A Contribution to the History of Theories of Induction in the Middle Ages

STUDIEN UND TEXTE

ZUR GEISTESGESCHICHTE

DES MITTELALTERS

Dr. ALBERT ZIMMERMANN

BAND XXXVIII

ARGUMENTATIONSTHEORIE

Scholastische Forschungen zu den logischen und

semantischen Regeln korrekten Folgems

HERAUSGEGEBEN VON

KLAUS JACOBI

EJ. BRILL

LEIDEN • NEW YORK • KÖLN

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Argumentarionstheorie : scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns / herausgegeben von Klaus Jacobi.

p. cm. — (Studien und Texte zur Geistesgeschichte des Mittelalters, ISSN 0169-8125 ; Bd. 38)

English and German.

Includes bibliographical references and indexes. ISBN 9004098224

1. Inference. 2. Logic, Medieval. S.Insolubilia (Logic) 4. Topic (Philosophy^ I. Jacobi, Klaus. II. Series. BC35.I6A74 1993

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Argumentationstheorie : scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns / hrsg. von Klaus Jacobi. - Leiden , New York ; Köln : Brill. 1993

(Studien und Texte zur Getstesgeschichte des Mitlelalters ; Bd. 38' ISBN 90-04-09822-4

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INHALT

Vorwort xi Einleitung des Herausgebers xiii General Introduction xxiii

I. TOPISCHE INFERENZ

Zur Einführung I 3 Introduction I 9 Sten Ebbesen (Copenhagen)

The Theory of loci in Antiquity and the Middle Ages 15 Hartmut Brands (Düsseldorf)

Topik und Syllogistik bei William of Sherwood 41 Christoph Kann (Paderborn)

Zur Behandlung der dialektischen Orter bei Albert von Sachsen 59 Claude Lafleur (Quebec)

Logic in the Barcelona compendium (With Special Reference to Aristotle's Topics and Sopkistici elencki) 81

II. THEORIE DER FOLGERUNG: EX IMPOSSIBILI QUIDLIBET

Zur Einführung II 101 Introduction II 112 Iwakuma Y. (Kyoto)

Parmponto.ni's Thesis ex impossibili quidlibet sequitur. Com-ments on the Sources of the Thesis from the Twelfth Century 123 William J. Courtenay (University of Wisconsin, Madison)

Joke Spruyt (Maastricht)

Thirteenth-Century Positions on the Rule 'ex impossibili

sequitur quidhbet' 161

Angel d'Ors (Universidad de Navarra)

Ex impossibili quodlibet sequitur (John Buridan) 195

Franz Schupp (Paderborn)

Zur Textrekonstruktion der formalen und materialen Folgerung in der kritischen Ockham-Ausgabe 213

Matthias Kaufmann (Erlangen)

Nochmals: Ockhams consequential und die materiale Implikation 223

Stephen Read (St Andrews, Scotland)

Formal and Material Consequence, Disjunctive Syllogism and Gamma 233

III. INKONSISTENZ

Zur Einführung III 263 Introduction III 270

A. Inkonsistenz durch Selbstbezüglichkeit: De insolubilibus

Ria van der Lecq (Utrecht)

The Role of Language-levels in the Medieval Discussion on

insolubilia 277

Fabienne Pironet (Liège)

John Buridan on the Liar Paradox: Study of an Opinion and Chronology of the Texts 293

B. Inkonsistenz in bezug auf Zugestandenes: De obligationibus

Mikko Yrjönsuuri (Joensuu)

The Role of Casus in some Fourteenth Century Treatises on Sophismata and Obligations 301

H.A.G. Braakhuis (Nijmegen)

C.H. Kneepkens (Nijmegen)

Willem Buser of Heusden's Obligationes-Treatise "Ob rogatum": A ressourcement in the Doctrine of Logical Obli-gation? 343 E.J. Ashworth (University of Waterloo)

Ralph Strode on Inconsistency in Obligational Dis-putations 363

IV. GRUNDLAGEN FÜR BEWEISE UND ARGUMENTATIONEN

Zur Einführung IV 389 Introduction IV 398

Elizabeth Karger (CNRS, Paris)

A Theory of Immediate Inferences Contained in Buridan's Logic 407

José Miguel Gambra (Universidad Complutense de Madrid) Medieval Solutions to the Sophism of Accident 431

L.M. de Rijk (Leiden)

Der Streit über das medium démonstrations: die Frucht eines Mißverständnisses? 451 Jeroen van Rijen (Rotterdam)

Some Medieval Analyses of the Logic of 'qua' 465 Ignacio Angelelli (University of Texas, Austin)

Augustinus Triumphus' Alleged destructie of the Porphyrian Tree 483

Gyula Klima (Magyar Tudomânyos Akadémia, Budapest) ' 'Socrates est species. ' ' Logic, Metaphysics and Psychology in St. Thomas Aquinas's Treatment of a Paralogism 491 Allan Back (Kutztown University)

V. ARGUMENTATIONSFORMEN FÜR SPEZIELLE UNTERSUCHUNGEN UND REDEZWECKE

Zur Einführung V Introduction V

A. Spezielle Gegenstandsbereiche

Mieczyslaw Markowski (Krakow)

Dialektische und rhetorische Argumentation an der Krakauer Universität im 15. Jahrhundert

Simo Knuuttila (Helsinki)

Über Praktische Argumentation und Logik des Wollens im Mittelalter

533

543

E.P. Bös (Leiden)

A Contribution to the History of Theories of Induction in the Middle Ages 553

577

Renate Würsch (Basel)

Die Lehre vom Enthymem in der Rhetorik des Aristoteles und ihre Weiterentwicklung bei Avicenna und Averroes 589

607

B. Das urteilende Subjekt C.F.J. Martin (Glasgow)

Rules for Demonstration and Rules for Answering Questions in Aquinas 621 Alexander Broadie (Glasgow)

Assent in Inference Theory 637 Katherine H. Tachau (University of Iowa)

VI. LOGIK UND THEOLOGIE

Zur Einfühlung VI 671 Introduction VI 679

François Beets (Liège)

"Definite" and "Necessary Truth" in Early Scholastic Logic and Argumentation 687

Hermann Weidemann (Bonn)

Modalität und Konsequenz. Zur logischen Struktur eines theologischen Arguments in Peter Abaelards Dialectica 695

Jan A. Aertsen (Amsterdam)

Der Satz vom Widerspruch in der mittelalterlichen Philosophie. Baron von Münchhausen, Thomas von Aquin und Nikolaus von Kues 707

Charles Lohr (Freiburg i. Br.)

Ramon Lull's Theory of Scientific Demonstration 729

Bibliographie 747

Indices 775 Index rerum

552 KLAUS JACOBI

A CONTRIBUTION TO THE HISTORY OF THEORIES

OF INDUCTION IN THE MIDDLE AGES

E.P. Bos (Leiden)

1. INTRODUCTION

"Induction" is one of the main terms to reconstruct science, at least in the period from Francis Bacon (1561-1626) to Sir Karl Popper (born 1902). Only from about 1930 other keywords to understand science were used, such as "falsification", "paradigm", "researchprogram", "anarchy" etcetera. Nevertheless, the term "induction" keeps playing a part, even within philosophies that use e.g. "paradigm" as their main concept.

