i. m. bochenski - a history of formal logic

1、A HISTORY OF FORMAL LOGIC BY I. M. BOCHE?SKI TRANSLATED AND EDITED BY IVO THOMAS UNIVERSITY OF NOTRE DAME PRESS 1961 -iii- Questia Media America, Inc. www.questia.com Publication Information: Book Title: A History of For

2、mal Logic. Contributors: I. M. Bochenski - author, Ivo Thomas - transltr, Ivo Thomas - editor. Publisher: University of Notre Dame Press. Place of Publication: Notre Dame, IN. Publication Year: 1961. Page Number: iii. A

3、 HISTORY OF FORMAL LOGIC is a revised translation by Ivo Thomas of the German edition, Formale Logik, by J. M. Bocheński, published and copyrighted by Verlag Karl Alber, Freiburg/München, in 1956 © 1961 by Univ

4、ersity of Notre Dame Press, Notre Dame, Indiana Library of Congress Catalog Card Number 58-- 14183 Printed in the U.S.A. PREFACE TO THE GERMAN EDITION This history of the problems of formal logic, which we believe to be

5、the first comprehensive one, has grown only in small part from the author's own researches. Its writing has been made possible by a small group of logicians and historians of logic, those above all of the schools o

6、f Warsaw and Münster. It is the result of their labours that the work chiefly presents, and the author offers them his thanks, especially to the founders Jan ?ukasiewicz and Heinrich Scholz. A whole series of scho

7、lars has been exceptionally obliging in giving help with the compilation. Professors E. W. Beth ( Amsterdam), Ph. Boehner O.F.M. (St. Bonaventure, N.Y.), A. Church ( Princeton), O. Gigon ( Bern), D. Ingalls (Harvard),

8、J. ?ukasiewicz ( Dublin), B. Mates ( Berkeley, California), E. Moody ( Columbia University, New York), M. Morard O.P. ( Fribourg), C. Regamey ( Fribourg/ Lausanne) and I. Thomas O.P. (Blackfriars, Oxford) have been kind

9、 enough to read various parts of the manuscript and communicate to me many valuable remarks, corrections and additions. Thanks to them I have been able to remove various inexactitudes and significantly improve the cont

10、ent. Of course they bear no responsibility for the text in its final state. The author is further indebted for important references and information to Mlle. M. T. d'Alverny, Reader of the Department of Manuscripts

11、of the BibliothU=00E8que Nationale in Paris, Dr. J. Vajda of the Centre National de la Recherche Scientifique in Paris, Professors L. Minio-Paluello ( Oxford), S. Hulsewé ( Leiden), H. Hermes and H. Scholz ( M

12、2;nster i. W.), R. Feys ( Louvain) and A. Badawi ( Fuad University, Cairo). Dr. A. Menne has been kind enough to read the proofs and make a number of suggestions. My assistant, Dr. Thomas Räber, has proved a real c

13、ollaborator throughout. In particular, I could probably not have achieved the translation of the texts into German without his help. He has also been especially helpful in the compilation of the Bibliography and the pr

14、eparation of the manuscript for press. -v- A HISTORY OF FORMAL LOGIC In the course of my researches I have enjoyed the help of several European libraries. I should like to name here those in Amsterdam ( University Libra

15、ry), Basel ( University Library), Göttingen (Niedersächsische Landes- und Universitätsbibliothek), Kolmar ( Stadtbibliothek), London ( British Museum and India Office Library), Munich ( Bayerische Staats

16、bibliothek), Oxford ( Bodleian Library) and Paris ( Bibliothèque Nationale); above all the Kern- Institut in Leiden and the institutes for mathematical logic in Louvain and Münster which showed me notable hosp

17、itality. Finally, last but not least, the Cantonal and University Library of Fribourg, where the staff has made really extraordinary efforts on my behalf. The completion of my inquiries and the composition of this book

18、was made materially possible by a generous grant from the Swiss national fund for the advancement of scientific research. This enabled me to employ an assistant and defray the costs of several journeys, of microfilms e

19、tc. My best thanks are due to the administrators of the fund, as to all who have helped me in the work. Since the manuscript was completed, Fr. Ph. Boehner O.F.M. and Dr Richard Brodführer, editor of the series 

20、9;Orbis Academicus', have died. Both are to be remembered with gratitude. 1.05 My opinion is that while the force of the inference lies in the terms, yet the whole proposition is to be denied. . . . Rightly the who

