Page "What the Tortoise Said to Achilles" Paragraph 50

The Wittgensteinian philosopher Peter Winch discussed the paradox in The Idea of a Social Science and its Relation to Philosophy ( 1958 ), where he argued that the paradox showed that " the actual process of drawing an inference, which is after all at the heart of logic, is something which cannot be represented as a logical formula ... Learning to infer is not just a matter of being taught about explicit logical relations between propositions ; it is learning to do something " ( p. 57 ).

Winch goes on to suggest that the moral of the dialogue is a particular case of a general lesson, to the effect that the proper application of rules governing a form of human activity cannot itself be summed up with a set of further rules, and so that " a form of human activity can never be summed up in a set of explicit precepts " ( p. 53 ).