10.
But we have still to explain "combination", for that was the third of the subjects we originally proposed to discuss. Our explanation will proceed on the same method as before. We must inquire: What is "combination", and what is that which can "combine"? Of what things, and under what conditions, is "combination" a property? And, further, does "combination" exist in fact, or is it false to a.s.sert its existence?
For, according to some thinkers, it is impossible for one thing to be combined with another. They argue that (i) if both the "combined"
const.i.tuents persist unaltered, they are no more "combined" now than they were before, but are in the same condition: while (ii) if one has been destroyed, the const.i.tuents have not been "combined"-on the contrary, one const.i.tuent is and the other is not, whereas "combination" demands uniformity of condition in them both: and on the same principle (iii) even if both the combining const.i.tuents have been destroyed as the result of their coalescence, they cannot "have been combined" since they have no being at all.
What we have in this argument is, it would seem, a demand for the precise distinction of "combination" from coming-to-be and pa.s.singaway (for it is obvious that "combination", if it exists, must differ from these processes) and for the precise distinction of the "combinable" from that which is such as to come-to-be and pa.s.s-away.
As soon, therefore, as these distinctions are clear, the difficulties raised by the argument would be solved.
Now (i) we do not speak of the wood as "combined" with the fire, nor of its burning as a "combining" either of its particles with one another or of itself with the fire: what we say is that "the fire is coming-to-be, but the wood is "pa.s.sing-away". Similarly, we speak neither (ii) of the food as "combining" with the body, nor (iii) of the shape as "combining" with the wax and thus fashioning the lump.
Nor can body "combine" with white, nor (to generalize) "properties"
and "states" with "things": for we see them persisting unaltered.
But again (iv) white and knowledge cannot be "combined" either, nor any other of the "adjectivals". (Indeed, this is a blemish in the theory of those who a.s.sert that "once upon a time all things were together and combined". For not everything can "combine" with everything. On the contrary, both of the const.i.tuents that are combined in the compound must originally have existed in separation: but no property can have separate existence.) Since, however, some things are-potentially while others are-actually, the const.i.tuents combined in a compound can "be" in a sense and yet "not-be". The compound may he-actually other than the const.i.tuents from which it has resulted; nevertheless each of them may still he-potentially what it was before they were combined, and both of them may survive undestroyed. (For this was the difficulty that emerged in the previous argument: and it is evident that the combining const.i.tuents not only coalesce, having formerly existed in separation, but also can again be separated out from the compound.) The const.i.tuents, therefore, neither (a) persist actually, as "body" and "white" persist: nor (b) are they destroyed (either one of them or both), for their "power of action" is preserved. Hence these difficulties may be dismissed: but the problem immediately connected with them-whether combination is something relative to perception"
must be set out and discussed.
When the combining const.i.tuents have been divided into parts so small, and have been juxtaposed in such a manner, that perception fails to discriminate them one from another, have they then "been combined Or ought we to say "No, not until any and every part of one const.i.tuent is juxtaposed to a part of the other"? The term, no doubt, is applied in the former sense: we speak, e.g. of wheat having been "combined" with barley when each grain of the one is juxtaposed to a grain of the other. But every body is divisible and therefore, since body "combined" with body is uniform in texture throughout, any and every part of each const.i.tuent ought to be juxtaposed to a part of the other.
No body, however, can be divided into its "least" parts: and "composition" is not identical with "combination", but other than it. From these premises it clearly follows (i) that so long as the const.i.tuents are preserved in small particles, we must not speak of them as "combined". (For this will be a "composition" instead of a "blending" or "combination": nor will every portion of the resultant exhibit the same ratio between its const.i.tuents as the whole. But we maintain that, if "combination" has taken place, the compound must be uniform in texture throughout-any part of such a compound being the same as the whole, just as any part of water is water: whereas, if "combination" is "composition of the small particles", nothing of the kind will happen. On the contrary, the const.i.tuents will only be "combined" relatively to perception: and the same thing will be "combined" to one percipient, if his sight is not sharp, (but not to another,) while to the eye of Lynceus nothing will be "combined".) It clearly follows (ii) that we must not speak of the const.i.tuents as "combined in virtue of a division such that any and every part of each is juxtaposed to a part of the other: for it is impossible for them to be thus divided. Either, then, there is no "combination", or we have still to explain the manner in which it can take place.
