paradoxes, then, you should seek to elicit by means of these common-place rules. now as for making any one babble, we have already said what we mean by ‘to babble’. this is the object in view in all arguments of the following kind: if it is all the same to state a term and to state its definition, the ‘double’ and ‘double of half’ are the same: if then ‘double’ be the ‘double of half’, it will be the ‘double of half of half’. and if, instead of ‘double’, ‘double of half’ be again put, then the same expression will be repeated three times, ‘double of half of half of half’. also ‘desire is of the pleasant, isn’t it?’ desire is conation for the pleasant: accordingly, ‘desire’ is ‘conation for the pleasant for the pleasant’.

all arguments of this kind occur in dealing (1) with any relative terms which not only have relative genera, but are also themselves relative, and are rendered in relation to one and the same thing, as e.g. conation is conation for something, and desire is desire of something, and double is double of something, i.e. double of half: also in dealing (2) with any terms which, though they be not relative terms at all, yet have their substance, viz. the things of which they are the states or affections or what not, indicated as well in their definition, they being predicated of these things. thus e.g. ‘odd’ is a ‘number containing a middle’: but there is an ‘odd number’: therefore there is a ‘number-containing-a-middle number’. also, if snubness be a concavity of the nose, and there be a snub nose, there is therefore a ‘concave-nose nose’.

people sometimes appear to produce this result, without really producing it, because they do not add the question whether the expression ‘double’, just by itself, has any meaning or no, and if so, whether it has the same meaning, or a different one; but they draw their conclusion straight away. still it seems, inasmuch as the word is the same, to have the same meaning as well.