 But the existence of such an entity seems to be rather precarious. Consider, for instance, the perfect triangle we were supposed to have in mind during the demonstration of Thales’ theorem. If it is a perfect triangle, it obviously has to have three sides, since a perfect triangle has to be a triangle, and nothing can be a triangle unless it has three sides. But of those three sides either at least two are equal or none, that is to say, the triangle in question has to be either isosceles or scalene (taking ‘isosceles’ broadly, including even equilateral triangles, for the sake of simplicity). However, since it is supposed to be the universal model of all triangles, and not only of isosceles triangles, this perfect triangle cannot be an isosceles, and for the same reason it cannot be a scalene triangle either. Therefore, such a universal triangle would have to have inconsistent properties, namely, both that it is either isosceles or scalene and that it is neither isosceles nor scalene. However, obviously nothing can have these properties at the same time, so nothing can be a universal triangle any more than a round square. So, apparently, no universal triangle can exist. But then, what was our demonstration about? Just a little while ago, we concluded that it could not be directly about any particular triangle (for it was not about the triangle in the figure, and it was even less about any other particular triangle not in the figure), and now we had to conclude that it could not be about a universal triangle either. But are there any further alternatives? It seems obvious that through this demonstration we do gain universal knowledge concerning all particulars. Yet it is also clear that we do not, indeed, we cannot gain this knowledge by examining all particulars, both because they are potentially infinite and because none of them perfectly satisfies the conditions stated in the demonstration. So, there must have been something wrong in our characterization of the universal, which compelled us to conclude that, in accordance with that characterization, universals could not exist. Therefore, we are left with a whole bundle of questions concerning the nature and characteristics of universals, questions that cannot be left unanswered if we want to know how universal, necessary knowledge is possible, if at all.