His particular targets were Giuseppe Peano, Burali-Forti and the philosopher and logician Louis Couturat, who belonged to the same logicist school as Bertrand Russell. In Science et Méthode (Flammarion, 1908), we read: "First we see Mr Burali-Forti define the number 1 as follows:
a definition eminently suited to conveying the idea of the number 1 to anyone who has never heard of it. I understand Peanian so poorly that I dare not venture a criticism, but I fear this definition may beg the question, since I see the numeral 1 on the left-hand side and One written out in full on the right."
"I hasten to add that Mr Couturat's definition of the number 1 is more satisfactory. One, he says in effect, is the number of elements in a class any two of whose elements are identical. It is more satisfactory, I say, in the sense that he does not use the word 'one' to define 1; on the other hand, he does use the word 'two'. But I fear that if Mr Couturat were asked what 'two' is, he would be obliged to use the word 'one'."
