(a) The objections to the choice principle were of two kinds. The main objection was put forward by Borel in 1905 in the Mathematische Annalen (Borel 1905), the journal which published Zermelo's paper, and it is also widely discussed in correspondence between some leading French mathematicians, and also published in that year in the same Journal (see Hadamard et al. 1905). The objection is basically that Zermelo's principle fails to specify a ‘law’ or ‘rule’ by which the choices are effected; in other words, the covering used is not explicitly defined, which means that the resulting well-ordering is not explicitly defined either. In a letter to Borel, Hadamard makes it clear that the opposition in question is really that between the assumption of the existence of an object which is fully described, and of the existence of an object which is not fully described (see Hadamard et al. 1905, esp. 262). In his reply, Zermelo remarks that the inability to describe the choices is why the choice principle is in effect an axiom, which has to be added to the other principles. In effect, the position is that if one wants to do certain things which, e.g., rely on the WOT, then the choice principle is indispensable. His position, to repeat, is like the one that Euclidean geometry takes towards parallels. 