"Induction" could be defined, in a traditional fashion, as a kind of non-demonstrative argument, in which the truth of the premisses does not logically entail the truth of the conclusion, but provides a good reason for believing the conclusion.1 For instance, the property "expanding" is attributed to the natural kind "iron" after a certain number of experiments with pieces of iron which were heated. Traditionally, induction is opposed to deduction, which is demonstrative.

From a systematical viewpoint, there are different kinds of problems involved in induction, which are intimately related.

First there are problems about the method. We may distinguish between "closed" and "open" induction. In the first kind the basis of the generalization is the enumeration of all instances involved. In this way, there is no logical problem in the entailment of the conclu-sion. The second kind, open inductive reasoning, which is indicated by the definition mentioned, is not logically valid: could it, however, in some way be reduced to a logically valid argument? If so, how? How should an inductive argument be analysed? How many obser-vations of particular instances (formulated in the premisses) are needed so that one may attach belief to the truth of the conclusion? To what extent should the instances be observed under the same

cir-1 See M. Black, "Induction" in The Encyclopedia of Philosophy, ed. P. Edwards,

554 E.P. BOS

cumstances? Is there induction only on the level of particular things, such that the conclusion states that a certain property belongs to all instances of a species, or does it also occur on the level of the species, such that the conclusion states that a property belongs to a genus?

Secondly, there are problems about what is presupposed by induc-tion: is there regularity in nature? On what basis should such regularity be assumed?

Finally, what kind of knowledge do the sense-faculties supply, and, moreover, what is the degree of certainty obtained by the in-tellect; what is the relation between senses and intellect in this respect?

These different kinds of problems are discussed in modern the-ories of induction. Mostly, their examples are drawn from the his-tory of modern science from Copernicus (1473-1543) onwards. "Induction" is the key-notion in the philosophies of science of David Hume, John Stuart Mill, John Maynard Keynes, Rudolph Carnap and Hans Reichenbach. The term not only belongs to the theory of science since Copernicus, however. Originally the word "inductio" is a Latin translation of the Greek "epagoge" and, as is well known, already occurs in a rather technical sense in Plato. This use by Plato, and especially by Aristotle, who may be called the father of induction-theory, resembles our modern notion. More-over, the kinds of problems mentioned above occur in Ancient and Medieval Philosophy as well.

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 555

works but not to be attributed to the master himself (is the author John of Cornwall?), the author advocates a view which is remark-able in that he comes close to describing open induction as a proced-ure of natural science; the implication is that man has no certainty of the principles of a science, due to the limited number of observa-tions which serve as the basis for inductive reasoning (3.5). The Medieval thinkers just mentioned (perhaps with the exception of Grosseteste) seem to belong to a continental tradition of the thir-teenth century. John Duns Scotus (3.6) and William of Ockham (3.7) belong to an English tradition. Duns Scotus uses a rule denot-ing the regularity of nature ordained by God as a basis for induction. In this way he lays the basis for our knowledge of the first principles of science. Ockham uses the rule which says that all agents of a cer-tain species can produce effects of a same species; he calls this an "extrinsic middle" to establish man's certain knowledge of scientific principles. Finally, I shall return to a continental tradition: John Buridan and Marsilius of Inghen (3.8) in some respects associate themselves with thirteenth century theories, though they are also representatives of the fourteenth century awareness that our science is hypothetical, because the world is radically dependent on Gods free will.

The views on induction of some of the thinkers mentioned have already been discussed by modern scholars. Of some, not all rele-vant texts have been studied. Other philosophers have not been in-vestigated at all. In this article I intend to sketch in main lines the different answers to the problems mentioned above, and bring their theories in historical perspective, and also to correct and add to the literature on the subject.

2. ARISTOTLE

Aristotle sometimes uses the term "induction" (Greek: epagoge) in a general way2: e.g. in Physics I, ii3 he says that "we should take as

starting-point that things which exist by nature, either all things, or

2 For the Ancient use of "epagoge", see N. Tsouyopoulos, "Die induktive Methode und das Induktionsproblem in der griechischen Philosophie", Zeitschrift fia dlgtnutne Wisscnsc/iaßslhmrie 5, 1974, pp. 94-122. For the Medieval use of

"mductio", see below, note 24.

556 E.p. BOS

some of them, move and change; and this is clear from the induc-tion". Aristotle apparently means: from a survey of individual in-stances. In other places "induction" is more a technical term refer-ring to a well-defined procedure, viz. to the progress (ephodos) from individuals (ta kath' hekasta) to universals (ta katholou)*. In various places Aristotle discusses "induction" as technical procedure both in dialectical and in scientific or demonstrative knowledge. In his Prior Analytics II, xxi and xxiii, where he is most explicit on induc-tion, the emphasis is on the relationship between inductive and syl-logistic argument; in the Posterior Analytics, the famous chapter II, xix, he primarily discusses the various states of knowledge leading from the sensory cognition of particulars to the intellectual grasp by the nous of first principles, in the Topics I, xii induction is treated as a kind of dialectical argument. Outside his logical works Aristotle discusses "induction" e.g. in his Metaphysics and elsewhere5.

Recently, Aristotle's theory of induction has been studied by especially Ross,6 von Fritz,7 Hess8 and Tsouyopoulos.9 Without going into details I wish to make some remarks on Aristotle's theory in order to gain proper understanding of the Medieval theories. Ac-cording to Hess,10 Aristotle distinguishes between at least two kinds of scientific induction, viz. "intuitive induction" and "complete in-duction". The first kind is discusses, so Hess concludes, in the Posterior Analytics, II, xix, where the universals, or first principles," are grasped by intuition, starting from sensory knowledge via memory and experience. The first principles conceived, then, are related either to changing things (then they are the starting point of

* E.g. Topica, I, 12, 105 a 13.

5 The places where Aristotle treats induction are systematically ordered by W. Hess, "Erfahrung und Intuition bei Aristoteles", Ptironesis, 15, 1970, pp. 48-82, pp. +9-50.

6 W.D. Ross in Aristotle's Prior and Posterior Analytics. A Revised Text with

Introduc-tion and Commentary, ed. W.D. Ross, Oxford: Clarendon, 1949, pp. 47-51.

7 K. von Fritz, Die Epagoge bei Aristoteles (Sitzungsberichte der Bayerischen Akademie der Wissenschaften, Philos.-hist. Kl., H.3, 1964), München: Verlag der Bayerischen Akademie der Wissenschaften, 1964.

8 W. Hess, op.cit. (n. 5).

9 N. Tsouyopoulos, op.cit. (n. 2).

10 W. Hess, op.cit. (n. 5), p. 55.

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 557

productive knowledge or techne), or to unchanging things (in which case they are the basis of scientific knowledge); whether the number of individuals known are all members of the species, or just some, is not made explicit by Aristotle. Anyway, the intellect grasps the universal on this basis.

The other kind is complete induction, in which the universal is grasped on the basis of a complete survey of the particulars sub-sumed. This kind is exemplified in the final chapters of the Prior Ana-lytics, where inductive argument apparently can have the form of a logically valid syllogism.12 Here Aristotle discusses the reduction of induction to syllogism on the level of the species. As the number of the species is limited according to Aristotle, he in fact gives an example of closed induction, and the example is not very exciting, therefore.13 I wish to emphasize that in scientific and in dialectical (i.e. non-scientific) argumentation, Aristode defines induction as a means leading to knowledge which starts from what is more know-able to man and ends with what is more knowknow-able in itself. Aristotle rejects Plato's theory of anamnesis, as is well known.14 The basis of universal knowledge is sensory perception. Perception of just one single instance is sufficient basis to grasp a universal,15 though in a rudimentary form. E.g. in the Posterior Analytics, Aristotle says:16 the particular (e.g. Kallias-E.P. Bos) is perceived, the act of percep-tion involves the universal, (e.g. "man", not "Kallias"). In the Prior Analytics^1 he says that there are some things which we know

immediately. For instance, when we know that some particular figure is a triangle, we know that it possesses two angles of which the sum is equal to the sum of two right angles. This is like recollection, Aristotle says while referring to Plato's Meno.

