The Strong Programme is officially "inductively based", i.e. warranted by its long list of alleged explanatory successes. The programme embodies an alternative, fall-back line of argument, however, which is purely philosophical. This is somewhat ironic in view of the school's aim of getting rid of philosophy; still, this strategy has a strong weapon at its disposal, viz. Wittgenstein's late philosophy. The chief argument consists of the so-called "rule-following considerations' which apparently show that all judgements, including those that record the outcome of scientific experiments, are unconstrained by "meanings' construed as objective, Platonic essences. Instead, they are only constrained by the ongoing linguistic practices of the community and are thus purely conventional. The ultimate determinants of judgement are social interests, which means that the "closure" of the scientific discovery process is brought about mainly by social factors. Unfortunately, this argument is based upon a misapplication of Wittgenstein's philosophy. Even worse, the argument leads to large-scale indeterminacy of meaning of scientific theories, much more radical than that postulated by Quine.