ON GENERATION AND CORRUPTION [29]
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 assumed 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 pass 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.
6
As for those who agree with Empedocles that the 'elements' of body are more than one, so that they are not transformed into one another-one may well wonder in what sense it is open to them to maintain that the 'elements' are comparable. Yet Empedocles says 'For these are all not only equal...' If it is meant that they are comparable in their amount, all the 'comparables' must possess an identical something whereby they are measured. If, e.g. one pint of Water yields ten of Air, both are measured by the same unit; and therefore both were from the first an identical something. On the other hand, suppose (ii) they are not 'comparable in their amount' in the sense that so-much of the one yields so much of the other, but comparable in 'power of action (a pint of Water, e.g. having a power of cooling equal to that of ten pints of Air); even so, they are 'comparable in their amount', though not qua 'amount' but qua Iso-much power'. There is also (iii) a third possibility. Instead of comparing their powers by the measure of their amount, they might be compared as terms in a 'correspondence': e.g. 'as x is hot, so correspondingly y is white'. But 'correspondence', though it means equality in the quantum, means similarity in a quale. Thus it is manifestly absurd that the 'simple' bodies, though they are not transformable, are comparable not merely as 'corresponding', but by a measure of their powers; i.e. that so-much Fire is comparable with many times-that-amount of Air, as being 'equally' or 'similarly' hot. For the same thing, if it be greater in amount, will, since it belongs to the same kind, have its ratio correspondingly increased. A further objection to the theory of Empedocles is that it makes even growth impossible, unless it be increase by addition. For his Fire increases by Fire: 'And Earth increases its own frame and Ether increases Ether." These, however, are cases of addition: but it is not by addition that growing
6
As for those who agree with Empedocles that the 'elements' of body are more than one, so that they are not transformed into one another-one may well wonder in what sense it is open to them to maintain that the 'elements' are comparable. Yet Empedocles says 'For these are all not only equal...' If it is meant that they are comparable in their amount, all the 'comparables' must possess an identical something whereby they are measured. If, e.g. one pint of Water yields ten of Air, both are measured by the same unit; and therefore both were from the first an identical something. On the other hand, suppose (ii) they are not 'comparable in their amount' in the sense that so-much of the one yields so much of the other, but comparable in 'power of action (a pint of Water, e.g. having a power of cooling equal to that of ten pints of Air); even so, they are 'comparable in their amount', though not qua 'amount' but qua Iso-much power'. There is also (iii) a third possibility. Instead of comparing their powers by the measure of their amount, they might be compared as terms in a 'correspondence': e.g. 'as x is hot, so correspondingly y is white'. But 'correspondence', though it means equality in the quantum, means similarity in a quale. Thus it is manifestly absurd that the 'simple' bodies, though they are not transformable, are comparable not merely as 'corresponding', but by a measure of their powers; i.e. that so-much Fire is comparable with many times-that-amount of Air, as being 'equally' or 'similarly' hot. For the same thing, if it be greater in amount, will, since it belongs to the same kind, have its ratio correspondingly increased. A further objection to the theory of Empedocles is that it makes even growth impossible, unless it be increase by addition. For his Fire increases by Fire: 'And Earth increases its own frame and Ether increases Ether." These, however, are cases of addition: but it is not by addition that growing