Within the framework of a discussion of demonstratio quia (which, I think, is related to inductively acquired knowledge, because it

12 This example is the famous syllogism:

If A (long-living) applies to C (the species man, horse, and mule] and also B (not having bile) applies to all C, then, if G is convertible with B, A applies to C (Pnor Analytics, II, xxiii, 68 b 19-24). See K. von Fritz, op.cit. (n. 7), pp. 14-16; W. Hess, op.cit. (n. 5), pp. 56-60; N. Tsouyopoulos, op.cit. (n. 2), pp. 107-114.

13 See W.D. Ross, Aristotle, London: Methuen/New York: Barnes and Noble, 1964 (1st published 1923), pp. 39-40.

14 See especially Aristotle, Posterior Analytics, II, xix, 99 b 27-28

15 Cf. William of Ockham's theory, below, section 3.7. 16 Posterior Analytics, II, xix, 100 a 16-b 1.

558 E.p. BOS

leads from the perception of a fact to the knowledge of a cause) and demonstratie propter quid, Aristotle discusses in Posterior Analytics II, ii18 the case of an eclips. If someone were on the moon, he would not inquire as to the fact or reason, but the answer to both questions would be immediately clear to him. According to Aristotle, the trans-ition from knowledge of one individual to knowledge of a universal is quite easy, it seems. The same applies for what Aristotle calls "in-duction". While rejecting Plato's theory of anamnesis, Aristotle does not give a detailed explanation of this transition. Possibly, the model for Aristotle's theory of science is mathematics, where from a single demonstration of e.g. Pythagoras' theorem, the theorem as such is known.

Two concluding remarks. First, the philosopher distinguishes19 between, on the one hand, things that always come to be in the same way, e.g. the upward movement of fire,20 and other things that usually come to be, e.g. snow in winter.21 On the other hand there are things which happen by chance (apo tyches) (e.g. a man who hap-pened to meet his debtor on the marketplace; he could have looked for his debtor) or automatically (apo tautomatou) (e.g. a chair thrown into the air comes down on its four legs).22 Induction can lead to scientific knowledge in the strict sense if it reveals the properties in things which are always the case. So, Aristotle assumes a kind of necessary behaviour of natural things. By its nature, the intellect can acquire certainty of these things. Aristotle possibly suggests that, if induction leads to principles according to which some things are the case for the greater part, or usually, there is a weaker degree of scien-tific knowledge. Instructive in this respect is the first chapter of Aristotle's Meteorology23 and the way in which Aristotle practices

e.g. meteorological science. In this theory on science Aristotle is stricter than in his scientific research.

18 II, ii, 90 b 26-28. 19 Physics, I, v, 196 b 10-13.

20 Cf. Charlton's commentary in Anstotlf's Physics I, II, ed./trad. W. Charlton, Oxford: Clarendon, 1970, p. 105.

21 See my note 20. F.M. Coraford, in Anstelle, The Physics, ed./trad. Ph.H Wicksteed and F.M. Cornford, London: Heinemann, rev.ed 1957, vol. I, p. 147, note b, gives as example: a man generally grows a beard.

22 Cf. W. Charlton's Commentary in Aristotle's Physics I, II, ed.cit. (n. 20),

p. 109.

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 559

Secondly, Aristotle does not explicitly raise the problem whether perception of a limited number of instances does not guarantee in itself a logically valid inference to a conclusion and whether, if this inference is made, the knowledge of the conclusion must be weaker than that of e.g. closed induction where the inference is valid. Aristotle suggests that man can obtain certain knowledge of the principles of a science, be it mathematics or natural science. Neither does Aristotle explicitly assign open induction to dialectics. The Medieval interpreters discussed these problems by taking up Aris-totle's remarks which they did not find, and in fact are not, unam-biguous in all respects. Instead they developed their own solutions different from the ones intended by Aristotle.

3. THE MIDDLE ACES

Now the Medieval views.2* During the period between Aristotle and the thirteenth century interesting views of induction were ad-vanced by the Epicureans, and were criticized by Stoics and Scep-tics.25 I shall not discuss them, because the writings of all these schools have not been influential in the Middle Ages; many of their books were not even known.

To understand Medieval views on induction of the thirteenth and fourteenth century, some of which I shall discuss here, one should bear in mind that Augustine's (354-430) thesis that true knowledge could only be obtained by divine illumination was very influential. Augustine was not acquainted with most of Aristotle's works. The churchfather was not so much interested in the study of nature which had its basis in sense-experience but rather in God and the soul. Ac-cording to Augustine, man needs illumination in order to obtain scientific knowledge. Characteristically, Augustine gives geometri-cal propositions as examples of truths which can be obtained without the help of the senses. Moreover, as a Christian Augustine allows for miracles in the course of nature: so a scientist should take this possi-bility into account.26

24 Most Medieval thinkers used "indixtio" both in a larger and a technical sense. In the larger sense it could mean: "applying a form to matter" or "observing several instances".

25 See Philodemus, On Methods of Inference, A Study in Ancient Empiricism, ed./trad. Ph.H. de Lacey, E.A. de Lacey, Philadelphia 1941, rev.ed. Napoli: Bib-liopolis, 1978, section XVI, pp. 156-164, lines 16-23.

560 E. P. BOS

Augustine emphasizes the weakness of the senses. He defines the operation of the senses as the soul working through the sense-organs, laying emphasis on the operation of the soul.27 There is a difference between the senses and the intellect more than in an Aristotelian theory. Though Augustine cannot be said to have a the-ory of induction in the proper sense, his general views on illumina-tion and on the relaillumina-tion between senses and intellect were in-fluential.28

In the centuries after Augustine, a Neo-platonic view on nature was predominant, for instance in the De divisione naturae of John Scotus Eriugena (ninth century) and in its popularizing version by Honorius of Autun (died after 1130), the Clavisphysicae ("The Key of Nature"). Inductive argument was not in the focus of their in-terest; the knowledge of the really existing natures was unproble-matic for them.

From about 1130 onwards, Aristotle's works became known in the Latin west. The notion of induction is used in a more technical sense. E.g. Thierry of Chartres (died before 1155) uses the term "in-ductio" in a general way not only for a process from particulars to a general conclusion,29 but also for an argument from particulars to particulars, e.g. that a theologian is not allowed to trespass the goal of theology just as this is forbidden in other sciences. In this argu-ment knowledge of the universal is implied.30

In the thirteenth century, however, theories of induction can more easily be found, especially in commentaries on Aristotle's works. First I shall discuss some Medieval thinkers who seem to be-long to a continental tradition, viz. Robert Grosseteste (to whom the label "continental" perhaps does not fit, he studied both in Paris as in Oxford, perhaps he should be located in an English tradition), Albert the Great, Thomas Aquinas, Giles of Rome, a Pseudo-John Duns Scotus (who might be some John of Cornwall). Within this group there are differences in interpretation viz. as far as they advocate Aristotelian or Augustinian principles of knowledge. Then

27 See e.g. Augustine, Df Gentsi'ad Utltram, VII, 15, 21. Cf. E. Gilson,

Introduc-tion à l'étude dt Saint Augustin, Paris: Vrin, 1929, p. 60.

