappropriate fashion (in Tim. II. 43, 2044,18 with omissions).

A. Extending the role of entities or principles within ones own theory

Proclus positive view about the composition of the heavens manifests two method-

ological virtues. First, it purports to provide an explanation of some obvious features of

the way that things appear to us. Some parts of the heavens are transparent; other parts

provide light; and yet other parts cast a shadow (as is evident in eclipses). This diversity in

appearances presents a problem for any theory that claims that there is only one elementpresent in the heavenswhether it be one of the familiar four or Aristotles fifth element.

However, it is unclear whether the properties of the four elements as we know them are

really adequate to explain the properties that seem to be exhibited by the heavenly bodies.

Proclus avoids this problem by supposing that the four elements come in different

gradations. This takes us on to the second methodological virtue of Proclus discussion.

Dirk Baltzly 273


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It would be obvious to his audience, though not perhaps to us, that Proclus theory

invokes general principles that find employment elsewhere in his theorizing. Proclus

account of the way in which all four elements are present in the heavens appeals to his

general principle that there is a decline of entities through the various levels of procession.The principle is articulated in Elements of Theology:

Prop. 38: In all that multiplies itself by procession, those terms which arise first are

more perfect than the second, and these than the next order, and so on throughout the

series.

Argument: For if procession is that which distinguishes product from cause, and there

is a deterioration (u(/fesij) in what comes second in relation to what comes first, thenthe first terms in such processions are more closely connected with the causes, since

they spring directly from them; and so on throughout. But that which is closer andmore akin to the cause is more perfect or complete (for causes are more complete than

effects (Prop. 7)); and the more remote is less perfect, as it loses the likeness of the

cause (ET 38, trans. after Dodds).

In addition, the terms in such a succession can rightfully be said to be the same thing.

In describing the mechanics of procession and reversion, Proclus insists that the product is

similar to the cause (ET. 29) and even that the product remains in the cause and also

proceeds (ET. 30). Thus what comes second may rightly be described as the same thing as

the higher cause but at a lower level of actuality.

26

The connection with Proclus general metaphysics is made explicit in the vocabulary

of the passage from in Timaeum just quoted. In Elements of Theology, Proclus distin-

guishes three modes of existence or subsistence for each predicate: in a causal way ( kat

ai)ti/an); as that very quality (kaq u/(parcin); and by participation (kata\ me/qecin).This threefold distinction between ways of being or having a quality corresponds to the

ontological division between an unparticipated, transcendent Form, the participated form

and the quality in the participant.27 So when he says that the earth that is present in the

heavens is there in a causal way while the fire here below is present by participation, he is

applying metaphysical principles that find employment elsewhere in his system to the

particular case at hand. The elements pre-exist (proupa/rxein) at the third level within

the hypostasis of Beingthat is, only a couple of doors down from the henads who

mediate between the One and all that comes after it (Platonic Theology III. 65, 22).28

Proclus gives a brief account of the various levels at which the four elements exist in the

passage that immediately follows his solution to the question of the composition of

the heavens quoted above (in Tim. II. 44, 2447, 22). This section applies the general


26 This is, of course, a very compressed explanation of the complex account of procession in Proclus.

Cf. Lloyd (1990), chapter 4 for a more detailed, but nonetheless very accessible summary.

27 Festugire (196668) believes that in Timaeum puts the same points in somewhat differentvocabulary: kat ai)ti/an = existing primarily (prwtw=j), while kaq u/(parcin = as a whole(kaq` o(lo/thj). The shift in vocabulary would be natural since the mode kaq u/(parcin iscorrelated with the whole of parts (o(/lon e)k tw=n merw=n), as well as with the status or order ofparticipated things (metexo/mena), cf. ET 67.

28 Siorvanes (op. cit.) catalogues the various ways in which the elements manifest themselves at

different levels within Proclus metaphysical hierarchy, pp. 2325.


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principles of Proclus metaphysics of emanation to the case of the elements. He even

invokes empirical considerations in favour of this specific claim that the elements come in

a variety of gradations.