Now, as we maintain, some things are such as to act and others such as to suffer action from them. Moreover, some things-viz. those Which have the same matter-"reciprocate", i.e. are such as to act upon one another and to suffer action from one another; while other things, viz. agents which have not the same matter as their patients, act without themselves suffering action. Such agents cannot "combine"-that is why neither the art of healing nor health produces health by "combining" with the bodies of the patients. Amongst those things, however, which are reciprocally active and pa.s.sive, some are easily-divisible. Now (i) if a great quant.i.ty (or a large bulk) of one of these easily-divisible "reciprocating" materials be brought together with a little (or with a small piece) of another, the effect produced is not "combination", but increase of the dominant: for the other material is transformed into the dominant. (That is why a drop of wine does not "combine" with ten thousand gallons of water: for its form is dissolved, and it is changed so as to merge in the total volume of water.) On the other hand (ii) when there is a certain equilibrium between their "powers of action", then each of them changes out of its own nature towards the dominant: yet neither becomes the other, but both become an intermediate with properties common to both.
Thus it is clear that only those agents are "combinable" which involve a contrariety-for these are such as to suffer action reciprocally. And, further, they combine more freely if small pieces of each of them are juxtaposed. For in that condition they change one another more easily and more quickly; whereas this effect takes a long time when agent and patient are present in bulk.
Hence, amongst the divisible susceptible materials, those whose shape is readily adaptable have a tendency to combine: for they are easily divided into small particles, since that is precisely what "being readily adaptable in shape" implies. For instance, liquids are the most "combinable" of all bodies-because, of all divisible materials, the liquid is most readily adaptable in shape, unless it be viscous. Viscous liquids, it is true, produce no effect except to increase the volume and bulk. But when one of the const.i.tuents is alone susceptible-or superlatively susceptible, the other being susceptible in a very slight degree-the compound resulting from their combination is either no greater in volume or only a little greater. This is what happens when tin is combined with bronze. For some things display a hesitating and ambiguous att.i.tude towards one another-showing a slight tendency to combine and also an inclination to behave as "receptive matter" and "form" respectively. The behaviour of these metals is a case in point. For the tin almost vanishes, behaving as if it were an immaterial property of the bronze: having been combined, it disappears, leaving no trace except the colour it has imparted to the bronze. The same phenomenon occurs in other instances too.
It is clear, then, from the foregoing account, that "combination"
occurs, what it is, to what it is due, and what kind of thing is "combinable". The phenomenon depends upon the fact that some things are such as to be (a) reciprocally susceptible and (b) readily adaptable in shape, i.e. easily divisible. For such things can be "combined" without its being necessary either that they should have been destroyed or that they should survive absolutely unaltered: and their "combination" need not be a "composition", nor merely "relative to perception". On the contrary: anything is "combinable"
which, being readily adaptable in shape, is such as to suffer action and to act; and it is "combinable with" another thing similarly characterized (for the "combinable" is relative to the "combinable"); and "combination" is unification of the "combinables", resulting from their "alteration".
Book II
1.
WE have explained under what conditions "combination", "contact", and "action-pa.s.sion" are attributable to the things which undergo natural change. Further, we have discussed "unqualified"
coming-to-be and pa.s.sing-away, and explained under what conditions they are predicable, of what subject, and owing to what cause.
Similarly, we have also discussed "alteration", and explained what "altering" is and how it differs from coming-to-be and pa.s.sing-away.
But we have still to investigate the so-called "elements" of bodies.
For the complex substances whose formation and maintenance are due to natural processes all presuppose the perceptible bodies as the condition of their coming-to-be and pa.s.sing-away: but philosophers disagree in regard to the matter which underlies these perceptible bodies. Some maintain it is single, supposing it to be, e.g. Air or Fire, or an "intermediate" between these two (but still a body with a separate existence). Others, on the contrary, postulate two or more materials-ascribing to their "a.s.sociation" and "dissociation", or to their "alteration", the coming-to-be and pa.s.sing-away of things.
