ThiscollectionofpapersstemsoriginallyfromaconferenceonProperty Theory,TypeTheoryandSemanticsheldinAmherstonMarch13-16 1986.The conference brought together logicians,philosophers, com- puter scientists and linguists who had been working on these issues (often in isolation from one another).Ourintent wastoboostdebate and exchange of ideas on these fundamental issuesat a time ofrapid changeinsemanticsandcognitivescience. The paperspublished in thiswork have evolved substantially since their original presentation at the conference. Given their scope, we thought it convenient to divide the work into two volumes.The first deals primarily withlogicaland philosophical foundations, the second with more empirical semantic issues.Whilethere isa common set of issuestyingthetwovolumestogether, theyareboth self-containedand canbereadindependentlyofoneanother. Twoofthepapersinthepresentcollection(vanBentheminvolume Iand ChierchiainvolumeII)werenotactuallyread attheconference. They are nevertheless included here for their direct relevance to the topicsofthevolumes. Regrettably, some of the papers that were presented (Feferman, Klein,and Plotkin) could not be included in the presentwork due to timingproblems. Wenevertheless thank theauthorsfortheircontribu- tionintermsofideasandparticipationinthedebate. The conference had a group of invited discussants whichincluded Emmon Bach,JanetFodor,Erhard Hinrichs, Angelika Kratzer, Fred Landman, Richard Larson,Godehard Link, Chris Menzel,Uwe Mon- nich,andCarlPollard.Wethankthemall(alongwiththeotherpartici- pants)fortheirstimulatingandlivelypresence.