Relations and Multiple Quantifiers in Predicate Logic
Thus far we have been using only one-place predicates. These are predicates that only require one name (put differently, these are properties that only require one object) to complete them. For example, _____ is red = Rx _____ is heavy = Hx _____ is a wife = Wx ( ∃ x)Rx is true if and only if there is at least one thing in the universe that is red. ( ∃ x)Hx is true iff there is at least one thing in the universe that is heavy, and so on. (x)Rx is true iff everything in the universe is red, and so on. But, as we all know, there are predicates that are more than one place. In other words, there are predicates that require more than one name to complete them (put differently, there are properties-- better-called relations--that require more than one object). For example ____ is heavier than ____ = Hxy ____ is taller than ____ = Txy ____ loves ____ = Lxy ____ is between ____, _____ = Bxyz (∃ x) (∃y )Hxy is true iff there is something ...