For light and flame are not the same thing, nor is flame the same thing as burning coal,

but from higher up there is a deterioration (u(/fesij) of fire down as far as Earth. It

proceeds from a more immaterial, purer and less corporeal condition until it gets to the

most fully enmattered and densely packed bodies. For there are even streams of fire

under the Earth, as Empedocles says at one point: beneath the surface of the earth

burn many fiery [streams] (DK, B52). Therefore we should not be amazed how it is

that the fire is not quenched even when it is in a liquid state ( e)n u(/dati). For all the

elements permeate (xwrei=) one another, though what predominates in one thing isdifferent from what predominates in another (in Tim. II.8, 229, 3).

Of course, Proclus also invokes proof texts from the Orphic poems to support his

view of the decline of the elements through the various hypostases.29 But we shouldnt let

what we would regard as methodological vices blind us to the presence of methodological

virtues. His use of the principles about deterioration and partial sameness in procession

parallels Aristotles use of the doctrine of natural place. In both cases the theorist employs

entities or principles that have other (allegedly) successful applications in his theory to the

particular problem at hand. Moreover, in both cases, these appeals are at least somewhat

connected to something that we can observein Aristotles case, fires tendency to go up

and in Proclus case, the diversity of things that are commonsensically regarded as kinds

of fire. Finally, we should note that Proclus theory of the various gradations in which the

elements exist provides him with an answer to Aristotles objection to those who make the

heavens contain a large quantity of fire. Proclus can reply that the fire up there is not like

the fire down here and it isnt hot. Thus there is no need to explain why everything down

here hasnt burned up.

IV. Proclus specific arguments against Aristotle

A. Opening moves

Proclus objections to Aristotles views on the composition of the heavens do not begin, as

one might expect, with his commentary on Timaeus 40a24the point at which Plato

says that the stars are made mostly of fire. Nor does it come up for explict discussion in

his commentary on 32b48 where he announces his own view. Rather, Aristotles view is

criticized even prior to this in the context of Proclus commentary on Timaeus 31b59. In

that lemma, Plato argues that the cosmos must be made from earth and fire since it was

generated and therefore is tangible and visible. Air and water will then be introduced as

Dirk Baltzly 275

29 Proclus and the neoplatonists use passages from the Rhapsodic Theogony in much the same way

that medieval commentators will use citations from the New or Old Testament. The justification is

that Pythagoras was instructed by Orpheus (Iamblichus, Life of Pythagoras 28,146). Plato, of

course, they thought of as another of the Pythagorean school. Somewhat ironically, the Orphic

Rhapsodic Theogony is a product of the Hellenistic period, though it doubtless incorporates earlier

material in the tradition.


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the geometric mean terms that are needed to bind together two solids. In his commentary

on this, Proclus chooses to entertain a potential counter-example to the claim that the

presence of fire is a necessary condition of visibility.

But perhaps the marvelous Aristotle will contest our account and claim that not all

visible things are so through participation in fire, for the chorus of stars and the great

sun itself are not composed of fire even though they are visible (in Tim. II. 9,811).

Proclus response to this initial Aristotelian criticism is somewhat concessive. He

admits that there is an important difference between the fire we see here on Earth and the

fire in the heavens.

But one might respond to Aristotle by saying that enmattered fire is one thing but

immaterial fire is anotherthat is, it is immaterial because compared to the matter ofthe things in the sublunary sphere it is immaterialand the one kind is perishable but

the other imperishable (in Tim II. 9,1114).

Since we have examined it first, we can see that this rather cryptic remark prefigures

Proclus positive solution to the problem. He will argue that the heavens are composed of

all four elements with fire predominating. In this respect he is true to Platos remark at

Timaeus 40a. But the elements are like almost everything else in Proclus metaphysics

they exist in different forms or gradations of being at different levels within the

metaphysical hierarchy of neoplatonism. Thus there is also ample reason to honour

Aristotles insight that the heavens are composed of materials that are importantly

different from the things that we are acquainted with here in the sublunary sphere. This,

however, is not the only way in which Proclus solution exploits Aristotelian ideas. The

passage at II.9,1114 invokes the idea that materiality is a question of degree. Aristotles

own distinction between form and matter is also a relative one: the bronze is matter for the

statue, but bronze itself is form in relation to some further level of organization. Proclus

makes being material or enmattered a similarly relational concept. Thus he supposes that

it is not inconsistent to talk about space as an immaterial body capable of interpenetrating

all other bodies. This seems to be one end of the spectrum of materiality. At the other end,

we find the condition of the elements in the lower reaches of the Earth.

