The virtuous tortoise

There is no philosophically interesting distinction to be made between inference-rules and premises. That there is such a distinction is often held to follow from the possibility of infinite regress illustrated by Carroll’s story of Achilles and the tortoise. I will argue that this is wrong on three separate grounds. Consequently, Carroll’s fable provides no motivation to abandon the traditional logical separation of arguments into their premises and conclusions. There is no proposition that must be taken to be a rule and must not be taken as a premise.