I. M. BOCHENSKI - A HISTORY OF AL LOGIC.doc

a history of formal logic by i. m. bocheski translated and edited by ivo thomas university of notre dame press 1961 -iii- questia media america, inc. publication information: book title: a history of formal 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 history of formal logic is a revised translation by ivo thomas of the german edition, formale logik, by j. m. bocheski, published and copyrighted by verlag karl alber, freiburg/mnchen, in 1956 1961 by university 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 the first comprehensive one, has grown only in small part from the authors own researches. its writing has been made possible by a small group of logicians and historians of logic, those above all of the schools of warsaw and mnster. 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 scholars 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), 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 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 content. 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. dalverny, reader of the department of manuscripts 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. hulsew ( leiden), h. hermes and h. scholz ( mnster 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 rber, has proved a real collaborator 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 preparation 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 library), basel ( university library), gttingen (niederschsische landes- und universittsbibliothek), kolmar ( stadtbibliothek), london ( british museum and india office library), munich ( bayerische staatsbibliothek), oxford ( bodleian library) and paris ( bibliothque nationale); above all the kern-institut in leiden and the institutes for mathematical logic in louvain and mnster which showed me notable hospitality. 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 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 etc. 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 brodfhrer, editor of the series orbis academicus, have died. both are to be remembered with gratitude. i. m. bocheski-vi- preface to the english edition a. general in this edition of the most considerable history of formal logic yet published, the opportunity has of course been taken to make some adjustments seen to be necessary in the original, with the authors full concurrence. only in 36, however, has the numeration of cited passages been altered owing to the introduction of new matter. those changes are as follows: german edition english edition 36.13 36.17 36.14 36.18 36.15-17 36.21-23 other alterations that may be noted are: the closing paragraphs of 15 have been more accurately suited to the group of syllogisms which they concern; 16.17 appears here as a principle rejected, not accepted, by aristotle; 27.28 has been re-interpreted and the lengthy citation dropped; a new sub-section, on the beginnings of combinatory logic, has been added to 49. a few further items have been added to the bibliography. on grounds of economy this last has been reproduced photographically; probably such german remarks and abbreviations as it contains will not much inconvenience its users. a word needs to be said about 5 a, technical expressions, which has naturally had to be largely re-written. in the orginal, the author expressed his intention of using aussage as a name for sentential expressions, and so for certain dispositions of black ink, or bundles of sound-waves. so understood, the word could be treated as generally synonymous with the scholastic propositio and the english sentence when used in an equally technical sense, and was deemed a tolerable translation of russells proposition the reference of which is often ambiguous. but these equations evidently cannot be maintained here; for one thing, they would warrant the change of proposition to sentence throughout quotations from -vii- russell; secondly we prefer, with a. church (1.01), to speak of propositional logic rather than sentential logic; and thirdly, one risks actual falsification of ones material by imposing on it a grid of sharp distinctions which for the most part belongs to a later period than anything here treated. as noted in the body of the work, the stoics and frege were alone in making the distinction between sign and significate as sharply as is now customary. so we have normally used proposition where the author used aussage -always, indeed, when the scholastic propositio needs translation. in part v usage is of course largely conditioned by the fact that so many citations now appear in their original language. b. abelard as to the contents, an evident lacuna is the absence of any texts from the 12th century a.d., and the author himself has suggested that 30.03 is quite insufficient reference to peter abelard, described in an epitaph as the aristotle of our time, the equal or superior of all logicians there have been (1.02), and in similar words by john of salisbury (1.03). we propose only to elaborate that single reference, by way of giving a taste of this twelfth century logic, closely based on boethius in its past, growing in an atmosphere of keen discussion in its present, evidently holding the seeds of later scholastic developments as exemplified in this book. abelards consequences are certainly not fully emancipated from the logic of terms (cf. 30.03) yet he realizes that propositions are always involved. his explanation of consequentia may first be noted: 1.04 a hypothetical proposition is called a consequence after its consequent, and a conditional after its condition. speaking later of a form of the laws of transposition (43.33) he says: 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 whole 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 rightly 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 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 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 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 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 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 common 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 (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 following 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 of 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 complete 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 signify, 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 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 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 utterance 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 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 everyones own experience will convince him 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 like 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 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 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 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 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 posited, 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 (the 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 simultaneously 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 is not animal there is not man, and conversely. when the first is true, the second will be proved true as follows, by inducing an impossibility. let us posit this as true: if there is man there is animal, and doubt about this: if there is not animal there is not man, i.e. whether animal negated negates man. we shall confirm this in the following way. either animal negated negates man or negated it admits man, so that it may * happen that when animal is denied of something man may exist in that thing. suppose it be conceded that when animal is denied, man may persist; yet it was formerly conceded that man necessarily requires animal, viz. in the consequence: if there is man there is animal. and so it is contingent that what is not animal, be animal; for what the antecedent admits, the consequent admits. . . . but this is impossible. . . . quite definitely propositional are the rules: 1.08 whatever follows from the consequent (follows) also from the antecedent; whatever implies the antecedent (implies) also the consequent; used in the derivation of categorical syllogisms. while it is clear that the primary source of all this doctrine of consequence is the de differentiis topicis of boethius, we can also see the germ of later developments in abelards realization that some are deducible from others ( 1.07, 1.09), and his examinations of some that he finds doubtful (1.10). it is noteworthy that categorical syllogisms are presented entirely by means of concrete instances and metalogical rules (regulae) -which are not reckoned as maxims since the inferential (or implicative) force of the premisses is derived entirely from the disposition of the terms, is, in abelards terminology, complexional, a term preserved in kilwardby. variables of the object-language are nowhere used. indeed, except in expositions of the boethian hypothetical syllogisms, the only place we find variables in abelard is a passage where he introduces a simple lettered diagram to help the intuition in an original argument: 1.11 if a genus was always to be divided into proximate species or proximate differences, every division of a genus _ * emending de rijks possint to possit -xi- would be dichotomous - which was boethiuss view. . . . but i remember having an objection to this on the score of (the predicament of) relation. . . . this will be more easily seen if we designate the members of the predicament by letters and distinguish its arrangement by a figure like this. if now c and d were mutually related on the one hand, b and c on the other, since b is prior to its species d, while d is together with (simul) its relative c, b would precede c; so that b would precede both its species and its relative; hence also itself. there follow two more arguments to show that the system supposed figured stands or falls entire with any one of its parts. there is no suggestion in abelard that syncategorematica, important for later theory of consequences, are a primary concern of logic, the purpose of which he states as follows: 1.12 logic is not a science of using or composing arguments, but of discerning and estimating them rightly, why some are valid, others invalid. but he is puzzled about the signification, if any, of syncategorematica, and refers to various contemporary views: 1.13 conjunctions and prepositions ought to have some signification of their own. . . . what concepts are designated by expressions of this kind, it is not easy to say. . . . some think that such expressions have sense but no reference (solos intellectus generare, nullamque rem subiectam habere) as they grant also to be the case with propositions. . . . there are also some who make out that logicians have quite removed such expressions from the class of significant ones. . . . the opinion i favour is that of the grammarians who make contributions to logic, that we should admit them as significant, but should say that their significance lies in their determining certain properties of the references (res) of the words governed by the prepositions. . . . conjunctions too, as indicating conjunction of things, determine a property in their regard, e.g. when i say: a man and a horse runs, by the conjunction and i unite them in runing, and at the same time indicate that by the and. -xii- the emergence of a logic of propositions from one of terms is e