 We are particularly seduced by the feeling or belief that an infinite mathematical disjunction makes good sense in the case where we can provide a recursive rule for generating each next member of an infinite sequence. For example, when we say “There exists an odd perfect number” we are asserting that, in the infinite sequence of odd numbers, there is (at least) one odd number that is perfect—we are asserting ‘\(\phi(1) \vee \phi(3) \vee \phi(5) \vee{}\) and so on’ and we know what would make it true and what would make it false (PG 451). The mistake here made, according to Wittgenstein (PG 451), is that we are implicitly “comparing the proposition ‘\((\exists n)\)…’ with the proposition… ‘There are two foreign words on this page’”, which doesn’t provide the grammar of the former ‘proposition’, but only indicates an analogy in their respective rules.