Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of (...) the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians. (shrink)
One of the tasks with which communication engineers are presented is that of devising a mechanism by which a significant sequence of words, a message, produced by somebody, the sender of the message, is reproduced at some other place, with the shortest practical time lag. The reproduction must be such that the receiver of the message will be able to understand what the sender meant by his message, at least, if he knows the sender's language. The following illustration is typical: (...) A writes on a sheet of paper “I love you” and wishes that B, 3000 miles away, should become aware of the full content of this message, with little delay and at a low cost. There will be institutions, in a capitalistic society, which will compete with each other in providing A, for a price, with the required service. Those companies which perform these services most satisfactorily, i.e., with an overall better combination of faithfulness, time lag, and cost, will get the job. The executives of these companies will hire engineers and put them to work on improving this overall combination. (shrink)
This volume comprises seven of the eight addresses presented before the International Colloquium on Mathematical Logic and Foundations of Set theory held at the Acadmey Building in Jerusalem, Israel, On November 11-14, 1968.
In June 22-27,1970, an International Working Symposium on Pragmatics of Natural Languages took place in Jerusalem under the auspices of The Israel Academy of Sciences and Humanities and the Division of Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Science.! Some thirty philosophers, logicians, linguists, and psychologists from Israel, U.S.A., West-Germany, England, Belgium, France, Scotland, and Denmark met in seven formal and a number of informal sessions in order to discuss some ofthe problems (...) around the use and acquisition oflanguage which in the eyes of an increasing number of scholars have been left under treated in the recent upsurge ofinterest in theoretical linguistics and philos ophy of language. More specifically, during the formal sessions the following topics were discussed: The validity of the syntactics-seman tics-pragmatics trichotomy The present state of the competence-performance issue Logic and linguistics The New Rhetoric Speech acts Language acquisition. The participants in the Symposium distributed among themselves re prints and preprints of relevant material, partly in advance of the meeting, partly at its beginning. Each session was introduced by one or two modera tors, and summaries of each day's proceedings were prepared and distri buted the next day. The participants were invited to submit papers after the symposium, written under its impact. The eleven essays published here are the result. (shrink)