Interregnum (Between Medieval and Modern)

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INTERREGNUM (BETWEEN MEDIEVAL AND MODERN)

The interregnum between medieval scholastic logic and modern mathematical logic may be taken as having begun about the middle of the fifteenth century. There is no clear mark of division; the change was a shift away from the characteristic interests of the twelfth to the fifteenth century, with nothing of comparable importance arising to take their place. At the same time, certain less desirable trends in scholastic logic were perpetuated. The result is that formal logic was reduced almost entirely to a very imperfectly presented syllogistic. Medieval influences continued to operate in the early years of the sixteenth century, and medieval authors were still sometimes read in the seventeenth, but by the time that William of Ockham's Summa Logicae was printed at Oxford in 1675, no one had written creatively in the idiom of scholastic logic for many years.

The interregnum was characteristically sterile, a cause for despondency when one thinks of the large place logic continued to occupy in the educational curriculum and of the innumerable writers who put manuals of logic on the market. The tendency to publish at all costs was encouraged by the post-Reformation and post-Tridentine growth of universities, colleges, and seminaries.

Valla

The first author to consider is the humanist Lorenzo Valla (1407–1457), best remembered for his writing on the forged donation of Constantine. In his Dialecticarum Libri Tres (1441), Valla gave no definitions of syllogistic figures and moods, evidently assuming that the reader would know about these. His aim was to confine the syllogistic to the first two figures, without the five moods of Theophrastus and Eudemus. To do this he would have had to reject subalternation, conversion, and reductio ad absurdum. About subalternation he was inconsistent; conversion he rejected as lacking brevity, ease, pleasantness, and utility; reductio ad absurdum he largely neglected. The five offending moods were called "Agrippine births," and of them all the most monstrous was "Frisemomorum, forsooth!"

Here we see the common humanist objection to the barbarity of scholastic terminology, but of course Valla was not objecting merely to comparatively recent Scholastics. His fullest invective was saved for the six moods of the third figure, which he thought insane and never found in use, unlike the first-figure and second-figure moods, which he accepted as dictated by nature to everyone, "even peasants, even women, even children." The standard means of reduction are but "remedies for sick syllogisms." The standing of the third figure would remain a point of dispute for a hundred years, until Ramus undercut Valla's argument by declaring that the figure was in obvious fact very commonly used (Institutionum Dialecticarum Libri Tres, Paris, 1554). Thus, Philipp Melanchthon (Compendiaria Dialectices Ratio, Basel, 1521) could not make up his mind on the subject.

Melanchthon

In Melanchthon (1497–1560), a most influential writer, the rhetorical approach to logic already appeared at a high state of development, although he retained some Aristotelian doctrine. The rhetorical tradition, derived from Cicero and Quintilian, had a place, albeit a very subordinate one, in scholastic logic. We can see it beginning to predominate in the Dialectica ad Petrum de Medicis (edited by D. M. Inguanez and D. G. Muller, Monte Cassino, 1943; composed about 1457), by Joannes Argyropoulos, who held that the detail of the theory of suppositio, which was the distinctive and most original scholastic contribution to logic, offered almost nothing to oratorical practice.

Thus, scholastic logic, which in its origins had borrowed considerably from grammar, began to yield to the third member of the trivium, rhetoric. Accordingly Melanchthon declared the fruit of dialectic to be the ability to speak with propriety and exactness on any theme, and he expounded the Ciceronian syllogism, with its five parts—propositio, approbatio, assumptio, assumptionis approbatio, and complexio —before the Aristotelian. (A century later a similar five-part syllogism, with proposition, reason, example, application, and conclusion, came into favor in the New Nyāya school of Indian logic.) In general, Melanchthon said, the natural reasoning common to the learned, children, and ordinary people is to be preferred to the "rancid commentaries of dialecticians." From this time on it was often felt desirable to include comparative lists of terminology, ancient and modern, as was done by a commentator on Rodolphus Agricola in 1538, by John Seton in 1572, and by John Sanderson in 1589.