(Some, for instance, postulate Fire and Earth: some add Air, making three: and some, like Empedocles, reckon Water as well, thus postulating four.) Now we may agree that the primary materials, whose change (whether it be "a.s.sociation and dissociation" or a process of another kind) results in coming-to-be and pa.s.singaway, are rightly described as "originative sources, i.e. elements". But (i) those thinkers are in error who postulate, beside the bodies we have mentioned, a single matter-and that corporeal and separable matter. For this "body" of theirs cannot possibly exist without a "perceptible contrariety": this "Boundless", which some thinkers identify with the "original real", must be either light or heavy, either cold or hot. And (ii) what Plato has written in the Timaeus is not based on any precisely-articulated conception. For he has not stated clearly whether his "Omnirecipient" exists in separation from the "elements"; nor does he make any use of it. He says, indeed, that it is a substratum prior to the so-called "elements"-underlying them, as gold underlies the things that are fashioned of gold. (And yet this comparison, if thus expressed, is itself open to criticism. Things which come-to-be and pa.s.s-away cannot be called by the name of the material out of which they have come-tobe: it is only the results of "alteration"
which retain the name of the substratum whose "alterations" they are. However, he actually says" that the truest account is to affirm that each of them is "gold"".) Nevertheless he carries his a.n.a.lysis of the "elements"-solids though they are-back to "planes", and it is impossible for "the Nurse" (i.e. the primary matter) to be identical with "the planes".
Our own doctrine is that although there is a matter of the perceptible bodies (a matter out of which the so-called "clements"
come-to-be), it has no separate existence, but is always bound up with a contrariety. A more precise account of these presuppositions has been given in another work": we must, however, give a detailed explanation of the primary bodies as well, since they too are similarly derived from the matter. We must reckon as an "originative source" and as "primary" the matter which underlies, though it is inseparable from, the contrary qualities: for the hot" is not matter for "the cold" nor "the cold" for "the hot", but the substratum is matter for them both. We therefore have to recognize three "originative sources": firstly that which potentially perceptible body, secondly the contrarieties (I mean, e.g. heat and cold), and thirdly Fire, Water, and the like. Only "thirdly", however: for these bodies change into one another (they are not immutable as Empedocles and other thinkers a.s.sert, since "alteration" would then have been impossible), whereas the contrarieties do not change.
Nevertheless, even so the question remains: What sorts of contrarieties, and how many of them, are to be accounted "originative sources" of body? For all the other thinkers a.s.sume and use them without explaining why they are these or why they are just so many.
2.
Since, then, we are looking for "originative sources" of perceptible body; and since "perceptible" is equivalent to "tangible", and "tangible" is that of which the perception is touch; it is clear that not all the contrarieties const.i.tute "forms" and "originative sources" of body, but only those which correspond to touch. For it is in accordance with a contrariety-a contrariety, moreover, of tangible qualities-that the primary bodies are differentiated. That is why neither whiteness (and blackness), nor sweetness (and bitterness), nor (similarly) any quality belonging to the other perceptible contrarieties either, const.i.tutes an "element". And yet vision is prior to touch, so that its object also is prior to the object of touch. The object of vision, however, is a quality of tangible body not qua tangible, but qua something else-qua something which may well be naturally prior to the object of touch.
Accordingly, we must segregate the tangible differences and contrarieties, and distinguish which amongst them are primary.
