In this paper we propose some reflections on Wittgenstein’s ideas about grammar and rules; then we shall consider some consequences of these for the foundations of set theory and, in particular, for the introduction of major concepts of set theory in education. For instance, a community of practice can decide to follow a particular rule that forbids the derivation of arbitrary sentences from a contradiction: since, according to Radford’s perspective, knowledge is the result of thinking, and thinking is a cognitive social praxis, the mentioned choice can be considered as a form of real and effective knowledge.
Bagni, Giorgio T.
""Obeying a rule": Ludwig Wittgenstein and the foundations of Set Theory,"
The Mathematics Enthusiast: Vol. 5
, Article 5.
Available at: http://scholarworks.umt.edu/tme/vol5/iss2/5