Books in the Studies in Logic: Mathematical Logic and Foundations series

Classifying objects --- thus collecting them into classes --- is anoperation both fundamental and common in everyday life as well as inscientific endeavours. Logic, philosophy, mathematics and computerscience analyse this activity by means of such notions as `class',`set', and `type'. Furthermore, according to the so-called ``logical(or naive) conception of classes", these notions are related to thenotion `concept' in that classes are considered `extensions' ofconcepts. This relationship, however, is a delicate one --- as wehave learned from the paradoxes of class theory. The contributions tothis volume shed new light both on concepts and classes and theirdelicate relationship. New and original approaches to these issues(e.g., map theory, epsilon-sets, intensional type theory, AFA settheory) are presented and discussed in the broader context of theirapplication to problems from informatics and linguistics. The focus ison such matters as unrestrictive comprehension, extensionality, therelationship between the notions of concept, class and extension, andon unfounded (circular and infinitely descending) patterns ofelementhood. These and related problems have always played a role inthe development of set theory and have always delivered motivation forthe development of unorthodox views and theories. This is alsodemonstrated in this volume by contributions dealing with the historyof Zermelo's axiomatization of set theory and Ackermann's class theorywith unrestrictive comprehension, respectively.The contributions of this volume are based on the presentation at aWorkshop on ``Alternative Set Theories --- Alternatives to Set Theory"held at the University of Southern Denmark in 2006.