バートランド・ラッセル(著),平野智治(訳)『数理哲学序説』序文
* 出典:バートランド・ラッセル(著),平野智治(訳)『数理哲学序説』(岩波書店,1954年8月刊。276+7pp. 岩波文庫 青33-649-1)
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Preface to Introduction to Mathematical Philosophy, 1919. | ||
(写真は、1918年のラッセル: From R. Clark's B. Russell and His World, 1981) 本書はもともと「入門(書)」として書かれたものであり、扱っている問題の徹底的な議論を目指すものではない。これまでは論理記号に精通した人でなければ理解できなかった諸成果を、初学者にも容易に理解できるようにのべることは有益であると思われる。現在なおかなり疑問視されている問題については、極力独断を避けるように努力した。そのため、考察する主題がある程度制限された。
バートランド・ラッセル |
THIS book is intended essentially as an 'Introduction,' and does not aim at giving an exhaustive discussion of the problems with which it deals. It seemed desirable to set forth certain results, hitherto only available to those who have mastered logical symbolism, in a form offering the minimum of difficulty to the beginner. The utmost endeavour has been made to avoid dogmatism on such questions as are still open to serious doubt, and this endeavour has to some extent dominated the choice of topics considered. The beginnings of mathematical logic are less definitely known than its later portions, but are of at least equal philosophical interest. Much of what is set forth in the following chapters is not properly to be called 'philosophy,' though the matters concerned were included in philosophy so long as no satisfactory science of them existed. The nature of infinity and continuity, for example, belonged in former days to philosophy, but belongs now to mathematics. Mathematical philosophy, in the strict sense, cannot, perhaps, be held to include such definite scientific results as have been obtained in this region; the philosophy of mathematics will naturally be expected to deal with questions on the frontier of knowledge, as to which comparative certainty is not yet attained. But speculation on such questions is hardly likely to be fruitful unless the more scientific parts of the principles of mathematics are known. A book dealing with those parts may, therefore, claim to be an introduction to mathematical philosophy, though it can hardly claim, except where it steps outside its province, to be actually dealing with a part of philosophy. It does deal, however, with a body of knowledge which, to those who accept it, appears to invalidate much traditional philosophy, and even a good deal of what is current in the present day. In this way, as well as by its bearing on still unsolved problems, mathematical logic is relevant to philosophy. For this reason as well as on account of the intrinsic importance of the subject, some purpose may be served by a succinct account of the main results of mathematical logic in a form requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. Here, however, as elsewhere, the method is more important than the results, from the point of view of further research ; and the method cannot well be explained within the framework of such a book as the following. It is to be hoped that some readers may be sufficiently interested to advance to a study of the method by which mathematical logic can be made helpful in investigating the traditional problems of philosophy. But that is a topic with which the following pages have not attempted to deal. Bertrand Russell |