Ramus

The syllogistic as a deductive system underwent considerable attrition in the rhetorical treatment of logic, but this cannot be ascribed exclusively to the new interests. John Dolz's Sillogismi (Paris, 1511), a work of purely scholastic inspiration, methodically examines arguments in the different moods and figures as though they had nothing to do with one another. Dolz gave thirty-two sets of objections to Barbara before going on to Celarent "to avoid prolixity." Although logic applied to itself was by no means unknown in Scholasticism, the idea of a closed logical system was little developed, and hence the piecemeal treatment so characteristic of the scholastic sophismata was easily extended to encroach on the systematic character of syllogistic. The fact that Aristotle began by presenting syllogisms in lists probably also contributed to this encroachment.

The process of fragmentation was given new impetus by Pierre de la Ramée (Peter Ramus, 1515–1572). This great master of Latin rhetorical style and innovator of educational theory developed a massive attack on the Aristotelian tradition in logic and an alternative corpus of logical material that quickly gave rise to a widespread Ramist scholasticism.

attack on aristotelian tradition

Ramus's Animadversiones Aristotelicae (Paris, 1556) tells in twenty books how Ramus turned from the clarity of Plato to the comparative chaos of Aristotle. Pretending to be analytical, Aristotle was almost completely deficient in that (Ramist) analysis that consists in systematic definition and division, and his doctrines are not supported by examples (are not, in fact, established by rhetorical syllogisms!). These are the standards Ramus applied as he worked through the Prior Analytics in his Book VII, firing off a broadside at every detail of Aristotelian or scholastic doctrine that occurred to him on the way. The typically rhetorical teaching that experience, observation, and usage are the proper guides in logic is prominent. Variables seldom make their appearance in this milieu, but Ramus's express attack on abecedarian examples—which, being examples of nothing, can be adapted to nothing—is remarkable.

ramist logic

The Dialecticae Libri Duo (Paris, 1556) is divided between invention, or discovery, and judgment, a distinction derived immediately from Agrippa and mediately from Cicero and Boethius. This distinction had been recalled among Scholastics—for example, at the opening of Kilwardby's popular thirteenth-century commentary on the Prior Analytics, often printed under the name of Giles of Rome. Like Descartes, whose methodological ideas supplanted his own, Ramus could not escape his antecedents. The first book covers topics, or loci; the second expounds the Ramist syllogistic, divided into the contracted syllogism (an enthymematic version of the Aristotelian third figure) and the explicated syllogism (comprising the second and first figures, in that order). There are no signs of quantification, all unquantified propositions that are not singular being deemed universal. A mood is general if it contains no singular term, special if it contains one, and proper if it contains two. Examples are taken from classical rhetoric and poetry; the propriety of such sources was vigorously attacked by a little-known anti-Ramist, Thomas Oliver of Bury, in his De Sophismatum Praestigiis Cavendis (Cambridge, U.K., 1604), on the ground that logic has very little place in poetry or forensic oratory.

This whole early version of an ordinary-language approach to logic was admirably countered by Gisbertus Isendoorn (Cursus Systematicus, Oxford, 1658). Writing directly against the famous Cambridge Ramist George Downame, Isendoorn said (p. 613): Observa … orationem et popularem discurrendi usum non esse mensuram et normam Logicae, sed rectam rationem et accuratam artem viamque concludendi (Mark that popular speech and usage are not the standard and norm of logic, but right reason and an exact method of reaching conclusions).

Manuals of Logic

With all the effort of the mid-sixteenth century to simplify logic, it is not surprising that vernacular manuals began to appear, although sparsely, at that time. In England there were Thomas Wilson's The Rule of Reason (London, 1551), Ralphe Lever's The Arte of Reason rightly termed Witcraft (London, 1573), Abraham Fraunce's The Lawiers Logike (London, 1588), and Thomas Blundevile's The Arte of Logicke (London, 1599); in France there was Philippes Canaye's treatise L'organe (Paris, 1589). Little further seems to have been published in English until John Newton's The English Academy (London, 1677).