28 See below, sections 3.1; 3.4 and 5.

29 See e.g. Thierry of Chartes, Commentaries on Boethius by Thierry of Chartres and his School, ed. N.M. Haring, Toronto: Pontificial Institute of Medieval Studies, 1971, pp 84, 90; 85, 26; 563, 46 etc.

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 561

I shall discuss the views of John Duns Scot and of William of Ock-ham, who are representative of an English tradition. Finally I shall return to the continent, and conclude with John Buridan and Marsilius of Inghen, who seem to return to thirteenth century interpretations.

3.1. Robert Grosseteste (1168/75-1253)

Robert Grosseteste's translation and commentary on the Posterior Analytics (composed 1208- 1230,31 or 1228-1230) was particularly influential. Grosseteste's theory on induction has been investigated in some detail: I refer to Weinberg,32 to McEvoy33 in an excellent study, and to Marrone.34

Grosseteste's theory of induction is eclectic: he uses Augustinian, Avicennian and Aristotelian elements. He emphasizes the active role of the senses in an Augustinian way. When discussing the way in which man acquires knowledge of the principles of science,35 Grosseteste says that the principles are in us in potency, and will be-come actually known by induction. The senses, active though they are, are only an occasion for intellectual knowledge, not the causes. When commenting on Aristotle's remark on Rallias (who is per-ceived as particular, though the act of knowledge involves the universal36), Grosseteste uses the metaphor of a man who comes from afar towards e.g. Socrates, and already has a general concept of what he sees, e.g. "body", "animal", before properly recog-nizing Socrates. This is a model to explain learning which can already be found in Aristotle37 and was often used in the Middle Ages.38 In explaining how learning takes place, Grosseteste's theory of induction is more Augustinian and Avicennian than e.g. Thomas Aquinas'.

31 Robertus Grosseteste, Commentant in Posleriontm Analyticorum libros, ed. P. Rossi, Firenze: Olschki, 1981, p. 21.

32 J. Weinberg, A Short History of Medieval Philosophy, Princeton: University

Press, 1965, pp. 136-137.

33 James McEvoy, The Philosophy of Robert Grosseteste, Oxford: Clarendon, 1982,

pp. 326-345.

54 S.P. Marrone, William of Auvergne and Robert Grosselesle, New Ideas of Truth in the Early Thirteenth Cmltay, Princeton: University Press, 1983.

35 Robert Grosseteste, Commmtarius in Posterionan Analyticorum Libras, ed.cit. (n. 31), II, 6, pp. 403sq.

36 See above, section 2.

37 Physics, I. i.

562 E.p. BOS

3.2. Albert the Great (ca. 1200-1280)

Albert the Great strikes us by his frequent remarks on the priority of empirical investigations over the interpretations of the words of the Ancient philosophers. Albert says: "It is not the task of natural science just to accept what it is told, but to investigate the causes of nature", and "proof on basis of the senses (i.e. induction) is most certain in the study of nature (in naturis rerum), and is worthier than theory (ratio) without experience".39 His theory of induction has been investigated early in this century by Auguste Mansion,40 whose paper, however, is confusing in some respects because he introduces two sorts of abstraction which are not very clearly defined.41

Albert's Commentary on the Prior Analytics is the best starting-point, I think, to investigate his view on induction. Albert distinguishes be-tween two main kinds of reasoning, viz. syllogism and induction. Syllogism is better known in itself, induction with regard to a knowing subject. Following Aristotle's lead, he discusses the pos-sibility to reduce induction to syllogism. Again following Aristotle Albert says in his Commentary on Aristotle's Topics that as such induc-tion is a movement (progressie) from singulars to a universal.42 In-duction is about all individuals belonging to the kind which is inve-stigated. The differences between science and dialectical thinking is that science is about what is necessary and what is true,43 dialectics is about what is probable and signs that are accepted, not the things themselves. Dialectical induction is not induction on the basis of a limited number. Only the exemplum ("example") is defined as infer-ence on the basis of one instance.

39 Albertus Magnus, Ausgewählte Texte, Lateinisch-Deutsch, ed./trad. A. Fries, Darmstadt: Wissenschaftliche Buchgcsellschaft, 1981, p. 5.

40 A. Mansion, "L'Induction chez Albert le Grand", Revue Neo-scolastujue 13, 1906, pp. 115-134; 245-26+, esp. pp. 117-129.

41 Moreover, Mansion discusses what he calls John Duns Scotus' view on in-duction, without distinguishing between Scotus' authentic works and the un-authentic Commentary on Anstotle's Prior Analytics. See also below section 3.5.

*2 Albert speaks of universalia by which he means: a universal can have different modes of being, either in nature, or in thought, or in word. See Albert the Great's Commentary on Aristotle's Topics, in B. AlbertiMagni Opera omnta, ed. A. Borgnet, Paris: Vives, 1890, vol II, Liber I, tractatus III, caput iv, p. 273.

43 See Albert the Great's Topica, ed.cit. (n. 42), liber I, tractatus I, caput ii,

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 563

Mansion's article on Albert's theory of induction** was quite remarkable in a time, in which scholars did not seem to be very much interested in Medieval logic. Nevertheless, the sharp distinc-tion he makes between "inductive reasoning"45 (both scientific and

dialectical) on the one hand, in which first principles are known on the basis of an investigation of individual instances, and, on the other hand, "abstractive induction",46 which leads to the

forma-tion of concepts and which is identical to "abstracforma-tion", is not help-ful to understand Albert's text, I think. For Albert the distinction between "inductive argument" and "abstractive induction" plays no part just as it did not play a part in Aristotle's works; the primary distinction is between what is known in itself (the syllogism) and what is better known to us (induction). Moreover, Mansion presents47 what in his view is John Duns Scotus' theory of

induc-tion as distinguished from Albert's theory on the basis of a study of the whole Wadding-Vives edition of Duns Scotus' works, whereas he did not know of a distinction between what is authentic and non-authentic in that edition.

Scientific induction leads to scientific knowledge in the strict sense. A scientist can make the formulation of his inductive argu-ment perfect by adding ' 'etcetera' ' (el sic de aliis or: et sic de singulis) to the instances mentioned (which formula will return in later writers).*8 So all instances are grasped by the scientist though they

are not explicitly mentioned.

In his Commentary on the Prior Analytics*9 Albert tries to establish

the relation between inductive and deductive, or syllogistic, argu-ment. Induction is a syllogism as regards the matter, not as regards the form. A syllogism does not always preserve its true nature, not even in Barbara. An example of an inductive argument in syllogistic form is:

** A. Mansion, op.cit. (n. 40).

45 Ibid., pp 117sqq. ** Ibid., pp 129sqq. « Ibid., pp. 123sqq.

w Cf. R. Ruzicka, "Induktion" in Historisches Wärterbuch der Philosophie, ed.