B. Criticizing competing theories

Proclus continues this line of thought by raising a puzzle for anyone who supposes that

there is some source of illumination other than fire.

And if someone were to say that the heavenly element is not fire, though it is visible

and capable of illuminating, we shall ask him from whence does the fire down here

(e)ntau=qa) derive this capacity?30 For if each is such as to generate the light that


30 Philoponus also argues from the similarity of the powers of celestial and terrestrial bodies to the

conclusion that they are composed from the same elements. For there is perhaps no [quality]

observed in the things there that does not also belong to the terrestrial bodies (Against Aristotle onthe Eternity of the World fr. 59, Wildberg (1987)). However, Philoponus seems to regard the fire

that composes the heavens as the very same sort of stuff as the fire herenot as Proclus does, a

higher grade of fire.


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enables perception, what reason could there be not to call each fire, though one be

without matter and the other enmattered? (I mean without matter or enmattered, as I

said before, distinguishing that kind [of matter] that stays forever in the same condition

and in its own proper form from the kind that is densest and doesnt retain forms) (inTim. II. 9, 2710,7).

Does this criticism tell against Aristotles theory? In some sense it should not. Aristotle

purports to explain both the heat from the Sun and the light from the stars and planets by

means of the fire sphere.31 But one might well be sceptical about whether the explanation

works for the light of the stars, even if one was inclined to accept it for the heat of the

Sun. So Proclus might be supposing that a thoughtful Aristotle would admit that there are

other sources of light than fire. In fact, the second-century commentator, Alexander of

Aphrodisias, took this to be Aristotles view.32

Invoking De Anima 418b1113, Alexanderclaims that divine things themselves are an alternative to fire as a source of light.

Whoever the intended target isAristotle or heterodox Aristoteliansthe character of

the objection is interesting. Proclus implies that anyone who supposes that there is such an

alternative source of illumination multiplies theoretical entities beyond necessity. Proclus

himself avoids the problems associated with positing two different kinds of things with the

power to illuminate by opting instead to distinguish gradations within a single kind of

thingthe kind of fire here in the sublunary is a source of both heat and light, while the

purer gradation of fire above is a source of light only. As we noted in the previous section,

this is a specific application of a general strategy for explaining plurality and difference interms of procession and deterioration.

C. Meeting objections to your own view (1)

In the following passage, Proclus comes to grips with the specifics of Aristotles argument

in De Caelo I.2

Suppose Aristotle had heard what we have said and urged the following objection: how

is it that if there is fire in the heavens they are moved in a circle and not in a straight

line? We would have to respond to him by invoking Plotinus view that every simple

body, when it is in its proper place, either remains motionless or is moved in a circle

lest it depart from its proper place. For if it is moved in another fashion, it will either

no longer be in its own place or else it is not yet in its proper place ( in Tim. II. 11,

2531).

The passage in Plotinus to which Proclus refers is Ennead II.2, On the movement of

heaven. Careful examination will show that Proclus is doing more than simply adopting a

response that Plotinus offers.

Dirk Baltzly 277

31 De Caelo II.7, 289b2021: The warmth and the light which proceed from them are caused by thefriction set up in the air by their motion.

32 Alexanders view is discussed by Simplicius in his De Caelo commentary at 442, 412. Ian

Mueller is translating this part of Simplicius commentary for Sorabjis Ancient Commentators on

Aristotle series. I am grateful to him and to Bob Sharples for their advice on this passage.


