 It is perhaps worth mentioning that similar remarks apply to the case of a necessary a priori connection between properties. It is a necessary a priori truth that all mathematicians are rational. Following our model, we can say that it is essential to the kind mathematician to be such that all of its instances are also instances of the kind rational (thing). It does not follow that Andrew Wiles, who is in fact a mathematician, could not fail to be rational—in which case he would also fail to be a mathematician. To give an even more perspicuous example, it is a necessary a priori truth that all bachelors are unmarried. It does not follow that Michael, who is in fact a bachelor, could not be married.