J. Ritter, K. Gründer, Bd. 4, Basel: Schwabe, 1976, col. 326.

49 Albert the Great, Analytua Priera, Liber II, tractatus vu, in B. Alberti Magni

564 E.P. BOS

everything which is this one or that one etcetera, is an animal; now, every man is this man or that man etcetera; therefore, every man is an animal.50

The matter referred to here is the present condition of the world, Albert says. It does not follow, he adds: "If there is a syllogism of an immediate proposition (to which by definition the inductive ar-gument leads), there is a syllogism in the proper sense". It is clear from the example given above that the middle term covers the dis-junction of singular instances together with the addition "etcetera". Albert emphasizes that induction can be reduced to a syllogism of the first figure, that is: an affirmative inductive argument can be reduced to a syllogism of the first figure, a negative inductive argu-ment to the second form of the first figure and then, by conversion of the minor premiss, to the first form of the second figure. The fact that such a reduction is possible does not mean, of course, that in-duction can be reduced to a syllogism in the proper sense, or for-mally. In a formally valid syllogism, Albert says, the middle term is the basis for conjoining the two extreme terms: in an inductive ar-gument one of the terms, which was extreme term in a formally valid syllogism is the middle term.

Albert notes that the inductive argument is valid ut nunc ("as of now"), i.e. given the present condition of the world. We will meet this notion again below in e. g. Thomas Aquinas, John Buridan and Marsilius of Inghen.51 That natural science studies things which happen to be ordered in the way they are, is considered in its full im-plications by John Duns Scotus and William of Ockham.52

From his Commentary on the Prior Analytics,53 however, we learn that Albert also recognizes inductio probabilis ("probable induc-tion"), which is about many particulars (not all) and leads to a con-clusion, provided there is no counter-example. Albert here presents an open induction that is valid in dialectical thinking, not in demon-strative knowledge. It should be treated in the Topics, he says. I could not detect where Albeit treats this kind of induction explicitly.

50 Ibid., p. 793b.

51 See sections 3.3 and 3.8 respectively.

52 See also below, sections 3.6 and 3.7.

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 565

From Albert's Topics one gets the impression that both scientific and dialectical induction is about all instances.

3.3. Thomas Aquinas (1124 -1274)

Thomas Aquinas did not elaborate very original views on induc-tion, it seems.54 His views primarily can be found in his Commentary (expositie) on Aristotle's Posterior Analytics (composed 1269-1272). Thomas did not write a commentary on the Prior Analytics, it seems. In other works55 where he mentions the term "induction", nothing interesting can be found.

Thomas distinguishes between "complete induction" (inductie compléta) and "incomplete induction" (induclio incompleta). Incom-plete induction obtains e.g. in rhetorics, so in dialectical, not in demonstrative thinking, because, Thomas says, the subject matter is unstable. A kind of incomplete induction is the exemplum ("exam-ple"). Complete induction, on the other hand, leads to knowledge of the universal, and is the only form leading to scientific knowledge. A conclusion is only necessary if all cases are covered. So Thomas strictly separates science which is about the necessary and covers all instances, from other kinds of knowledge.56

The universal is considered as an eternal property, just as in mathematics: figure and number. The mind is able to grasp the universal, Thomas says. The mind, that is: the possible intellect, is receptive of universal knowledge. This is Thomas' interpretation of Aristotle. The universal is object of consideratie ("consideration"), in which the unity of the universal is grasped. Characteristically, Thomas says that memory grasps the res in the particular: Thomas apparently interprètes a res as a nature realized in a concrete in-dividual. Thomas emphasizes the form in the thing.57

Just like his master Albert the Great Thomas Aquinas does not seem to realize that in e.g. natural science not all cases of a particular kind can be investigated and that this fact influences the degree of certainty of the knowledge obtained. This is Thomas' strong inter-pretation of Aristotle. The formula "natural inclination of the

54 Cf. R. Ruzicka, op.cit. (n. 48), col. 326.

55 Commentary on the Ethics, 6, 3 (1H8); Summa contra GtntilisUberl, 13; liber II, 80; liber III, 35.

56 Thomas Aquinas, In Anaiyiica Posteriora txpositio, I, xlii, 381 (10).

566 E.P. BOS

intellect" which is favoured by e.g. John Buridan and Marsilius of Inghen58 in their commentaries of Aristotle, is not in Thomas'

Ex-position on the Posterior Analytics, as far as I know. In its turn, the for-mula seems to be a strong expression of Thomas' view, empha-sizing, an active role of the intellect even more than Thomas did.

3.4. Giles of Rome (1243/7 -1316)

Though during some time Giles of Rome (Aegidius Romanus) was a pupil of Thomas Aquinas', he had many views different from his master's. Giles' Commentaries (expositions interspersed with "prob-lems" (dubia)) on the Prior and Posterior Analytics composed before 1288, are the main source I used in order to study his theory of induction.

In his Commentary on the Prior Analytics59 Giles' opinion on the rela-tion between inductive and deductive argument coincides almost lit-erally with Albert the Great's text.60 He distinguishes between a

complete and an incomplete syllogism. He defines a complete syllo-gism in the same way as Albert and Thomas Aquinas; an incomplete or "diminished" (diminuta) syllogism is an inductive argument (de-fined in Aristotle's Topics) which argues from a particular case to a particular case,61 as is evident in rhetorics, where the rhetorician tries to adduce arguments for an individual case.

In his Commentary on the Posterior Analytics6^ Giles discusses the part played by senses and intellect, as well as the nature of scientific knowledge. Here he shows an Augustinian tendency which separates him from e.g. Thomas Aquinas. Like Grosseteste Giles draws a dividing line between senses and intellect. The senses are only an accidental cause of a man's intellectual knowledge, he says. They stimulate the intellect and are the "remote" principles (as Giles calls them) of our scientific knowledge. The senses, in their turn, are to some extent active, viz. in discovering difference and similarity in objects. The first principles are not so much a product

58 See below, section 3.8.

^ Giles of Rome, Commentaria in libres Priorum Artalyticorum Artstotelis, Liber II, Venetiis 1488; repr. Frankfurt am Main: Minerva, 1968, p. 79a.

60 See above, section 3.2.

61 Cf. Thierry of Chartres, ed.cit. (n. 29), p. 489, line 53.

62 Giles of Rome, Commtntaria in libros Posteriorum Analyticorum, Venetiis 1488,

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 567

of consideration (consideratie) by the intellect as in Thomas Aquinas. The knowledge of the universal (cognitio universalis), i.e. the act of knowledge, forms together with the universal known

(universalecogni-tion), i.e. the universal nature in things existing apart from the

multitude, a product generated from them (aggeneratum), a third thing, which is the principle known, the result of induction.

Man possesses the worthiest disposition to know the first prin-ciples. According to Giles63 it may be called "worthiest" because

man possesses certainty about his knowledge. So it is worthiest be-cause it enables our human intellect to reflect on its own knowledge: we know that we know the first principles. This notion of self-reflection, too, seems to be Augustinian.

To conclude these short remarks on Giles, of whom we shall know much more once the forthcoming new critical edition has been ac-complished: Giles interprètes Aristotle's theory of induction with Augustinian overtones.

3.5. Pseudo-John Duns Scotus (John of Cornwall (died after 1320)?)

In this paragraph I shall discuss a quaestio in the commentary (questions) on the Prior Analytics, viz. question viii of book II to be found in the edition Wadding-Vivès64 of the works ascribed to John

Duns Scotus. This edition contains not only the works of John Duns Scotus, as is well known, but also many commentaries that cannot be ascribed to the great Franciscan master. These should be ascribed to e.g. Thomas of Erfurt, Antonius Andreas, Vitalis de Furno, et-cetera. Neither the questions on the Prior (nor those on the Posterior

Analytics which follow them, and of which it is sometimes suggested

that they are by the same author as the questions on the Prior

Analyt-ics)65 can be ascribed to John Duns Scotus, it seems. It is not cer-tain, however, who the real author is.