18/27

Why then does fire not stay still when it has come to heaven? It is, is it not, because the

nature of fire is to be in motion (h( fu/sij t%= puri\ e)n kikh/sei). So if it does notmove in a circle, going on in a straight line will dissipate it; so it must move in a circle.

But this is the doing of providence; rather, it is something in it which comes fromprovidence, so that if it comes to heaven it moves in a circle of its own accord (e)cau)tou=). It seeks to go on in a straight line, but has no longer any place to go; for it has

no place beyond itself; this is the last. So it runs in the space it occupies and is its own

place; it came there not in order to stay still but to move. The centre of a circle

naturally stays still, but if the outside circumference stayed still it would be a big centre

(II.2.1, 2333, trans. Armstrong (1966)).

Plotinus discussion relies on the assumption that it is the nature of fire to be in motion.

But there is no argument in Plotinus for this assumption. Proclus, however, will provide atheory of the elements that justifies this claim. Moreover, there are aspects of Plotinus

discussion that seem inconsistent. It is hard to tell whether the circular motion of the fire

in the heavens is an intrinsic feature of the fireas he suggests when he says that it moves

of its own accordor a result of the fact that it has run out of room to move in a straight

line.33 Finally, the remark about the stationary circumference constituting a big centre just

seems misguided. Even if it were stationary, the circumference is not a single point, and

therefore is not a point equidistant from every point on the circumference. Plotinus may

have something less literal in mind, but taken at face value, the remark makes no sense.

Proclus may have taken some inspiration from this passage of Plotinus, or he maysimply refer to Plotinus since the neoplatonists generally like to appeal to previous

authorities in their commentaries. But he develops a position that adapts the idea of

essentially moving fire to an Aristotelian framework of natural place:

Since the heavenly realm is fiery of necessity, then if it moves, it moves in a circle.

Likewise for the earth: if it were moved, it would be moved in a circle in order that it

should not abandon its place in the middle. Whenever fire is carried upward, it is

carried upward because it was in an alien place; and the clod of earth is carried

downward for the same reason. Generally speaking, the movement of the elements in a

straight line results from their being in a position that is contrary to their natures. So it

is simply a mistake to say that when fire is moved straight up it is moved in

accordance with nature. For it is particularly in accordance with nature when it

occupies its proper place. But whenever it is carried to its proper place, it is so because

where it was earlier was contrary to its nature. When this is demonstrated it is then

obvious how it is that the heavenly fire, since it is moved, moves in a circleand so

there is no problem for Platos teaching on this point ( in Tim II.11, 3112,12).


33 One suspects that Plotinus view is that the circular motion of the celestial fire is not intrinsic. It is

at least not explanatorily ultimate in Plotinus short essay. The circular movement of the fire in the

heavens is in response to the presence of Soul. If Soul stopped the fire too would stop (II.2.1,

445). Does this mean that the circular motion of fire is forced? If so, then this raises problems if

one accepts Aristotles premise that no forced motion can be eternal. Perhaps Plotinus would adopt

Alexanders position that the motion of the heavens is due to both Soul and also the nature of whatconstitutes them. Cf. Simplicius, in Cael. 387, 519.


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Clearly, there are also some affinities between this passage and Xenarchus claim that

when fire exists it moves in a circleit is only when it is in the process of becomingthat it

moves in a straight line.34 Proclus, however, adapts this line of argument to a revised

version of Aristotles own idea of natural place as a cause of natural motion. Moreover,Proclus will confront the question of the difference between the natural motion of earth

and that of fire. Fire, when it is in its proper place, moves in a circle. What about earth? If

its motion in its natural place is different from that of fire, what explains this fact?

Nothing in either Plotinus or Xenarchus speaks to this question.

Note that Proclus says in the passage just quoted that if the Earth were moved in its

proper place, it would be moved in a circle (eiper e)kineito, ku/kl% an e)kinh/qh).

There were different traditions on how to interpret Plato at Timaeus 40b9. On one reading,

Plato implies that the Earth turns on its axis. On another, there is no such implication.35

Proclus is among those who do not accept the idea that Plato made the material Earth

rotate on its axis.36 He is able to appeal to one of the three defining properties of the

element earth (which predominates here on Earth) in order to justify this claim. Fire, on

the other hand, is essentially such as to be in motion. In the next section we will examine

his theory of the elements and their essential properties.