Wilson's pioneer effort is interesting chiefly for its novel terminology; for example, the major, minor, and middle terms are called the "terme at large," the "severall terme," and the "double repeate." Blundevile introduced an arithmetical syllogism and used a catechetical method. This method had been used by Matthias Flacius Illyricus in Paralipomena Dialectices (Basel, 1558; composed 1550), which gives a very detailed treatment of the venerable pons asinorum. Canaye's book was also devoted largely to the pons asinorum, being distinguished by the dissection of the traditional rectangular figure into two circular ones. The same subject had been dealt with in Christopher Corner's Ratio Inveniendi Medium Terminum (Basel, 1549), which set a new standard of scholarship by appending a Greek text of relevant chapters of Aristotle. Thus, Aristotelian subjects were being pursued, in somewhat new ways, at the same time that the widespread Ramist innovations were taking hold.

Something of the same development can be seen in commentaries on the Prior Analytics, from the sixteenth-century editions of Kilwardby, through the work of Lefèvre d'Étaples (Faber Stapulensis), with his emphasis on tabular presentation; that of Agostino Nifo (Niphus Suessanus), who professed to follow the Greek commentators but wrote a long treatise on conversion in the scholastic manner; Burana's urbane commentary, with lengthy appendixes by his teacher Bagolinus and an interesting prefatory glimpse of the logical curriculum in a north Italian university; Monlorius's commentary, relatively brief but careful; to that of Pacius, with its businesslike presentation, schemes, and figures, a work praised by Sir David Ross in his own commentary. Within this developing tradition of Aristotelian scholarship we may also put the Apparatus Syllogistici Synopsis of Joannes Albanus (Bologna, 1620), which elaborately examined the crescent-shaped and triangular diagrams that descended from Greek sources to the Aristotelians of the Renaissance.

In a field in which syllogistic occupied so large a place one must note widespread incompetence in the matter of classification by figure. This is, of course, a point settled by definition, as Lorenzo Maiolo (Epiphyllides in Dialecticis, Venice, 1497) and John Wallis (Institutio Logicae, Oxford, 1687) saw. These two were exceptional, however. Franciscus Titelmans (De Consideratione Dialectica Libri Sex, Paris, 1544) found the distinction between major and minor premises a hard thing for youths; Richard Crakanthorp (Logicae Libri Quinque, London, 1622) omitted the fourth figure without rejecting it and found it hard to determine the number of moods. The basic trouble was that the later medievals, following a lead given by Boethius, defined the major premise as the first stated, the major term as the extreme therein, and so on, whereas Philoponus had defined the major term as the predicate of the conclusion, the major premise as the premise containing the major term, and so on. Each of the schemes can be worked out consistently, but they give different classifications and arc mutually incompatible. This was seldom understood; it was a common fault to speak of indirect conclusions in connection with Philoponian definitions or to define with Philoponus and then take, for example, Balnama as fourth figure, instead of first figure with transposed premises.

In the Oxford logicians one does not find twenty-four moods in four figures correctly worked out on a Philoponian basis until Henry Aldrich (Artis Logicae Compendium, Oxford, 1691; this first edition was anonymous). The principles of the matter remained so little understood that even Augustus De Morgan (Formal Logic, 1847) could say, "Consider the fourth and first figures as coincident and the arbitrary notion of arrangement by major and minor vanishes," and W. S. Jevons (Elementary Lessons in Formal Logic, 1876) described fourth-figure syllogisms as ill arranged and imperfect and unnatural in form. "Unnatural" as a description of fourth-figure syllogisms was first used by Averroes, and his opinion was reinforced by Giacomo Zabarella (1533–1589); both meant to make a point of genuine formal logic, but they used some phrases that permitted a psychological interpretation. Sir William Hamilton's treatment of the matter (Lectures on Logic, 1860, Vol. IV), with lists of authors for and against the fourth figure and indirect moods of the second and third, is useless without knowledge of these authors' definitions and therefore of what they were favoring or opposing. A writer of a very different style was John Hospinianus (1515–1575), who proceeded on a combinatory basis and found that by admitting singular and indefinite propositions to the syllogistic and by identifying certain moods, he could obtain thirty-six valid moods out of a possible 512.

