Much reference has been made to Paul Ernest's "philosophy of mathematics education" to legitimise a strong fallibilist trend in mathematics education. This article presents the argument that: (1) This philosophy makes unwarranted assumptions that have been taken as "given". For example, that "absolutist" or "Platonist" views of mathematics necessarily imply the transmission model of teaching mathematics. (2) The very basis of this philosophy contains a contradiction: that mathematics cannot be separated from its social origins, yet mathematics has a logical necessity that is independent of its origin. (3) This philosophy downplays mathematics as a formal, academic system of knowledge in the attempt to promote a child-centred pedagogy or the mathematics of social practices. (4) Ernest's attempt to semiotically reduce proof to calculation is flawed. This article explores what is meant by fallibilism in relation to the views of many educationalists who appear not to like mathematics as a formal, academic body of knowledge and draws out the educational implications of these views.