21、le sequent and antecedent proposition is to be denied, since the inference lies between the entire propositions, though the force of the inference depends on the terms. . . . So that the hypothetical proposition is rig

22、htly said not to be composed of simple terms, but to be conjoined from several propositions, inasmuch as it propounds that what the sequent proposition manifests, follows from what the precedent (manifests). So that the

23、 denial is not to be effected according to the terms alone, but according to the entire propositions between which the relation of consequence is propounded. -viii- Consequences themselves are distinguished from their

24、metalogical formulations (cf. the commentary preceding 31.14), the latter being called 'maximae propositiones' and defined thus: 1.06 That proposition which contains the sense of many consequences and manifests

25、the manner of proof common to their determining features (differentiae) according to the force of their relationship, is called a 'maximal proposition'. E.g. along with these consequences: 'if it is man, it

26、 is animal', 'if it is pearl, it is stone', 'if it is rose, it is flower', 'if it is redness, it is colour' etc., in which species precede genera, a maximal proposition such as the following

27、is adduced: of whatever the species is predicated, the genus too (is predicated). . . . This maximal proposition contains and expresses the sense of all such consequences and manifests the way of yielding inference com

28、mon to the antecedents. There is a rich store of maxims in Abelard, but it is not always easy to see whether they belong to the logic of terms or propositions. This ambiguity has been noted with reference to Kilwardby

29、(cf. § 31, B) where one might be tempted to think that it was unconscious. But the terminology is not subject to direct attention in Kilwardby; in Abelard it is, and the ambiguity is noted and accepted. The follow

30、ing passage may need apology for its length, but not for its great interest in respect of terminology, semantic considerations (on which we cannot here delay), maxims both of validity and invalidity, and the reduction o

31、f some of them to others, 1.06 and 1.07 are enough to establish the basis and essentials of § 31 firmly in the 12th century. 1.07 'Antecedent' and 'consequent' are sometimes used to designate comple

32、te enunciations as when in the consequence: if Socrates is man, Socrates is animal, we say that the first categorical is antecedent to the second; sometimes in the designation of simple terms (dictio) or what they sign

33、ify, as when we say in regard to the same consequence that the species is antecedent to the genus, i.e. 'man' to 'animal', the nature or relationship provides inferential force. . . But whether we take

34、'antecedent' and 'consequent' for simple terms or complete enunciations, we can call them the parts of hypothetical enunciations, i.e. the parts of which the consequences are composed and of which they

35、consist, not parts of which they treat. For we cannot accept as true this consequence: if he is man, he is animal, if it treats of utterances (vocibus) be they terms or propositions. For it is false that if -ix- the utt

36、erance 'man' exists, there should also be the utterance 'animal'; and similarly in the case of enunciations or their concepts (intellectibus). For it is not necessary that he who has a concept generated

37、by the precedent proposition should also have one generated from the consequent. For no diverse concepts are so akin that one must be possessed along with the other; indeed everyone's own experience will convince h

38、im that his soul does not retain diverse concepts and will find that it is totally occupied with each single concept while he has it. But if someone were to grant that the essences of concepts follow on one another lik

39、e the essences of the things from which the concepts are gained, he would have to concede that every knower has an infinity of concepts since every proposition has innumerable consequences. Further, whether we treat of

40、 enunciations or of their concepts, we have to use their names in a consequence; but if 'man' or 'animal' are taken as names either of enunciations or concepts, 'if there is man there is animal'

41、 cannot at all he a consequence, being composed entirely of terms, as much as to say: 'if man animal'; indeed as a statement it is quite imperfect. To keep, therefore, a genuine relation of consequence we must

42、concede that it is things which are being treated of, and accept the rules of antecedent and consequent as given in the nature of things. These rules are as follows: 1. on the antecedent being posited, the consequent

43、is posited; 2. on the consequent being destroyed, the antecedent is destroyed, thus: 'if there is man there is animal', 'if there is not animal there is not man'; 3. neither if the antecedent is posite

44、d, is the consequent destroyed, 4. nor if the antecedent is destroyed need the consequent be destroyed 5. or posited, just as 6. neither if the consequent is destroyed is the antecedent posited, 7. nor if the same (t

45、he consequent) is posited is it (the antecedent) either posited 8. or removed. Since the last ((6)-(8)) are equivalent to the former ((3)-(5)) as also their affirmatives are mutually equivalent, the two sets must be si

46、multaneously true or false. The two first rules are also in complete mutual agreement and can be derived from one another, e.g. if it is conceded: if there is man there is animal, it must also be conceded: 'if there