This paper provides a theoretical rationale for distinguishing four basic argument forms. On the basis of a survey of classical and contemporary definitions of argument, a set of assumptions is formulated regarding the linguistic and pragmatic aspects of arguments. It is demonstrated how these assumptions yield four different argument forms: (1) first-order predicate arguments, (2) first-order subject arguments, (3) second-order subject arguments, and (4) second-order predicate arguments. These argument forms are then further described and illustrated by means of concrete examples, and it is explained how they are visually represented in the Periodic Table of Arguments.