The explicit of one of the manuscripts containing the Commentary

on the Posterior Analytics says that this commentary are "quaestiones

( . . . ) datae a domino Johanne de Sancto Gtrmo.no de Cornubia" ,* which

63 Ibid., dubium 5.

M Ps. John Duns Scotus, h Libns I et II Pnonan Anafylicomm Arulolelis

Quaes-tiones, in: Johannes Duns Scotus, Opera Omnia, ed. L. Wadding, Lyon 1639; repr. Paris: Vives, 1891-95 und Hildesheim: Olms, 1968, vol. H, pp. 195-197.

65 See my next paragraph.

66 See Ch. Lohr, "Medieval Latin Aristotle Commentaries", Traditio, 27,

568 E.P. BOS

perhaps only means "questions edited by John of Saint Germain of Cornwall". According to Grajewsky67 the two commentaries are "probably the work of John of Cornubia", but Grajewski does not give any reference. Gilson68 says that Smeets69 attributes the com-mentaries to Johannes de Cornubia. (Unfortunately, I did not have the opportunity to examine the type-written study,70 nor could I lay hands on the article by Goelz,71 who also seems to discuss the authenticity of the commentaries). To identify John of Saint Ger-main of Cornwall, Lohr refers to an article by P. Glorieux on Jean de Saint-Germain.72 However, in this article he is not named "Jean de Saint Germain de Cornualles". Nor is he named as possi-ble author of the Questions on the Prior and Posterior Analytics, contained in the Wadding-Vives edition in which I am interested here. The question of the authorship of either commentary cannot be solved at the present.73

The quaestio is quite interesting. The author discusses the problem whether or not it is necessary to form an inductive argument on the basis of all singular instances in order to have a good induction (utrum ad bonam inductionem oporteat indium in omnibus singularibus). He distinguishes between a necessary inference (consequentia necessaria) and a good inference (consequentia bona). An inductive argument is a necessary inference when all instances are considered by the induc-tion.74 Complete induction results in evident knowledge. E.g. if

67 M. Grajcwsky, "Duns Scotus in the Light of Modern Research", in Truth in Contemporary Crisis, Proceedings oj'îhf American Catholic Philosophical Association, 1942,

p. 180.

68 E. Gilson, Jean Dans Scot Introduction à ses positions fondamentales, Paris: Vnn, 1952, p. 673.

69 U. Smeets, Lineamtnta oibliograpfiiae Scotisticae, Romae 1942, pp. 8-9.

70 Cf. O. Schäfer, Johannes Duns Scotus, Bern: Francke, pp. 7, 9, 11. 71 B. Goelz, "Die echten und unechten Werke des Duns Scotus nach dem gegenwärtigen Stand der Forschung", in Sechste und Siebte Lektorenkonferenz der deut-schen Franziskaner fir Philosophie und Theologie, Werl in Westfalen: Franziskus-Druckerei, 1934, pp. 53-60.

72 P. Glorieux, "Jean de Saint-Germain, maître de Paris et copiste de

Worcester", in Mélanges Auguste PeUer, Louvain: Bibliothèque de l'université -Editions de l'Institut Supérieur de philosophie, 1947, pp. 513-529.

73 Note that Ch.S. McDermot in "Notes on the Assertoric and Modal Preposi-tional Logic of thé Pseudo-Scotus", History of Philosophy, 10, 1972, p. 274, note 6 mentions Bochenski's concern that the author of the commentary on the first book of Prior Analytics might not be the same as the commentator on the second book. McDermot rejects Bochenski's reasons to assume a discrepancy.

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 569

there exist only three men, Socrates, Plato and Cicero, then if Socrates is running, Plato is running and Cicero is running, it fol-lows necessarily that every man is running, provided a universal premiss is added: every man is Socrates, Plato and Cicero.75 The pseudo-Duns Scotus pays attention to probable knowledge, where not all instances are considered. Induction about a limited number of in-stances results in probable knowledge or belief. Many inductions are good in which not all instances are investigated. A universal conclu-sion is acceptable provided there is no counter-example or difference on the basis of which a universal conclusion cannot be applied to other instances. So a scientist obtains both evident as well as proba-ble principles which are evident but also probaproba-ble, on the basis of sense-perception, memory and experience.76 Though he does not explicitly discuss the relation between probability and evidence here, to his mind probability and evidence, here perhaps in a lower degree, go together.

So, this kind of knowledge results in faith, or persuasion, i.e. a kind of opinion. It is remarkable that according to our author induc-tion in natural science results in probable knowledge. A scientist cannot consider all cases. Natural laws like "all fire is hot" and, even more remarkable, "everything heavy in a high place, when not impeded, descends downwards" are probable knowledge.

The author of our questions is faced with an objection: how many instances must probable induction have? He answers77 that this de-pends: sometimes many, sometimes few, according to the diversity of matter and the diversity of the intellect of the one who must assent to a proposition. He seems to mean that on the pure human level all is uncertain according to the subject matter and intellect. It seems to me that the author of this commentary on the Prior Analytics comes closer to our modern notion of induction than any of the other philosophers discussed here.78

75 Ibid., conflusio 2. Perhaps John Buridan discusses this argument, see below,

section 3.8.

76 Ibid., conclusio 3.

" Ibid., p. 196b

78 In his article on Albert the Great's theory of induction Auguste Mansion also

570 E.P. BOS

3.6. John Duns Scolus (ca. 1265-1308)

Up to here the authors whose works are dicussed seem to belong to a continental tradition of the thirteenth century, except perhaps Grosseteste. Now I shall pay some attention to the principles of the theories of induction advocated by two great English thinkers, John Duns Scotus and William of Ockham. Their interpretations of in-duction run along lines which differ not only from the theories up-held by the thinkers discussed above, but also from each other.

First John Duns Scotus. His view can mainly be found in his Com-mentary on the Sentences, Ordinatio, written about 1300-1301. Duns Scotus develops his theory in reaction to the views of Henry of Ghent. In Duns Scotus' eyes, Henry's view on knowledge leads to scepticism, for Henry advocated that we could have no certain knowledge of our changing world, but that we need divine illumi-nation.

It is not my intention to discuss Duns Scotus' views here in detail. I refer to Gilson79 and, more interesting, to Weinberg's analyses.80 Weinberg's analyses of the conditions of agreement prerequisite to induction are excellent and need no further elaboration in this paper. Those conditions are dependent on other principles which I shall bring forward here.

Duns Scotus says that man can obtain certain knowledge:81 first of so-called first principles, e.g. the principle of non-contradiction, the principle that a whole is bigger than one of its parts; secondly of man's own acts. That certainty and evidence can be obtained of these two kinds of truth may seem acceptable to us. It is more in-teresting to note why Duns Scotus claims certainty for empirical and inductive knowledge as well. Both kinds of knowledge are explained

Anneliese Maier quotes a part of the question discussed here (see A. Maier, Metaphysische Hintergründe der spatscholastischen Naturphilosophie, Rome: Edizioni di Storia e Letteratura, p. 384, n. 12) to underline that according to the Scholastic philosophers, incomplete induction was a means to obtain persuasion, but she fails to point out that our pseudo-Duns Scotus was highly original in drawing conse-quences as regards science.

