The principal object of a refutation is a thesis, that is, an asserted proposition. By extension, the term ‘refutation’ is also said of arguments, which conclude to theses, persons, who hold them, or views, which aggregate them around a common theme or topic.
The methods of refutation available for a given type depend on the type of the object whose refutation is sought, and are greater in proportion with the complexity of the object itself. Thus, the refutation of a thesis consists in a proof that it is not the case. The refutation of a view consists in either the refutation of any thesis constitutive of that view or a proof of its inconsistency. The refutation of an argument consists in a proof of that it is not demonstrative. Hence, a refutation of an argument may consist in a proof that it is invalid, that any of its parts is irrelevant to its conclusion, that any of its parts are inconsistent with each other, that knowledge of any of its premises depends on knowledge of its conclusion, or that any of its premises or conclusions fail to be the case. The refutations available for more complex objects thus extend those available for less complex ones.
The types of refutations of theses will be proportionate to the types of thesis, and hence to the types of assertible propositions. Most basically, propositions may be simple, asserting or denying one thing of one thing, or complex, asserting or denying many of many things, one of many, or many of one. What is asserted is called the predicate; what it is asserted of, the subject. A complex proposition may be formed 1) by linking propositions via connecting terms like ‘or’, ‘if’, or ‘and’, 2) by the composition of complex predicates or subjects through analogous means, or 3) by the use of a common term to designate multiple things by a single name.