Here we see something of the trouble that is connected with the ostensive (and therefore exclusively extensional) approach to concepts. The property embodied by the class just formed is in fact : the length ( = longest axis) of this particular rose I am pointing to, instead of the length of 7cm, because if we knew this length of the rose in advance, we then already had characterized the property, and would not need a class of individuals to characterize it. The intention of mathematical Logic is to go around such a direct assessment of a property, and it does so by trying not to explicitly mention this property before coming up with a class of relevant individuals. So by not mentioning ' 7cm ' we are left with ' length of this rose ', that is, the property embodied by the class is length of this rose. The class was formed by choosing objects whose longest axis (that is, their length) was the same as that of the rose, that is, objects that are length-similar or length-identical to this rose (which can be determined, not necessarily by measuring the rose's length and measuring the length of all the other objects [which procedure should be avoided], but just by lining up the objects in such a way that their longest axes lie parallel to each other). In this way, indeed, we did not have to measure the rose as to its length and thus explicitly mention ' 7cm ' ( In the same way we can find out that two sets of objects are such that the number of objects contained in the one set is the same as that in the other, without counting these objects, namely by finding out that it is possible to establish a one-to-one relationship or mapping between the elements of the two sets).
This ostensive procedure of defining properties necessarily involves a particular object that is pointed to. We then say that all the objects we have chosen are X-similar to that particular object. But if we really want to now what X is we must examine this particular object after all !