In this paper, a theory T H based on combining type freeness with logic is introduced and is then used to build a theory of properties which is applied to determiners and quantiiers. It is well known that mixing type freeness and logic leads to contradictions. For example, by taking the following syntax of terms: t := xjx:tjt 1 t 2 j:t and applying the term x::xx to itself one gets a contradict...