Unless noted otherwise, ‘theory’ will always mean ‘interpreted theory’; uninterpreted theories say nothing and have no ontological commitments. When the theory is couched within first-order logic, the interpretation is given by standard Tarskian semantics. In particular, each monadic predicate of the language of the theory has been assigned a class as its interpretation; each n-ary predicate has been assigned a class of n-tuples; the quantifiers are interpreted objectually by way of assignments to the variables. On the other hand, it is not supposed that the domain of the quantifiers has been fixed once and for all. Sometimes, in applying the criteria, alternative domains are considered, and the theory is evaluated for truth under the various alternatives.