For all ages and all levels of difficulty, these puzzles range from those that can be solved in minutes to those that will beguile for hours.

    A range of puzzles dealing with word play and logic, mathematics and philosophy, featuring Alice and the creatures of Wonderland.

    It demonstrates how to encourage, develop, and foster the processes which seem to come naturally to mathematicians.

    Both volumes provide exercises and their solutions.Volume 2, Intensional logic and Logical Grammar, begins with an introduction to the various principles of intensional semantics, and then provides a treatment of various intensional logics, such as modal propositional logic and modal predicate logic, and tense logic. It also introduces type theory, lambda-abstraction, and categorical syntax. Type theory and intensional logic are combined in the well-known intensional type logic employed by Montague. After the necessary technical logical machinery is thus presented, a detailed introduction to Montague Grammar as a specimen of logical grammar follows. The final chapter is dedicated to an introduction of three new developments in logical grammar: the theory of generalized quantifiers, flexible categorical syntax, and discourse representational theory.L. T. F. Gamut is a collective pseudonym for J. F. A. K. van Benthem, J. A. G. Groenendijk, D. H. J. de Jongh, M. J. B. Stokhof, all senor staff members in the Institute for Logic, Language & Computation at the University of Amsterdam, and H. J. Verkuyl emeritus professor at the University of Utrecht.

    The origins of Zermelo's Axiom of Choice, as well as the controversy that it engendered, certainly lie in that intersection. Since the time of Aristotle, mathematics has been concerned alternately with its assumptions and with the objects, such as number and space, about which those assumptions were made. In the historical context of Zermelo's Axiom, I have explored both the vagaries and the fertility of this alternating concern. Though Zermelo's research has provided the focus for this book, much of it is devoted to the problems from which his work originated and to the later developments which, directly or indirectly, he inspired. A few remarks about format are in order. In this book a publication is indicated by a date after a name; so Hilbert 1926, 178 refers to page 178 of an article written by Hilbert, published in 1926, and listed in the bibliography.

    It was his work that set Husserl on to the road of phenomenology and intentionality, that inspired Meinong's theory of the object which influenced Bertrand Russell, and the entire Polish school of philosophy.^Descriptive Psychology presents a series of lectures given by Brentano in 1887; they were the culmination of his work, and the clearest statement of his mature thought. It was this later period which proved to be so important in the work of his student, Husserl.This is the first English translation of his work. Benito Muller has added a concise introduction which places Brentano within the history of philosophy and psychology, and locates his influence in contemporary thought.

    This has shown in the variety of reactions received from readers of the first edition of the present Book. Many have reacted to issues raised in its philosophical discussions, while some have even solved a number of the open technical questions raised in the logical elaboration of the latter. These results will be recorded below, at a more convenient place. In the seven years after the first publication, there have been some noticeable newer developments in the logical study of Time and temporal expressions. As far as Temporal Logic proper is concerned, it seems fair to say that these amount to an increase in coverage and sophistication, rather than further break-through innovation. In fact, perhaps the most significant sources of new activity have been the applied areas of Linguistics and Computer Science (including Artificial Intelligence), where many intriguing new ideas have appeared presenting further challenges to temporal logic. Now, since this Book has a rather tight composition, it would have been difficult to interpolate this new material without endangering intelligibility.