The readings in this chapter discuss some miscellaneous issues about the nature of reasoning.

Lewis Carroll’s well-known (to philosophers) story about Achilles and the Tortoise implicitly illustrates the distinction between premises in an argument and rules of inference. When a person makes an inference, say, from premises A and B to conclusion Z, it seems that they must be aware of the logical relationship between the premises and the conclusion-that is, it seems that they must know that if A and B are true, Z is; otherwise, they would not accept the inference. Lewis Carroll’s story shows, however, that if we think of this knowledge as an additional premise the person must accept, then an infinite regress ensues.