 This question was ultimately connected with the problem of understanding the atomistic continuum. The arithmetized conception—in the sense of Dedekind or Cantor, where real numbers are identified with suitable sets of rationals—shifted the attention towards arbitrary infinite sequences of natural numbers. But this notion was not so easy to accept. According to Bernstein (Bernstein 1905a, p. 449), an infinite sequence (or an infinite set) must be given by a genuine rule. But what is a rule? Since one must be liberal (in order not to have just special classes of reals, if one is too restrictive), one is naturally driven to think of arbitrary finitely described laws, shifting the attention towards the syntax of the rules. However, unless one considers ordinary language, no such syntax is available and this engenders indeterminacy (this is Peano’s diagnosis, see below Peano 1902–1906).