D. Meeting objections to your own view (2)

Proclus initial response to Aristotles argument against the compostion of the heavens

from fire needs to be buttressed with a general theory of the elements. He needs some

justification for the claim that fire is essentially in motion and earth is essentially at rest.He first attacks Aristotles theory of the elements and then articulates his own alternative.

Aristotles theory of the elements assigns two powers to each of the four elements.

However, it is worthwhile to consider Proclus arguments against one power theories as

a prelude to his attack on Aristotle because he develops the same themes throughout.

Some of those who provide physical theories grant a single power to each of the

elements: they give to fire heat, but to air coolness, to water dampness, but to earth

dryness. These theorists entirely stray from the truth. First because they destroy the

possibility of an orderly cosmos. For on the assumption that the elements have entirelycontrary powers, then unless there were something common between them, it would be

impossible for them to be harmonised with one another.37 Next, the people who give

this kind of theory make the things that are most contrary right next to one another

Dirk Baltzly 279

34 Simplicius in Cael. 20, 24 ff and 40, 2022.35 The various options are surveyed by Cornford (1957), 12034.36 in Tim. III. 13344. For an excellent discussion of the Earths motion in Proclus, see Siorvanes

(1996), 3014. Siorvanes notes that there is a sense in which Proclus also endorses the view that

the Earth has axial rotation. Like every other heavenly body, the Earth has a soul and an intellect.

Souls have a variety of vehicles, depending on how deeply enmeshed they are with matter. Wehumans, for instance, have three different shellsthe material body; the pneumatic or spiritualbody; and, at the furthest remove from gross matter, an astral or aetherial body. The Earth has the

highest form of vehicle: an astral or aetherial body. This kind of body is extremely tenuous,

luminous and seems to be related to the very highest form of fire found in the celestial region.

Though the Earths material body is stationary at the centre of the cosmos, its astral body revolves

(in Tim. III. 135,1420).37 Cf. Aristotle Gen et Corr 330a3033.


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the hot (fire) to the cold (air) and the wet (water) to the dry (earth). But it is necessary

to make things that conflict further away than things that are less alien to one another.

For such is the nature of opposites (in Tim. II. 37,1726).

In the next few lines Proclus describes Aristotles theory, but assigns his views to

Ocellus the Pythagorean. The reason for this is that there was a forgery from the

Hellenistic period allegedly by the pre-Socratic Pythagorean Ocellus which describes,

among other Peripatetic views, Aristotles theory of the elements. To appreciate Proclus

objection, it may be helpful to represent this theory in a chart:

Fire Hot + Dry

Air Hot + Moist

Water Cold + Moist

Earth Cold + Dry

Proclus first notes that such a theory gives a common power to some pairs of elements.

In this respect it makes better sense than the previous one. But by having at most one

common power and one different one, the Aristotelian/Ocellus theory is also unable to

explain the existence of an orderly cosmos:

[T]hey no more give them association than separation, but rather they have in equalmeasure preached their conflict and harmony. But what sort of cosmos will result from

this? What sort of order will they have, since they are both most alien to one another

and not coordinate and at the same time most akin to one another and arranged

together? For they are in equal measure at war and at peace, and both establish and

dissolve communion in equal fashion. But if this communion is similarly destroyed and

implanted, the universe will no more be than not be (ou)de\n ma=llon estai h ou)kestai to\ pa=n). (in Tim. II. 38,716.)38

Next Proclus turns to Aristotles arrangement of the elements. Note that the naturalplace of fire and that of earth are most distant from one another. But when we consider the

powers characteristic of the elements, earth is more opposed to air than it is to fire. After

all, it shares one power with firebeing drybut it shares no common power with hot

and moist air. Proclus concludes that this theory errs in making each extreme term more

opposed to some intermediate than it is to the opposite extreme. In all other cases, where

we have things in the same genus, the extremes are more opposed to one another than they

are to the intermediates. And, he adds, even if one were to reject the application of that

general principle to the specific case at hand, there would still be a puzzle about the

natural motions of earth and fire. By Aristotles lights, the natural motions of these twoelements are opposites: upward and downward. But how could it be that nature has

assigned them opposite motions and natural places farthest from one another if they arent


38 Proclus here uses a perfectly standard Platonic pattern of inference. If x is both F in some respect

and not-F in some other respect, then x is no more F than not F. Cf. Rep. 479b and Makin (1993).


