It is common to consider an area of science as a system of real or sup posed truths which not only continuously extends itself, but also needs periodical revision and therefore tests the inventive capacity of each generation of scholars anew. It sounds highly implausible that a science at one time would be completed, that at that point within its scope there would be no problems left to solve. Indeed, the solution of a scientific problem inevitably raises new questions, so (...) that our eagerness for knowledge will never find lasting satisfaction. Nevertheless there is one science which seems to form an exception to this rule, formal logic, the theory of rigorous argumentation. It seems to have reached the ideal endpoint of every scientific aspiration already very shortly after its inception; using the work of some predecessors, Aristotle, or so it is at least assumed by many, has brought this branch of science once and for all to a conclusion. Of course this doesn't sound that implausible. We apparently know what rigorous argumentation is; otherwise various sciences, in particular pure mathematics, would be completely impossible. And if we know what rigorous argumentation is, then it cannot be difficult to trace once and for all the rules which govern it. The unique subject of formal logic would therefore entail that this science, in variance with the rule which holds for all other sciences, has been able to reach completion at a certain point in history. (shrink)

Another striking deviation with regard to philosophical tradition consists in the fact that contemporary schools in the philosophy of mathematics, with the exception again of Brouwer's intuitionism, hardly ever refer to mathematical thought.

Many philosophers have considered logical reasoning as an inborn ability of mankind and as a distinctive feature in the human mind; but we all know that the distribution of this capacity, or at any rate its development, is very unequal. Few people are able to set up a cogent argument; others are at least able to follow a logical argument and even to detect logical fallacies. Nevertheless, even among educated persons there are many who do not even attain this relatively (...) modest level of development. According to my personal observations, lack of logical ability may be due to various circumstances. In the first place, I mention lack of general intelligence, insufficient power of concentration, and absence of formal education. Secondly, however, I have noticed that many people are unable, or sometimes rather unwilling, to argue ex hypothesi; such persons cannot, or will not, start from premisses which they know or believe to be false or even from premisses whose truth is not, in their opinion, sufficient ly warranted. Or, if they agree to start from such premisses, they sooner or later stray away from the argument into attempts first to settle the truth or falsehood of the premisses. Presumably this attitude results either from lack of imagination or from undue moral rectitude. On the other hand, proficiency in logical reasoning is not in itself a guarantee for a clear theoretic insight into the principles and foundations of logic. (shrink)

SummaryThe germs of future development, contained in Aristotle's logical works, are indicated, and their influence on the later evolution of logic is explained.The history of symbolic logic since Boole's Mathematical analysis and De Morgan's Formal logic, both of which were published in 1847, is divided into four approximately subsequent phases, viz.:1. algebra of logic; this phase is characterized by Boole's work;2. logical foundation of mathematics; this phase is characterized by Frege's, Peano's and Russell's work, by the discovery of the antonomies (...) of logic and set theory, by the Couturat‐Poincaré debate and by the rise of Brouwer's intuitionism;3. intuitive metamathematics, concentrating in Hilbert's attempts towards a consistency proof for classical analysis; the discovery of Gödel's theorem necessitated a change of policy;4. axiomatic methodology, deriving from Hilbert's metamathematics and culminating so far in Tarski's semantics. — E. W. B. (shrink)

A few days before his death my husband requested me to write a few words of thanks on the publication of this collection of articles. He had already prepared the greater part of the volume for the press and had also decided on the title Science a Road to Wisdom. His original selection was somewhat more comprehensive, which is still partly reflected in the Preface. Knowing how much he wished to see this collection published, I respectfully and lovingly fulfil his (...) request, thanking Else M. Barth and J. J. A. Mooij for their extensive and expert care in putting the final touches to the volume. ADDITION TO THE TRANSLATION Finally, I wish to thank Peter G. E. Wesly for his willingness to undertake the translation of the book into English. c. P. C. BETH-PASTOOR IX PREFACE In this republication of a number of philosophical studies I have refrained from including articles of a specialized nature on symbolic logic and the methodology of the exact sciences. There was no cause to include my contributions towards the didactics of mathematics and physics, nor did I consider it appropriate to reprint pieces of a predominantly polemical nature. I decided, however, that a very modest selection from my purely historical work would not be out of place. (shrink)

In contributing a foreword to this book I am complying with a wish my husband expressed a few days before his death. He had completed the manuscript of this work, which may be considered a companion volume to his book Formal Methods. The task of seeing it through the press was undertaken by Mr. J. J. A. Mooij, acting director of the Institute for Research in Foundations and the Philosophy of Science (Instituut voor Grondslagenonderzoek en Filoso:fie der Exacte Wetenschappen) of (...) the University of Amsterdam, with the help of Mrs. E. M. Barth, lecturer at the Institute. I wish to thank Mr. Mooij and Mrs. Barth most cordially for the care with which they have acquitted themselves of this delicate task and for the speed with which they have brought it to completion. I also wish to express my gratitude to Miss L. E. Minning, M. A., for the helpful advice she has so kindly given to Mr. Mooij and Mrs. Barth during the proof reading. C. P. C. BETH-PASTOOR VII PREFACE A few years ago Mr. Horace S. (shrink)