Definition and substitutability
How can the accuracy of a definition be checked? For most semantic theories, a minimum requirement on a term’s definition is the following:
• substitution of the definiens for the definiendum should be truth preserving in all contexts.
For example, ‘keep in equilibrium’ can be accepted as the definition of balance if it is possible to substitute this phrase for balance in all the con texts in which balance occurs without rendering any of them false. All the sentences in (25), for example, remain true if ‘keep in equilibrium’ is substituted:
Substituting ‘keep in equilibrium’ into these sentences will change their register, and the resulting utterances will often sound considerably less idiomatic and more technical (e.g. Now, children, you have to keep the egg in equilibrium on the spoon). Nevertheless, the fact that the sentences remain true is taken to be a sign of the adequacy of the definition. The rationale of this requirement is the principle of identity under substitution articulated by the seventeenth-century German philosopher Leibniz: eadem sunt, quae sibi mutuo substitui possunt, salva veritate (Latin for ‘things are the same which can be substituted one for the other with truth intact’). If a defi niens can be substituted for a defi niendum salva veritate, i.e. with the sentence in which the terms occur remaining true, then the defi niendum and the definiens should be considered identical in meaning.
Preservation of truth is not the only possible criterion for the regulation of definitions. Instead, the criterion of preservation of meaning (in an informal sense of this term) is also conceivable. On this view, a definition is accepted if it can be substituted for the definiendum ‘with sense intact’ (salvo sensu): if, that is, it involves neither addition nor loss of meaning with respect to the meaning of the definiendum. This suggestion raises an important problem, however: since it is the definition itself that is supposed to reveal an expression’s meaning, the best way to determine that two words have the same meaning is to compare their definitions. Preservation of meaning as a criterion of definitional adequacy is therefore circular.
