the writer and the reader.
First we see Burali-Forti define the number 1 as follows:
a definition eminently fitted to give an idea of the number 1 to persons who had never heard speak of it.
I understand Peanian too ill to dare risk a critique, but still I fear this definition contains a petitio principii, considering that I see the figure 1 in the first member and Un in letters in the second.
However that may be, Burali-Forti starts from this definition and, after a short calculation, reaches the equation:
which tells us that One is a number.
And since we are on these definitions of the first numbers, we recall that M. Couturat has also defined 0 and 1.
What is zero? It is the number of elements of the null class. And what is the null class? It is that containing no element.
To define zero by null, and null by no, is really to abuse the wealth of language; so M. Couturat has introduced an improvement in his definition, by writing:
which means: zero is the number of things satisfying a condition never satisfied.
But as never means in no case I do not see that the progress is great.
I hasten to add that the definition M. Couturat gives of the number 1 is more satisfactory.
One, says he in substance, is the number of elements in a class in which any two elements are identical.
It is more satisfactory, I have said, in this sense that to define 1, he does not use the word one; in compensation, he uses the word two. But I fear, if asked what is two, M. Couturat would have to use the word one.