O. Among many striking and thought-provoking ideas that the later Wittgenstein provides are his considerations on following a rule. An important part of Wittgenstein’s contribution stemming from the rule-following considerations lies in presenting a new picture of logical and mathematical necessity. The picture in question, which we shall call anthropological conventionalism, necessity. The picture in question, which we shall call anthropological conventionalism, enjoys, as we shall see shortly, the unusual merit of going between the Scylla of uncompromising conventionalism and the Charybdis of platonism in mathematics.