'Et moi, .... si j'avait su comment en revenir, One service mathematics has rendered the je n'y semis point all: human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent: therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non inearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a...

The Third International Kant Congress met at the University of Rochester from March 30 through April 4, 1970. Over two hundred students of Kant's philosophy from Europe, Africa, and North and South America attended. The Congress was organized by a Committee consisting of Gottfried Martin of the University of Bonn and myself as co-chairmen, and the following members: Professors Ingeborg Heidemann (Bonn), Gerhard Funke (Mainz), Edmond Ortigues (Rennes), Stephan Korner (Bristol), W. H. Walsh (Edinburgh), George A. Schrader, Jr. (Yale), and John R. Silber (University of Texas). Generous financial...

The present volume is intended to give an overall picture of research in pro gress in the field of generative grammar in various parts of Europe. The term 'generative grammar' must, however, be understood here rather broadly. What seemed to be an easily definable technical term several years ago is becoming more and more vague and imprecise. Research in generative gram mar is carried on according to rather diversified methodological principles and being a generative grammarian is often more a matter of confession than any adherence to the common line of methodology which can be traced back to...

The present selection from the Wissenschaftslehre (Sulzbach 1837) of Bernard Bolzano (1781-1848) aims at giving a compact view of his main ideas in logic, semantics, epistemology and the methodology of science. These ideas are analyzed from a modern point of view in the Introduction. Furthermore, excerpts from Bolzano's correspondence are included which yield important remarks on his own work. The translation of the sections from the Wissenschaftslehre are based on a German text, which I have located in the Manuscript Department of the University Library in Prague (signature: 75 B 459). It...

Keckermann remarked of the sixteenth century, "never from the begin- ning of the world was there a period so keen on logic, or in which more books on logic were produced and studies oflogic flourished more abun- dantly than the period-in which we live. " 1 But despite the great profusion of books to which he refers, and despite the dominant position occupied by logic in the educational system of the fifteenth, sixteenth and seven- teenth centuries, very little work has been done on the logic of the post- medieval period. The only complete study is that of Risse, whose account, while...

The present work has three principal objectives: (1) to fix the chronology of the development of the pre-Euclidean theory of incommensurable magnitudes beginning from the first discoveries by fifth-century Pythago- reans, advancing through the achievements of Theodorus of Cyrene, Theaetetus, Archytas and Eudoxus, and culminating in the formal theory of Elements X; (2) to correlate the stages of this developing theory with the evolution of the Elements as a whole; and (3) to establish that the high standards of rigor characteristic of this evolution were intrinsic to the mathematicians' work....

I first became interested in De dialectica in 1966, while I was doing re- search on Augustine's knowledge of logic. At the time I made a transla- tion of the Maurist text and included it as an appendix to my doctoral dissertation (Yale, 1967). In 1971 I thoroughly revised the translation on the basis of the critical text of Wilhelm Crecelius (1857) and I have re- cently revised it again to conform to Professor Jan Pinborg's new edition. The only previously published translation of the whole of De dialectica . is N. H. Barreau's French translation in the Oeuvres completes de Saint Augustin...

The selections contained in these volumes from the papers and letters of Leibniz are intended to serve the student in two ways: first, by providing a more adequate and balanced conception of the full range and penetration of Leibniz's creative intellectual powers; second, by inviting a fresher approach to his intellectual growth and a clearer perception of the internal strains in his thinking, through a chronological arrangement. Much confusion has arisen in the past through a neglect of the develop ment of Leibniz's ideas, and Couturat's impressive plea, in his edition of the Opuscu/es et...

When this book was first published, more than five years ago, I added an appendix on How the Pythagoreans discovered Proposition 11.5 of the 'Elements'. I hoped that this appendix, although different in some ways from the rest of the book, would serve to illustrate the kind of research which needs to be undertaken, if we are to acquire a new understanding of the historical development of Greek mathematics. It should perhaps be mentioned that this book is not intended to be an introduction to Greek mathematics for the general reader; its aim is to bring the problems associated with the early...