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by their very nature maximally opposed (in Tim. II. 38,1731)? Finally, Proclus alleges

that Aristotles own arguments require that fire and earth be contraries:

Aristotle also makes it clear that earth is contrary to fire, for, since he also wishes toshow how it is that it is necessary for there to be more than a single kind of body, he

says something like the following: but if there is earth it is also necessary that there

should be fire since if one of a pair of opposites exists by nature the other also exists by

nature.39 So it turns out that Aristotle was not able to show that the elements are many

in any other way than by saying that fire is contrary to earth ( in Tim. II. 39, 714).

D. Proclus own theory and the extension of mathematics

Proclus theory of the elements assigns three powers or properties to each element. The

assignment is based on Platos remarks about the elements in the Timaeus, especially at

56a. Plato notes that fire is more readily moved than the other elements and that it is such

as to cut things because of the sharpness of its pyramidal shape. It ranks first in fineness or

tenuousness and for this reason has permeated all things (58b). Taking his cue from this,

Proclus proposes the following correlation between powers and elements:

Fire tenuousness or smallness of

particles (leptome/reia)

sharpness40

(o)cu/thj)

easy mobility

(eu)kinhsi/a)

(pyramid)41

Air tenuousness or smallness ofparticles

bluntness(a)mblu/thj)

easy mobility (octahedron)

Water density or thickness of

parts (paxume/reia)

bluntness easy mobility (icosahedron)

Earth density or thickness of

particles

bluntness difficult to move42

duskinhsi/a

(cube)

Proclus justifies his three-power theory in this way:

[The powers are assigned this way] in order that each element may have in common

two powers with what is alongside it, but one difference, just as was shown in the case

of mathematical [solids] where the sides of the middle terms were derived from each of

the extreme terms [31, 27]. It is also assigned this way so that earth is arranged in an

opposite manner to fire with respect to all its powers, and so that the extreme terms

(fire and earth) have two middle terms and so do the ones that are next to one another

(i.e. air and water). The middles in the first case are solids themselves (i.e. the air and

Dirk Baltzly 281

39 As Festugire (196668) notes, this exact text is not to be found in any of the works of Aristotle

that we possess. He suggest that perhaps Proclus paraphrases Gen et Cor 330a48.40 In particular of the acute angles in the pyramid-shaped fire particles in Timaeus 56d, 61e.41 I have listed the regular solids that Plato assigns to each of the four elements, though Proclus does

not discuss them at this point in his commentary. I discuss the relevance of these shapes to thepowers of the elements in what follows.

42 Sometimes Proclus actually says immobility, a)kinhsi/a. This too is a contrary of sorts to what iseasily moved.


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water are middle terms between fire and earth), but in the second case the middle terms

are the powers that air and water have in common (i.e. bluntness and easy mobility)

(II. 39, 2440, 2).

The discussion of middle terms refers to Platos argument for the claim that the world

is composed of four elements (Timaeus 32a). Timaeus argues that since the Demiurge

wanted to make the cosmos both visible and tangible, it was necessary that there should be

both fire and earth in it. But, he says, there must also be two other elements in it if the fire

and earth are going to be combined through the best kind of bondthat of proportion or

analogia. Between planes a single middle term is sufficient to create proportion. But the

cosmos is three-dimensional, so we must have two middle terms.

