Sometimes this inconvenience would not be unavoidable, but sometimes also it is essential. A relation is incomprehensible without two terms; it is impossible to have the intuition of the relation, without having at the same time that of its two terms, and without noticing they are two, because, if the relation is to be conceivable, it is necessary that there be two and only two.
V
Arithmetic
I reach what M. Couturat calls the ordinal theory which is the foundation of arithmetic properly so called. M. Couturat begins by stating Peano's five assumptions, which are independent, as has been proved by Peano and Padoa.
1. Zero is an integer.
2. Zero is not the successor of any integer.
3. The successor of an integer is an integer.
To this it would be proper to add,
Every integer has a successor.
4. Two integers are equal if their successors are.