Contrarieties correlative to touch are the following: hot-cold, dry-moist, heavy-light, hard-soft, viscous-brittle, rough-smooth, coa.r.s.e-fine. Of these (i) heavy and light are neither active nor susceptible. Things are not called "heavy" and "light" because they act upon, or suffer action from, other things. But the "elements" must be reciprocally active and susceptible, since they "combine" and are transformed into one another. On the other hand (ii) hot and cold, and dry and moist, are terms, of which the first pair implies power to act and the second pair susceptibility. "Hot" is that which "a.s.sociates"
things of the same kind (for "dissociating", which people attribute to Fire as its function, is "a.s.sociating" things of the same cla.s.s, since its effect is to eliminate what is foreign), while "cold" is that which brings together, i.e. "a.s.sociates", h.o.m.ogeneous and heterogeneous things alike. And moise is that which, being readily adaptable in shape, is not determinable by any limit of its own: while "dry" is that which is readily determinable by its own limit, but not readily adaptable in shape.
From moist and dry are derived (iii) the fine and coa.r.s.e, viscous and brittle, hard and soft, and the remaining tangible differences.
For (a) since the moist has no determinate shape, but is readily adaptable and follows the outline of that which is in contact with it, it is characteristic of it to be "such as to fill up". Now "the fine" is "such as to fill up". For the fine" consists of subtle particles; but that which consists of small particles is "such as to fill up", inasmuch as it is in contact whole with whole-and "the fine"
exhibits this character in a superlative degree. Hence it is evident that the fine derives from the moist, while the coa.r.s.e derives from the dry. Again (b) the viscous" derives from the moist: for "the viscous" (e.g. oil) is a "moist" modified in a certain way. "The brittle", on the other hand, derives from the dry: for "brittle" is that which is completely dry-so completely, that its solidification has actually been due to failure of moisture. Further (c) "the soft"
derives from the moist. For "soft" is that which yields to pressure by retiring into itself, though it does not yield by total displacement as the moist does-which explains why the moist is not "soft", although "the soft" derives from the moist. "The hard", on the other hand, derives from the dry: for "hard" is that which is solidified, and the solidified is dry.
The terms "dry" and "moist" have more senses than one. For "the damp", as well as the moist, is opposed to the dry: and again "the solidified", as well as the dry, is opposed to the moist. But all these qualities derive from the dry and moist we mentioned first." For (i) the dry is opposed to the damp: i.e. "damp" is that which has foreign moisture on its surface ("sodden" being that which is penetrated to its core), while "dry" is that which has lost foreign moisture. Hence it is evident that the damp will derive from the moist, and "the dry" which is opposed to it will derive from the primary dry. Again (ii) the "moist" and the solidified derive in the same way from the primary pair. For "moist" is that which contains moisture of its-own deep within it ("sodden" being that which is deeply penetrated by foreign mosture), whereas "solidigied" is that which has lost this inner moisture. Hence these too derive from the primary pair, the "solidified" from the dry and the "solidified"
from the dry the "liquefiable" from the moist.
It is clear, then, that all the other differences reduce to the first four, but that these admit of no further reduction. For the hot is not essentially moist or dry, nor the moist essentially hot or cold: nor are the cold and the dry derivative forms, either of one another or of the hot and the moist. Hence these must be four.
3.
The elementary qualities are four, and any four terms can be combined in six couples. Contraries, however, refuse to be coupled: for it is impossible for the same thing to be hot and cold, or moist and dry. Hence it is evident that the "couplings" of the elementary qualities will be four: hot with dry and moist with hot, and again cold with dry and cold with moist. And these four couples have attached themselves to the apparently "simple" bodies (Fire, Air, Water, and Earth) in a manner consonant with theory. For Fire is hot and dry, whereas Air is hot and moist (Air being a sort of aqueous vapour); and Water is cold and moist, while Earth is cold and dry.
Thus the differences are reasonably distributed among the primary bodies, and the number of the latter is consonant with theory. For all who make the simple bodies "elements" postulate either one, or two, or three, or four. Now (i) those who a.s.sert there is one only, and then generate everything else by condensation and rarefaction, are in effect making their "originative sources" two, viz. the rare and the dense, or rather the hot and the cold: for it is these which are the moulding forces, while the "one" underlies them as a "matter". But (ii) those who postulate two from the start-as Parmenides postulated Fire and Earth-make the intermediates (e.g. Air and Water) blends of these. The same course is followed (iii) by those who advocate three. (We may compare what Plato does in Me Divisions": for he makes "the middle" a blend.) Indeed, there is practically no difference between those who postulate two and those who postulate three, except that the former split the middle "element" into two, while the latter treat it as only one. But (iv) some advocate four from the start, e.g. Empedocles: yet he too draws them together so as to reduce them to the two, for he opposes all the others to Fire.