For whenever of three numbers which are either solids or squares the middle termbetween any two of them is such that what the first term is to it, it is the last, and

conversely, what the last term is to the middle, it is to the first, then, since the middle

term turns out to be both first and last, and the last and the first likewise turn out to be

middle terms, they will all of necessity turn out to have the same relationship to one

another, and, given this, will all be unified (Timaeus 31c532a7, trans. Zeyl).

Both Plato and Proclus speak of plane and solid numbers. This terminology evolved

from the Pythagorean practice of representing numbers spatially. A plane number is one

with two factors, corresponding to the sides of the gnomon by means of which it might berepresented. Thus Euclid vii, df. 16:

[W]hen two numbers multiplied together produce a third, the number so produced is

called plane (e)pi/pedoj), and the numbers which were multiplied are called its sides(pleurai/).

So, for example, 6 is a plane number whose sides are two and three. A number that is

the product of three factors is called solid (stereo/j, Euc. vii, df. 17). Square numbers

are a species of plane numbers where the sides are equal. Naturally, the length of the side

corresponds to the square root of the number (df. 18). Oblong (promh/khj or

e(teromh/khj) numbers are those where the sides are not equal. 8 and 27 are examples ofcubic numbers and can be thought of as cubes with equal sides corresponding to their cube

roots (Euclid vii, df. 19).

Platos meaning in this passage has been the subject of debate. The translation either

solids (cubes?) or squares is a bit of interpolation from Platos stark ei)/te o)/gkwn ei)/teduna/mewn. Heath argued that Plato intended to restrict the theorem to squares andcubes.43 If a2 and b2 are two square numbers, then a2 : ab = ab : b2. But in the case of two

cubes a3 and b3, a3 : a2b = a2b : ab2 = ab2 : b3. This was thought by Heath and later

Cornford to be the force of Platos subsequent remark that between two planes a single

medium is sufficient, but between cubes two middle terms are needed. Both these

theorems are proved in Euclid (viii, 11 and 12).


43 Heath (1921), 297. See also Cornford (1957), 4352.


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The matter is complicated because the same thing holds for similar planes and solids

(Euc. viii, 18 and 19). Planes and solids are similar when their sides are in proportion

(Euc. vii, df. 21). That is to say, if a b and c d are similar plane numbers, then a : c = b

: d. The same applies for the case of similar solid numbers. In this case, as length is tolength, so breadth is to breadth and height is to height.44 Naturally squares and cubes are

all similar since their sides are exactly the same.

Throughout his discussion, Proclus assumes that Plato is here discussing the wider

category of similar planes and solids (II. 29,18 ff.). He provides a recipe for finding the

two terms that stand in continuous geometric proportion between similar solids. The

method can be easily illustrated in the case of cubes. Take two cubic numbers like 8 and

27. We want to construct a series of middle terms that will give us the geometric

proportion or analogia that Plato thinks is the perfect bond. In this sequence there will be

one middle term that is closer to 8 and one that is closer to 278, x, y, 27. Proclus

instructs us to determine the value of x by taking two sides from the closer extreme and

one side from the further extreme, i.e. 2 2 3 or 12. For y, we take two sides from 27,

but only one from 8, i.e. 3 3 2 or 18 (in Tim. II. 31, 2032, 2). These values give you a

series in which each term exceeds the next by one and a half times. Thus it satisfies

Platos condition for the perfect bond.

The procedure that Proclus gives us works in the case of similar solids that are not

cubes too. Take two merely similar solids like 12 (2 2 3) and 96 (4 4 6). (These

solids are similar since the length, breadth and height are all in the ratio 2:1.) The hitch

is that you can follow Proclus recipe for taking sides from each and generate numbers

that wont be in continuous geometric proportion. So, 16 and 72 each take two sides or

factors from the extreme closest to them and one from the extreme further away. But 12,

16, 72, 96 isnt a continuous geometrical proportion. Of course, Proclus recipe will also

cook up 24 and 48 which do.

Proclus argues that these features of solid numbers are manifested at the level of the

solid bodies that are the elements.

Suppose fire is tenuous, sharp and easily moved. . . . Therefore, since earth is the

contrary to fire, it will have the contrary powers: density, bluntness and immobility.

