Peanian Implicature

Speranza

In 1890 Peano introduced the use of iota and inverted iota to distinguish a one-member class from its member, which permitted him to overcome previous confusion between ∈ ("being a member of"), ⊃ ("contained in"), and = ("equal to").

In general, Peano showed the importance of distinguishing the properties of a class from those of the individuals of that class, a need shown, for example, by his "sophism" (actually, a paralogism):

"Peter and Paul are apostles; the apostles are twelve; therefore Peter and Paul are twelve."

Incidentally, by Peter and Paul, Peano did NOT mean Strawson and Grice.