Publisher Summary This chapter discusses relations between the study of reasoning and the theory of implication. The chapter illustrates that, in order to understand the relations between reasoning and logic, it is crucial not to confuse issues of implication with issues of inference. Inference and implication are very different things and the relation between them is rather obscure. Logic as a theory of implication is a very different sort of theory from logic as a theory of reasoning or methodology. Historically the term "logic" has been used in both ways. Current usage favors restriction of the term "logic" to the theory of implication. The theory of reasoning is best called "the theory of reasoning" or "methodology". There are many technical studies of implication and of logic understood as the theory of implication. Inference and reasoning are not well understood. This is because a theory of inference or reasoning must be part of a theory of rationality and rationality is not well understood.