In languages with just first order quantifiers (e.g. English LF a la Heim & Kratzer 1998) whether a sentence is valid (logically true, true in all models) depends on the valence of the lexical predicates in L. If all are one place, P1s, then validity is algorithmic (decidable); this fails once a single lexical two place predicate, P2, is added (Boolos and Jeffrey 1989). We illustrate this with a simple non-mathematical example from English. E.g. lexical P2s like like plus first order quantifiers enable us to construct sentences that are false in all finite models but true in some infinite ones. Mere P1s cannot force their models to be infinite (B&L 1989). Building on this we show that object quantifiers are logically more expressive than subject quantifiers (contra Heim & Kratzer). So while all subject quantifiers may occur on objects, many object quantifiers do not occur grammatically on subjects. Further, the logical richness of P2s also supports the existence of non-compositional quantifiers determined by <subject, object> pairs that map the P2 denotation directly to 0 or 1.