In fact, however, fire and air, and each of the bodies we have mentioned, are not simple, but blended. The "simple" bodies are indeed similar in nature to them, but not identical with them. Thus the "simple" body corresponding to fire is "such-as-fire, not fire: that which corresponds to air is "such-as-air": and so on with the rest of them. But fire is an excess of heat, just as ice is an excess of cold. For freezing and boiling are excesses of heat and cold respectively. a.s.suming, therefore, that ice is a freezing of moist and cold, fire a.n.a.logously will be a boiling of dry and hot: a fact, by the way, which explains why nothing comes-to-be either out of ice or out of fire.
The "simple" bodies, since they are four, fall into two pairs which belong to the two regions, each to each: for Fire and Air are forms of the body moving towards the "limit", while Earth and Water are forms of the body which moves towards the "centre". Fire and Earth, moreover, are extremes and purest: Water and Air, on the contrary are intermediates and more like blends. And, further, the members of either pair are contrary to those of the other, Water being contrary to Fire and Earth to Air; for the qualities const.i.tuting Water and Earth are contrary to those that const.i.tute Fire and Air.
Nevertheless, since they are four, each of them is characterized par excellence a single quality: Earth by dry rather than by cold, Water by cold rather than by moist, Air by moist rather than by hot, and Fire by hot rather than by dry.
4.
It has been established before" that the coming-to-be of the "simple" bodies is reciprocal. At the same time, it is manifest, even on the evidence of perception, that they do come-to-be: for otherwise there would not have been "alteration, since "alteration" is change in respect to the qualities of the objects of touch.
Consequently, we must explain (i) what is the manner of their reciprocal transformation, and (ii) whether every one of them can come to-be out of every one-or whether some can do so, but not others.
Now it is evident that all of them are by nature such as to change into one another: for coming-to-be is a change into contraries and out of contraries, and the "elements" all involve a contrariety in their mutual relations because their distinctive qualities are contrary. For in some of them both qualities are contrary-e.g. in Fire and Water, the first of these being dry and hot, and the second moist and cold: while in others one of the qualities (though only one) is contrary-e.g. in Air and Water, the first being moist and hot, and the second moist and cold. It is evident, therefore, if we consider them in general, that every one is by nature such as to come-to-be out of every one: and when we come to consider them severally, it is not difficult to see the manner in which their transformation is effected.
For, though all will result from all, both the speed and the facility of their conversion will differ in degree.
Thus (i) the process of conversion will be quick between those which have interchangeable "complementary factors", but slow between those which have none. The reason is that it is easier for a single thing to change than for many. Air, e.g. will result from Fire if a single quality changes: for Fire, as we saw, is hot and dry while Air is hot and moist, so that there will be Air if the dry be overcome by the moist. Again, Water will result from Air if the hot be overcome by the cold: for Air, as we saw, is hot and moist while Water is cold and moist, so that, if the hot changes, there will be Water. So too, in the same manner, Earth will result from Water and Fire from Earth, since the two "elements" in both these couples have interchangeable "complementary factors". For Water is moist and cold while Earth is cold and dry-so that, if the moist be overcome, there will be Earth: and again, since Fire is dry and hot while Earth is cold and dry, Fire will result from Earth if the cold pa.s.s-away.
It is evident, therefore, that the coming-to-be of the "simple"
bodies will be cyclical; and that this cyclical method of transformation is the easiest, because the consecutive "clements"
contain interchangeable "complementary factors". On the other hand (ii) the transformation of Fire into Water and of Air into Earth, and again of Water and Earth into Fire and Air respectively, though possible, is more difficult because it involves the change of more qualities. For if Fire is to result from Water, both the cold and the moist must pa.s.s-away: and again, both the cold and the dry must pa.s.s-away if Air is to result from Earth. So" too, if Water and Earth are to result from Fire and Air respectively-both qualities must change.