Extremely influential on manuals of the eighteenth and nineteenth centuries was Logique, ou l'art de penser (1662; The Port-Royal Logic ), by Antoine Arnauld and Pierre Nicole. Even Aldrich, who disliked its novel terminology and Cartesian standpoint, may well have been prompted by it to his strict deductive treatment, for he shows no acquaintance with any other likely influence. The authors' epistemological interests certainly contributed much to the psychologism that was soon to infect logic, but such headings as conception, judgment, and reasoning were not new in promoting this tendency. Canaye had already spoken of syllogism as the third operation of the mind, which leaves the premises and arrives at the conclusion. Such terminology is symptomatic of a change that occurred in the mid-seventeenth century. The Port-Royal section on method—a most popular subject in this period—more explicitly opened the way to the discursive excesses that would soon masquerade as logic, culminating, perhaps, in Henry Kett's Logic Made Easy, or A Short View of the Aristotelic System of Reasoning, and Its Application to Literature, Science, and the General Improvement of the Mind (Oxford, 1809).

A book praised by Leibniz and rather above the average, although not completely out of the common rut, is the Logica Hamburgensis (Hamburg, 1638), by Joachim Jung, or Jungius. One notable feature of this book is the marking of the lines of a syllogistic demonstration by letters, which are then used as references for showing by what principles which line follows from which others. Such a rather exact method of proof was very exceptional in logic before modern times, but contemporaneously with Jung, Pierre Hérigone introduced a similar method in mathematics (Cursus Mathematicus, Paris, 1634–1637). Jung was thoroughly acquainted with the possible use of contraposition as a means of syllogistic proof but was no more successful in his discussion of the fourth figure than so many others had been. Under the medieval heading of consequences he noted the argument a recto ad obliquum, which can be found in Aristotle's Topics II, 8, 114a18.

Some considerations, usually brief, of such standard medieval subjects as consequences and supposition theory continued to appear—for instance, those of Chrysostom Javellus (Compendium Logicae, Lyons, 1580), Robert Sanderson (Logicae Artis Compendium, Oxford, 1618), and Henry Aldrich—but these were exceptions. Arnold Geulincx hoped to repopularize such treatises by his Logica Fundamentis Suis a Quibus Hactenus Collapsa Fuerat Restituta (Leiden, 1662). He was able to relate alternation, conjunction, and negation by means of their truth conditions according to the laws that are often called after De Morgan or William of Ockham but that go back, at least in part, to the Syncategoremata of Peter of Spain. These laws were also known to the mathematician Gerolamo Saccheri, whose Logica Demonstrativa (Turin, 1697) is outstandingly original in its high degree of organization, its reflections on the assumptions necessary to logic, and its use of indirect proof, in the pattern of the so-called mirabilis consequentia, to the effect that what follows from its own negation is true. Unfortunately the few signs of revival and advance discernible at the close of the seventeenth century did not produce any general or permanent result, and even the work of Leibniz met with little response.

Bibliography

interregnum

Dürr, Karl. "Die Syllogistik des Johannes Hospinianus (1515–1575)." Synthese 9 (1952): 472–484.

Hamilton, William. "Logic: The Recent English Treatises on That Science" (1833). In Discussions on Philosophy and Literature, Education and University Reform, 116–174. London and Edinburgh: Longman, Brown, Green and Longmans, 1852.

Howell, W. S. Logic and Rhetoric in England, 1500–1700. Princeton, NJ: Princeton University Press, 1956.

Ong, W. J. Ramus, Method, and the Decay of Dialogue. Cambridge, MA: Harvard University Press, 1958.

Risse, Wilhelm. Die Logik der Neuzeit, Vol. I (1500–1640). Stuttgart and Bad Cannstatt: Frommann, 1964.

Thomas, Ivo. "The Later History of the Pons Asinorum." In Contributions to Logic and Methodology in Honor of J. M. Bocheński. Amsterdam: North-Holland, 1965.

Thomas, Ivo. "The Liar: A New Historical Detail." Notre Dame Journal of Formal Logic 6 (1965): 201–208.

Thomas, Ivo. "Medieval Aftermath: Oxford Logic and Logicians of the Seventeenth Century." In Oxford Studies Presented to Daniel Callus. Oxford: Clarendon Press, 1964.

Thomas, Ivo. "The Setting of Classical Logic." Notre Dame Scholastic 101 (1960): 16–17.

Ivo Thomas (1967)

Encyclopedia of Philosophy