79 E. Gilson, Jean Duns Scot (n. 68), pp. 556-573.

80 J. Weinberg, Abstraction, Relation and Induction. Three Essays in the History of

Thought, Madison-Milwaukee: The University of Wisconsin Press, 1965, pp. 139-142.

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 571

in the same way. Empirical knowledge cannot be naive, so to say, but should be guaranteed by self-evident sentences. The following is primary: ' 'whatever happens in many cases by a cause that is not free, is the natural effect of that cause" (quicquid evenit ut in pluribus ab aliqua causa non libéra, est effectus naturalis iltius causae, the "ut in pluribus"-principle). There is a certain order in nature, according to which there isaptitudo, "aptitude, a kind of natural inclination" be-tween causes and effect. I shall describe, omitting details, the case of a stick seen in water: it appears to be broken. However, our mind is certain that the stick is not broken, because the intellect possesses this proposition which reposes in it: "the harder object is not broken by the touch of something soft which gives way before it". Induction is explained in a parallel manner by Duns Scotus. He gives examples of two kinds of induction leading to different degrees of certainty. In the background is Duns Scotus' claim that there is stability for some time in nature; Duns criticizes any Heraclitean position.82 This stability is guaranteed by Gods ordained power (potentia or-dinata).

The first example leads to the strongest degree of certainty. It is introduced by Duns Scotus within the related framework of a demon-stratio propter quid ("demondemon-stration of the reasoned fact"). Some-times we have experience of the truth of the conclusion that the moon is frequently eclipsed. We often see this to be the case. Now we apply the above mentioned "ut in pluribus"-principle (leading us to the determination of the natural cause of the phenomenon). By the method of "division" (divisio),al according to which other

ciples of explanation are rejected, we discover the self-evident prin-ciple that, when an opaque body is placed between a visible object and a source of light, the transmission of light to the object is prevented. We then determine that this self-evident principle ap-plies to the case under consideration; then knowledge of the reas-oned fact is obtained.

The other example can easily be recognized as an example of in-duction. We may have experience that a certain kind of herb is fre-quently united with the property of heat. Now we apply the ut in />foniu5-principle leading us to the knowledge that, given that a herb of a certain kind exists, it is the natural cause of the property of heat.

82 Ibid., p. 133 (n 219).

572 E.p. BOS

According to Duns Scotus, the intellect requires the senses only as an occasion; ultimately, knowledge is based on the ut in pluribus-principle, which does not depend on the testimony of the senses. We may call this a Platonic view on the relation between senses and in-tellect.

I conclude that in Duns Scotus' theory, induction is primarily ex-plained with the help of formal principles, based on the assumption of stability given by God.

3.7. William of Ockham (ca. 1285-1347)

In his Ordinatio (composed about 1320) Ockham advocates a more naive theory of induction than his predecessor.84 I shall sketch his position in main lines, referring to Weinberg,85 among others for more details about Ockham's requirements of agreement in the in-stances which are at the basis of the inductive inference. Webering's discussion86 is in some respects less satisfactory, I feel.87

According to Ockham all scientific knowledge starts with ex-perience. In line with Aristotle's words in the Topics Ockham says that if one single instance of a certain species has a property B, and if another has the same property, etcetera, one can arrive at the knowledge that all instances of the same species have the property B.88 Now, if the species is a species speciatissima, after perception of one instance only, we may conclude to a general law; e.g. if we see that this particular instance of heat makes warm, we may conclude that aWheat can make warm on the basis of a self-evident principle: "there is no more reason for this instance to be hot than for another' '. Weinberg denies this possibility for Ockham, but without reason. Weinberg did not adduce the example relevant here, viz. that all heat can heat, which is a necessary truth in Ockham's logic

84 William of Ockham, Scriptum in librum primum Senîtntiarum, Ordinatio, prologus et distinctie prima (Opera theologica I), éd. G. Gâl, S. Brown, St. Bonaventure, N.Y.: The Franciscan Institute, 1967, prologus, pp. 92-95.

85 J. Weinberg, op.cit. (n. 80), pp. 141-150.

86 D. Webering, Theory of Demonstration According to William Ockham, St. Bonaventura, N.Y.: The Franciscan Institute / Louvain: Nauwelaerts / Pader-born: Schôningh, 1953, esp. pp. 73-75.

07 See below, this paragraph.

80 William of Ockham, Summa logicaf (Opera Philosophica I), ed. Ph. Boehner,

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 573

and which is based on the perception of a single example.89 If the species is of a higher Ie vel, then always, or often (!), so Ockham says, verification of a single instance of each species under the more general species is required.90 Ockham adds that often observation

of many instances is needed when the species examined is a most special species. One should be careful, Ockham says: there might be another cause of the hotness.

According to Ockham, induction is not valid in the way of a syllo-gism, that is: on the basis of an intrinsic principle; induction is valid on basis of an extrinsic principle: "all agents of the same special spe-cies produce effects of the same kind".

This procedure has been described in scholarly literature. To call Ockham the "father of empiricism", as Baudry did,91 is going too

far: for Ockham, too, induction is possible on the basis of one in-stance, and introduces self-evident principles leading to certain knowledge. As an explanation I suggest that Ockham explains learning, and induction as part of it, with the model of someone ap-proaching Socrates from afar: he knows that there is a body, and, when approaching, there is an animal, and then upon seeing the single individual Socrates properly, he knows Socrates is a man.92

3.8. John Buridan (ca. 1300 -1358 or shortly afterwards) and Marsilius of Inghen (short before 1340-1396)

I shall now go back to two continental philosophers belonging to the fourteenth century: John Buridan and Marsilius of Inghen. As they advocate practically the same theory of induction, they may be discussed together. John Buridan's view may be found in various places: in his Commentaries on the Metaphysics, and on the Physics, but primarily in his Commentaries (questions) on the Prior Analytics and the Posterior Analytics composed about 1340. Marsilius of Inghen wrote

89 D. Webering, op.cit. (n. 86), p. 72 is not precise in this respect: he says that

the inference leads to "all heat heats", which would be contingent in Ockham's logic.

90 D. Webering, op.cit. (n. 86) fails to make this distinction on his p. 73. 91 L. Baudry, Lexique philosophique de Guillaume d'Ockkam. Etude des notions fon-damentales, Paris: Lethielleux, 1958, p. 120.

92 William of Ockham, Expositie in libres Physiaman Aristatelis (Opéra

574 E.p. BOS

his commentaries on Aristotle's logical works93 about 1370 or even

somewhat later. These commentaries have not yet been edited. I am very grateful to prof. H. Hubien (Liège) for letting me use his transcription of Buridan's Commentaries (questions) on Aristotle's Prior and Posterior Analytics. Buridan's view of induction has been studied in main lines by Maier94 and recently by Thijssen95 on the

basis of Buridan's Commentaries on the Posterior Analytics, Metaphysics and Physics, without using Buridan's Commentary on the Prior Analytics, which, from Aristotle onwards, is the principle source for theories of induction.

