Abstract

These essays offer an exposition and defense of William Hamilton's theory that categorical propositions implicitly involve quantification over the predicate term; e.g., for Hamilton, “All S is P” is more accurately rendered as, “All S is some P.” This makes good sense if we treat this proposition as an embedded identity statement, i.e., “If anything is an S then there is some P it is identical with.” This approach yields a coherent theory of the distribution of terms that can be used for evaluating the validity of both immediate inferences and categorical syllogism. It also captures a fragment of the identity theory.