Ceteris-Paribus Qualifiers

Antecedent-strengthening, a trivially valid inference of classical logic of the form: P → Q ? (P & R) → Q, has a counterpart in everyday reasoning that often fails. A plausible solution to the problem involves assuming an implicit ceteris paribus (CP) qualifier that can be explicated as an additional conjunct in the antecedent of the premise. The qualifier can be explicated as ‘everything else relevant remains unchanged’ or alternatively as ‘nothing interferes’. The qualifier appears most prominently in the context of the discussion of laws in the sciences, where these laws are often expressed with a CP qualifier. From an analysis of the qualifier’s role in the problem of antecedent-strengthening, we can learn more about CP qualifiers in general and in their application to the laws used in the sciences.