nnot be generated from something incorporeal nor from a body which is not an element； and the only remaining alternative is that they are generated from one another。
7
We must； therefore； turn to the question； what is the manner of their generation from one another？ Is it as Empedocles and Democritus say； or as those who resolve bodies into planes say； or is there yet another possibility？ （1） What the followers of Empedocles do； though without observing it themselves； is to reduce the generation of elements out of one another to an illusion。 They make it a process of excretion from a body of what was in it all the time…as though generation required a vessel rather than a material…so that it involves no change of anything。 And even if this were accepted； there are other implications equally unsatisfactory。 We do not expect a mass of matter to be made heavier by compression。 But they will be bound to maintain this； if they say that water is a body present in air and excreted from air； since air becomes heavier when it turns into water。 Again； when the mixed body is divided； they can show no reason why one of the constituents must by itself take up more room than the body did： but when water turns into air； the room occupied is increased。 The fact is that the finer body takes up more room； as is obvious in any case of transformation。 As the liquid is converted into vapour or air the vessel which contains it is often burst because it does not contain room enough。 Now； if there is no void at all； and if； as those who take this view say； there is no expansion of bodies； the impossibility of this is manifest： and if there is void and expansion； there is no accounting for the fact that the body which results from division cfpies of necessity a greater space。 It is inevitable； too； that generation of one out of another should come to a stop； since a finite quantum cannot contain an infinity of finite quanta。 When earth produces water something is taken away from the earth； for the process is one of excretion。 The same thing happens again when the residue produces water。 But this can only go on for ever； if the finite body contains an infinity； which is impossible。 Therefore the generation of elements out of one another will not always continue。 （2） We have now explained that the mutual transformations of the elements cannot take place by means of excretion。 The remaining alternative is that they should be generated by changing into one another。 And this in one of two ways； either by change of shape； as the same wax takes the shape both of a sphere and of a cube； or； as some assert； by resolution into planes。 （a） Generation by change of shape would necessarily involve the assertion of atomic bodies。 For if the particles were divisible there would be a part of fire which was not fire and a part of earth which was not earth； for the reason that not every part of a pyramid is a pyramid nor of a cube a cube。 But if （b） the process is resolution into planes； the first difficulty is that the elements cannot all be generated out of one another。 This they are obliged to assert； and do assert。 It is absurd； because it is unreasonable that one element alone should have no part in the transformations； and also contrary to the observed data of sense； according to which all alike change into one another。 In fact their explanation of the observations is not consistent with the observations。 And the reason is that their ultimate principles are wrongly assumed： they had certain predetermined views； and were resolved to bring everything into line with them。 It seems that perceptible things require perceptible principles； eternal things eternal principles； corruptible things corruptible principles； and； in general； every subject matter principles homogeneous with itself。 But they； owing to their love for their principles； fall into the attitude of men who undertake the defence of a position in argument。 In the confidence that the principles are true they are ready to accept any consequence of their application。 As though some principles did not require to be judged from their results； and particularly from their final issue！ And that issue； which in the case of productive knowledge is the product； in the knowledge of nature is the unimpeachable evidence of the senses as to each fact。 The result of their view is that earth has the best right to the name element； and is alone indestructible； for that which is indissoluble is indestructible and elementary； and earth alone cannot be dissolved into any body but itself。 Again； in the case of those elements which do suffer dissolution； the 'suspension' of the triangles is unsatisfactory。 But this takes place whenever one is dissolved into another； because of the numerical inequality of the triangles which compose them。 Further； those who hold these views must needs suppose that generation does not start from a body。 For what is generated out of planes cannot be said to have been generated from a body。 And they must also assert that not all bodies are divisible； coming thus into conflict with our most accurate sciences； namely the mathematical； which assume that even the intelligible is divisible； while they； in their anxiety to save their hypothesis； cannot even admit this of every perceptible thing。 For any one who gives each element a shape of its own； and makes this the ground of distinction between the substances； has to attribute to them indivisibility； since division of a pyramid or a sphere must leave somewhere at least a residue which is not sphere or a pyramid。 Either； then； a part of fire is not fire； so that there is a body prior to the element…for every body is either an element or composed of elements…or not every body is divisible。
8
In general； the attempt to give a shape to each of the simple bodies is unsound； for the reason； first； that they will not succeed in filling the whole。 It is agreed that there are only three plane figures which can fill a space； the triangle； the square； and the hexagon； and only two solids； the pyramid and the cube。 But the theory needs more than these because the elements which it recognizes are more in number。 Secondly； it is manifest that the simple bodies are often given a shape by the place in which they are included； particularly water and air。 In such a case the shape of the element cannot persist； for； if it did； the contained mass would not be in continuous contact with the containing body； while； if its shape is changed； it will cease to be water； since the distinctive quality is shape。 Clearly； then； their shapes are not fixed。 Indeed； nature itself seems to offer corroboration of this theoretical conclusion。 Just as in other cases the substratum must be formless and unshapen…for thus the 'all…receptive'； as we read in the Timaeus； will be best for modelling…so the elements should be conceived as a material for composite things； and that is why they can put off their qualitative distinctions and pass into one another。 Further； how can they account for the generation of flesh and bone or any other continuous body？ The elements alone cannot produce them because their collocation cannot produce a continuum。 Nor can the composition of planes； for this produces the elements themselves； not bodies made up of them。 Any one then who insists upon an exact statement of this kind of theory； instead of assenting after a passing glance at it； will see that it removes generation from the world。 Further； the very properties； powers； and motions； to which they paid particular attention in allotting shapes； show the shapes not to be in accord with the bodies。 Because fire is mobile and productive of heat and combustion； some made it a sphere； others a pyramid。 These shapes； they thought； were the most mobile because they offer the fewest points of contact and are the least stable of any； they were also the most apt to produce warmth and combustion； because the one is angular throughout while the other has the most acute angles； and the angles； they say； produce warmth and combustion。 Now； in the first place； with regard to movement both are in error。 These may be the figures best adapted to movement； they are not； however； well adapted to the movement of fire； which is an upward and rectilinear movement； but rather to that form of circular movement which we call rolling。 Earth； again； they call a cube because it is stable and at rest。 But it rests only in its own place； not anywhere； from any other it moves if nothing hinders； and fire and the other bodies do the same。 The obvious inference； therefore； is that fire and each several element is in a foreign place a sphere or a pyramid； but in its own a cube。 Again； if the possession of angles makes a body produce heat and combustion； every element produces heat； though one may do so more than another。 For they all possess angles； the octahedron and dodecahedron as well as the pyramid； and Democritus makes even the sphere a kind of angle； which cuts things because of its mobility。 The difference； then； will be one of degree： and this is plainly false。 They must also accept the inference that the mathematical produce heat and combustion； since they too possess angles and contain atomic spheres and pyramids； especially if there are； as they allege； atomic figures。 Anyhow if these functions belong to some of these things and not to others； they should explain the difference； instead of speaking in quite general terms as they do。 Again； combustion of a body produces fire； and fire is a sphere or a pyramid。 The body； then； is turned into spheres or pyramids。 Let us grant that these figures may reasonably be supposed to cut and break up bodies as fire does； still it remains quite inexplicable that a pyramid must needs produce pyramids or a sphere spheres。 One might as well postulate that a knife or a saw divides things into knives or saws。 It is also ridiculous to think only of division when allotting fire its shape。 Fire is generally thought of as combining and connecting rather than as separating。 For though it separates bodies different in kind； it combines those which are the same； and the combining is essential to it； the functions of connecting and uniti