This second method of coming-to-be, then, takes a longer time. But (iii) if one quality in each of two "elements" pa.s.s-away, the transformation, though easier, is not reciprocal. Still, from Fire plus Water there will result Earth and Air, and from Air plus Earth Fire and Water. For there will be Air, when the cold of the Water and the dry of the Fire have pa.s.sed-away (since the hot of the latter and the moist of the former are left): whereas, when the hot of the Fire and the moist of the Water have pa.s.sed-away, there will be Earth, owing to the survival of the dry of the Fire and the cold of the Water. So, too, in the same Way, Fire and Water will result from Air plus Earth. For there will be Water, when the hot of the Air and the dry of the Earth have pa.s.sed-away (since the moist of the former and the cold of the latter are left): whereas, when the moist of the Air and the cold of the Earth have pa.s.sed-away, there will be Fire, owing to the survival of the hot of the Air and the dry of the Earth-qualities essentially const.i.tutive of Fire. Moreover, this mode of Fire"s coming-to-be is confirmed by perception. For flame is par excellence Fire: but flame is burning smoke, and smoke consists of Air and Earth.
No transformation, however, into any of the "simple" bodies can result from the pa.s.singaway of one elementary quality in each of two "elements" when they are taken in their consecutive order, because either identical or contrary qualities are left in the pair: but no "simple" body can be formed either out of identical, or out of contrary, qualities. Thus no "simple" body would result, if the dry of Fire and the moist of Air were to pa.s.s-away: for the hot is left in both. On the other hand, if the hot pa.s.s-away out both, the contraries-dry and moist-are left. A similar result will occur in all the others too: for all the consecutive "elements" contain one identical, and one contrary, quality. Hence, too, it clearly follows that, when one of the consecutive "elements" is transformed into one, the coming-to-be is effected by the pa.s.sing-away of a single quality: whereas, when two of them are transformed into a third, more than one quality must have pa.s.sedaway.
We have stated that all the "elements" come-to-be out of any one of them; and we have explained the manner in which their mutual conversion takes place. Let us nevertheless supplement our theory by the following speculations concerning them.
5.
If Water, Air, and the like are a "matter" of which the natural bodies consist, as some thinkers in fact believe, these "clements"
must be either one, or two, or more. Now they cannot all of them be one-they cannot, e.g. all be Air or Water or Fire or Earth-because "Change is into contraries". For if they all were Air, then (a.s.suming Air to persist) there will be "alteration" instead of coming-to-be. Besides, n.o.body supposes a single "element" to persist, as the basis of all, in such a way that it is Water as well as Air (or any other "element") at the same time. So there will be a certain contrariety, i.e. a differentiating quality: and the other member of this contrariety, e.g. heat, will belong to some other "element", e.g. to Fire. But Fire will certainly not be "hot Air". For a change of that kind (a) is "alteration", and (b) is not what is observed. Moreover (c) if Air is again to result out of the Fire, it will do so by the conversion of the hot into its contrary: this contrary, therefore, will belong to Air, and Air will be a cold something: hence it is impossible for Fire to be "hot Air", since in that case the same thing will be simultaneously hot and cold. Both Fire and Air, therefore, will be something else which is the same; i.e. there will be some "matter", other than either, common to both.
The same argument applies to all the "elements", proving that there is no single one of them out of which they all originate. But neither is there, beside these four, some other body from which they originate-a something intermediate, e.g. between Air and Water (coa.r.s.er than Air, but finer than Water), or between Air and Fire (coa.r.s.er than Fire, but finer than Air). For the supposed "intermediate" will be Air and Fire when a pair of contrasted qualities is added to it: but, since one of every two contrary qualities is a "privation", the "intermediate" never can exist-as some thinkers a.s.sert the "Boundless" or the "Environing" exists-in isolation. It is, therefore, equally and indifferently any one of the "elements", or else it is nothing.