Buridan clearly says that induction is not a scientific, but a dialec-tical process. It does not give scientific proof, but the principles of scientific proof. Inductive argument is not a consequentia formalis ("formal inference"), which is valid regardless the terms used, but in the case of perishable objects a consequentia materialis ut nunc ("a material inference which is valid for the present circumstances"), or, to use Buridan's words, it is an inference in which it is impossible that the antecedent is true and the consequent false given the present circumstances.96 It is not a consequentia materialis simplex ("material

inference without qualification"), of which it is impossible, so Buridan says, that the antecedent is true and the consequent false in whatever case.97 Induction can be reduced to a formally valid

in-ference: I shall return to this reduction below.

By way of sense-experience, memory, inspection of all circum-stances, and after ascertaining that there is no counterexample (in-stantia) the intellect arrives, by its natural inclination to the true, to a first principle. Such a principle is evident (a characteristically four-teenth century criterion) and universal. It is a necessary truth, but

93 Relevant for this subject are: Marsilius of Inghen, Quaestiones super libris

Prto-rum AnalyticoPrto-rum, Venetiis, 1516, repr. Frankfurt am Main: Minerva, 1968. For Marsilius' Commentary (questions) on Aristotle's Posterior Analytics, as yet unedited, I consulted ms Vienna, Österreichische Staatsbibliothek, V.P.L. 5159, ff. 268r-3lOv.

94 A. Maier, op.cit. (n. 78), p. 384.

95 J.M.M.H. Thijssen, "John Buridan and Nicholas of Autrecourt on Causali-ty and Induction", Traditio XLI1I (1987), pp. 237-255.

96 Buridan's view on the consequentia ut nunc, and Marsilius' rejection of this

kind of inference, see E.P. Bos, "John Buridan and Marsilius of Inghen on Conse-quences", in The Logic of John Buridan (Acts of the Third European Symposium on Medieval Logic and Semantics, Copenhagen 16-21 November 1975), ed. J. Pinborg, Copenhagen: Museum Tusculanum, 1976, pp. 61-68.

97 Perhaps one could say—borrowing a modern philosophical expression—:

CONTRIBUTION TO THE HISTORY OF THEORIES OF INDUCTION 575

not necessary in an unqualified sense (which is only true of the proposition Deus est ("God exists")). Nor is it a nécessitas conditionalis (conditional necessity); this kind of necessity is defined as follows: if the subject-term and the predicate-term refer to (supponit pro) something, then they supposit for the same; this necessity is not about the present world but about any world whatsoever, e.g. "if there is a vacuum, then it is a place". Now, in our present world a vacuum does not exist, nor can it exist. The principle arrived at by induction is a nécessitas de quando (necessity "of when") referring to the present circumstances and the present order of the uni-verse.98

Buridan is faced with an objection that a scientist cannot invest-igate all instances and that every induction therefore is incomplete. His answer to this problem is worth attention. Buridan says that in some cases complete induction is possible, e.g. in the cases of the stars, the heavens and the planets. In other cases it is impossible. In the latter cases the intellect guarantees the truth of the principle in virtue of its natural inclination to the true.99 Then, "et sic de aliis"

("et-cetera") is added to the list of instances investigated.100 Buridan ac-knowledges that this is not a logical procedure. However, when et sic de aliis is added, the inference itself is formally valid, he says. His ex-ample is: "hoc rheubarbarum purgabat choleram, et illud, et sic de singulis, ergo omne rheubarbarum purgit choleram" ("this rabarber purged era, and that one, etcetera, therefore all rabarber purges chol-era").101 Buridan does not go so far as to acknowledge that a scien-tist normally uses incomplete induction and that therefore his induction can not lead to certainty.

One of the objections resembles an argument to be found in the quaestio wrongly attributed to John Duns Scotus and discussed

98 John Buridan, Quaestiones in libros Priorum Analyticonan, Liber primus,

quaes-tio 25 (transcripquaes-tion H. Hubien). Cf. Marsilius of Inghen, Quaesquaes-tiones super hbros Priorum Analyticorum, ed.cit. (n. 93), f. 16ra; sec also Marsilius of Inghen, Treatises on the Properties of Terms A First Critical Edition of the Suppositions, Ampliatimes, Appella-tiones, RestrictmnesarutAtienatiorus, ed./trad. E P. Bos, Dordrecht-Boston-Lancaster: Reidel, 1983, pp. 2+7-248.

99 The same in Albert of Saxony (?), Questiones in Analylica Posteriora, Ms Krakau, BMiotheca Jagiellanska 621, f. 137va-138ra.

100 Ibid., question 20.

101 Besides Buridan adds the conditions that there be no counterinstance,

576 E.p. BOS

above.102 It is said that in induction it is always possible that the antecedent is true and the consequent false: for there may be other examples. Buridan agrees so far. The difference between the Pseudo-Duns Scotus' view and that of Buridan is that according to the latter, evident knowledge of a universal, temporally necessary (ut nunc) principle is guaranteed because of the intellect's natural incli-nation to the true. To my mind, this decisive element is missing in A. Maier's text where she says103 that "incomplete inductive argu-ments can give sufficient certainty in natural science".

According to the two Parisian philosophers, evidence is ascer-tained by induction and the intellect's natural inclination to the true. They are aware that induction deals with a contingent order. Both philosophers have a theory of induction which resembles both thir-teenth century theories, especially that of Thomas Aquinas, and in a lesser degree those of Duns Scotus and of William of Ockham.

CONCLUSION

"Induction-theory" shows a great variety in the Middle Ages. However, it is not yet formulated as in modern philosophy. In com-parison with Aristotle Medieval theories of induction make the step from particulars to the universal principles much more complicated, and are more explicit on the problem.

102 My section 3.5.

DIALEKTISCHE UND RHETORISCHE ARGUMENTATION AN DER KRAKAUER

UNIVERSITÄT IM 15. JAHRHUNDERT

Mieczyslaw Markowski (Krakow)

In dem am Anfang des 15. Jahrhunderts ausgearbeiteten Lehr-programm des erneuerten Studium Generale in Krakau ist der Logik eine besondere Rolle zuteil geworden. Sie sollte ein Instru-ment des wissenschaftlichen Denkens sein, war jedoch vor allem als eine Wissenschaft der Regeln korrekten Folgerns und der logischen Argumentationstechnik gedacht. Da sie den Erkenntnisbedürfnis-sen der Zeit dienen sollte, konzentrierte man sich im Logikunter-richt auf die UnterLogikunter-richtsmethoden, die zur Entwicklung der damals bevorzugten Wissenschaften beitrugen, zu denen die Naturphi-losophie (mit der Physik an erster Stelle) und die MoralphiNaturphi-losophie gehörten. Zu dieser Entwicklung sollten die Argumentations-theorie, die Erkenntnistheorie und die Epistemologie beitragen. Bei der Bearbeitung dieser Theorien nutzten die Krakauer Logiker selbstverständlich das vorhandene wissenschaftliche Erbe der Ver-gangenheit, insbesondere die Schriften des Aristoteles und seiner Kommentatoren, deren Ansichten sie manchmal nach eigenen Er-kenntnisbedürfnissen modifizierten. Dies waren vor 1456, als in Krakau ein gemäßigter buridanischer Terminismus herrschte, andere als danach, als man begann, den Kölner und Pariser Realis-mus einzuführen. Der Einfluß dieser beiden philosophischen Richtungen ist die Ursache, daß wir von zwei verschiedenen Krakauer Argumentationstheorien im 15. Jahrhundert sprechen dürfen. Obwohl sie Ergebnis der Arbeiten vieler Philosophen wa-ren, gingen sie alle aus einer bestimmten methodologischen, gnoseologischen und epistemologischen Haltung hervor.