Cantor says nothing about what it might mean to call the well-ordering hypothesis a ‘law of thought’, and he never did return to this question directly; however, in one form or another, this claim is key. It could be that Cantor at this time considered the WOH as something like a logical principle.[16] This, however, is not particularly clear, especially since the study of formal logic adequate for mathematical reasoning was only in its infancy, and the set concept itself was new and rather unclearly delimited. Another suggestion is that well-orderability is intrinsic to the way that ‘well-defined’ sets are either presented or conceived, e.g., that it is impossible to think of a collection's being a set without at the same time allowing that its elements can be arranged ‘discretely’ in some way, or even that such arrangement can be automatically deduced from the ‘definition’. Thus, if one views sets as necessary for mathematics, and one holds that the concept of set itself necessarily involves the discrete arrangement of the elements of the set, then WOH might appear necessary, too. But all of this is imprecise, not least because the notion of set itself was imprecise and imprecisely formulated. One clear implication of Cantor's remark is that he regards the WOH as something which does not require proof. Nonetheless, not long after he had stated this, Cantor clearly had doubts both about the well-orderability of the continuum and about cardinal comparability (see Moore 1982: 44). All of this suggested that the WOH, and the associated hypothesis that the alephs represent the scale of infinite cardinality, do require proof, and cannot just be taken as ‘definitional’. Thus, it seemed clear that the whole Cantorian project of erecting a scale of infinite size depends at root on the correctness of the WOH.