Since, then, there is nothing-at least, nothing perceptible-prior to these, they must be all. That being so, either they must always persist and not be transformable into one another: or they must undergo transformation-either all of them, or some only (as Plato wrote in the Timacus)." Now it has been proved before that they must undergo reciprocal transformation. It has also been proved that the speed with which they come-to-be, one out of another, is not uniform-since the process of reciprocal transformation is relatively quick between the "elements" with a "complementary factor", but relatively slow between those which possess no such factor.
a.s.suming, then, that the contrariety, in respect to which they are transformed, is one, the elements" will inevitably be two: for it is "matter" that is the "mean" between the two contraries, and matter is imperceptible and inseparable from them. Since, however, the "elements" are seen to be more than two, the contrarieties must at the least be two. But the contrarieties being two, the "elements" must be four (as they evidently are) and cannot be three: for the couplings" are four, since, though six are possible, the two in which the qualities are contrary to one another cannot occur.
These subjects have been discussed before:" but the following arguments will make it clear that, since the "elements" are transformed into one another, it is impossible for any one of them-whether it be at the end or in the middle-to be an "originative source" of the rest. There can be no such "originative element" at the ends: for all of them would then be Fire or Earth, and this theory amounts to the a.s.sertion that all things are made of Fire or Earth.
Nor can a "middle-element" be such an originative source"-as some thinkers suppose that Air is transformed both into Fire and into Water, and Water both into Air and into Earth, while the "end-elements" are not further transformed into one another. For the process must come to a stop, and cannot continue ad infinitum in a straight line in either direction, since otherwise an infinite number of contrarieties would attach to the single "element". Let E stand for Earth, W for Water, A for Air, and F for Fire. Then (i) since A is transformed into F and W, there will be a contrariety belonging to A F. Let these contraries be whiteness and blackness.
Again (ii) since A is transformed into W, there will be another contrariety: for W is not the same as F. Let this second contrariety be dryness and moistness, D being dryness and M moistness. Now if, when A is transformed into W, the "white" persists, Water will be moist and white: but if it does not persist, Water will be black since change is into contraries. Water, therefore, must be either white or black. Let it then be the first. On similar grounds, therefore, D (dryness) will also belong to F. Consequently F (Fire) as well as Air will be able to be transformed into Water: for it has qualities contrary to those of Water, since Fire was first taken to be black and then to be dry, while Water was moist and then showed itself white.
Thus it is evident that all the "elements" will be able to be transformed out of one another; and that, in the instances we have taken, E (Earth) also will contain the remaining two "complementary factors", viz. the black and the moist (for these have not yet been coupled).
We have dealt with this last topic before the thesis we set out to prove. That thesis-viz. that the process cannot continue ad infinitum-will be clear from the following considerations. If Fire (which is represented by F) is not to revert, but is to be transformed in turn into some other "element" (e.g. into Q), a new contrariety, other than those mentioned, will belong to Fire and Q: for it has been a.s.sumed that Q is not the same as any of the four, E W A and F. Let K, then, belong to F and Y to Q. Then K will belong to all four, E W A and F: for they are transformed into one another. This last point, however, we may admit, has not yet been proved: but at any rate it is clear that if Q is to be transformed in turn into yet another "element", yet another contrariety will belong not only to Q but also to F (Fire). And, similarly, every addition of a new "element"
will carry with it the attachment of a new contrariety to the preceding elements". Consequently, if the "elements" are infinitely many, there will also belong to the single "element" an infinite number of contrarieties. But if that be so, it will be impossible to define any "element": impossible also for any to come-to-be. For if one is to result from another, it will have to pa.s.s through such a vast number of contrarieties-and indeed even more than any determinate number. Consequently (i) into some "elements" transformation will never be effected-viz. if the intermediates are infinite in number, as they must be if the "elements" are infinitely many: further (ii) there will not even be a transformation of Air into Fire, if the contrarieties are infinitely many: moreover (iii) all the "elements"
become one. For all the contrarieties of the "elements" above F must belong to those below F, and vice versa: hence they will all be one.