An Intensional Formalization of Generic Statements

Abstract

A statement is generic if it expresses a generalization about the members of a kind, as in, ’Pear trees blossom in May,’ or, ’Birds lay egg’. In classical logic, generic statements are formalized as universally quantified conditionals: ’For all x, if ..., then ....’ We want to argue that such a logical interpretation fails to capture the intensional character of generic statements because it cannot express the generic statement as a simple proposition in Aristotle’s sense, i.e., a proposition containing only one single predicate. On the contrary, we’ll show that lambda abstraction and combinatory logic can help us transform the classical, non-simple and extensional expression of generic statements into a new, simple and intensional formalization, through the introduction of an operator that we will call ALL*. We will show that this new operator allows for the possibility of a single predication, e.g. fly(), because it builds, out of a concept like ’bird’, a concrete universal, e.g. ’birds’, upon which the single predicate can be applied to authentically formalize a generic statement, e.g. ’birds fly’.