And surely we see all these things manifested in earth. This is a case of things that are

in conflict and moreover are solids and specifically similar solidsfor their sides and

powers will be in proportion; for as the dense is to the tenuous, the blunt is to the sharp

and the immobile is to that which is easily moved. But similar solids are the ones

whose sides and powers are in proportionor if you wish to put it in the physical

manner of speaking (ei bou/lei fusikwj le/gein), similar bodies are the oneswhere the powers that constitute those bodies are in proportion (in Tim. II.

39,1940, 2).

As in the case of the factors in similar solid numbers, the sides of the elements stand

in the same relation to one another. Each of the three powers that defines fire and earth are

opposites. This is the physical reflection of the mathematical requirement that similar

Dirk Baltzly 283

44 Theon of Smyrna, 37, 4.


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solid numbers should have sides that are proportional.45 As in the case of the continuous

geometric proportion between solid numbers, there are possible combinations of three

powers that are not represented in Proclus table of the four elements. Thus there is a

potential alternative to air that is dense which combines the tenuousness and sharpness offire with the immobility of earth. Another alternative form of air would combine the

sharpness and easy mobility of fire with the density of earth. Siorvanes claims that Proclus

supposes that there are actually no such elements because the shapes of the octahedron

and icosahedron assigned to air and water respectively rule out any of the triple combina-

tions of powers other than those that Proclus uses.46

Among the methodological virtues that we noted in Aristotles discussion of the

composition of the heavens was that he tries to show that his theory extends the scope of

an established mathematical idea. In this respect, we can cite his claim that there are three

simple motions (up, down and in a circle) because there are three dimensions and, in

addition, two simple magnitudes: the line and the circle (Cael. 268b1826). Proclus

theory of the elements shows a similarindeed, a much more complex and convincing!

extension of the principles of mathematics into his physical theory. This theory of the

elements helps to justify his claim that fire is essentially such as to be in motion while

earth is essentially stationary. This, in turn, makes his response to Aristotles argument

about the natural motion of the heavenly bodies more convincing than the similar

responses of Xenarchus and Plotinus.

V. Conclusion: reconciling Aristotle with Plato

At the outset we noted that the neoplatonists generally like to portray Plato and Aristotle

as in agreement about most things. After these criticisms of Aristotles theory of the

elements and the composition of the heavens from the aether, Proclus finds a verbal

formula for showing that, deep down, Aristotle really agrees with Plato after all.

It is permissible to say both that there are four unmixed elements of everything, and

also that there are fivetaking, on the one hand, the whole heaven as one thing, on the

other taking the complete elements which are encompassed within the terrestrial

region. But the five elements are said to be elements of the cosmos, surely on account

of the fact that the cosmos has been constituted from them, while the four elements

count as the elements of each of these [five]. For the heavens are composed out of the


45 Proclus typically marks the way in which a thing is manifested at different levels of being by using

adverbs like fusikwj or maqhmatikw=j (II. 20,19). One could just as easily translate in thephysical mode or in the mathematical mode.

46 Siorvanes (1996), 228. The difference between bluntness and sharpness corresponds to the facts

about whether the angles in the assigned solid figures are acute or obtuse. Siorvanes says thattenuity or grossness (density) correspond to the size factor (p. 259, n. 40). Moreover, he thinks

that the facts about mobility depend upon the kind of triangle that the Platonic scheme uses to

compose the faces of the solids. (The cubes of earth have faces composed of half-squares, having

sides in the ratio 1, 1, 2, but the others are composed of half-equilateral triangles.) Thus only earthcan have the property of being not easily moved. My only reservation about this is the dependence

of tenuousness or density upon the size factor. If the half-equilaterials come in a variety of sizes,

as Cornford thought, then there could be air particles smaller than a given fire particle, in spite of

the fact that the former is composed of many more parts than the latter.


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Cherniss, H.F., Arist

Documents

Australasian Journal of Philosophy Volume 80 Issue 3 2002 [Doi 10.1080%2F713659466] Baltzly, D. -- What Goes Up- Proclus Against Aristotle on the Fifth Element