Abstract
This chapter is devoted to the too often neglected study of inference in the Middle Ages, an era that saw an enormous flourishing of studies on loci on the theoretical level as well as its function as an educational tool in society. We consider a small selection of medieval authors (Garlandus Compotista, William of Sherwood, Peter of Spain and Peter Abelard), with an emphasis on Abelard and Peter of Spain. The latter’s treatise on logic (Summulae logicales) has had such success as a logic introduction textbook; up to the 17th century one hundred and sixty-six editions were produced (Boehner 1952). We also emphasize that the medieval notion of habitudo as a relation between two poles (“from…to”, e.g. locus from cause to effect), if systematically applied, substantiates the notion of locus.
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Notes
- 1.
There are, however, notable exceptions. Stump (1989) has provided a very comprehensive overview of dialectical and logical studies in the Middle Ages, although her work is not focused on their implications for contemporary argumentation studies. Green Pedersen (1984) has written a comprehensive review of the study of topics in the Middle Ages, discussing Aristotle and Boethius as the sources of medieval elaboration. Some aspects may also be found in other texts: for example, Walton et al. (2008) devote a chapter to the history of schemes, in which they briefly touch upon the importance of other medieval authors, such as Abelard, William of Sherwood, Peter of Spain, Robert Kilwardby, Boethius of Dacia, Burleigh and others (Walton et al. 2008: 291ff). More specifically, Walton et al. (2008: 290-291) clearly highlight the importance of the notion of maximal proposition (maxim) by Abelard to explain what they call the "mechaninsm of an argument scheme" (ibid.), while Macagno and Walton (2006) discuss Abelard’s contribution in relation to their theory of argumentation schemes. Accurate analyses of the contribution of the tradition of topics throughout history have also been proposed by Manfred Kienpointner (see Ch. 5, Sect. 5.3 in this volume and Kienpointner 1987).
- 2.
Our readers may note that the authors cited in this chapter are all men. Unfortunately, we did not find any contributions by women matching in importance and relevance. Similar considerations hold for the preceding chapters and the next one. Discussing the historical reasons for this situation is beyond the scope of the present volume. For discussion on the role of medieval women logicians, we recommend the work by S. L. Uckelman, in particular Uckelman (2016a) and Dutilth Novaes and Read (2016: 12–13). We are grateful to Michael Baumtrog for his suggestion to consider the work by Dutilth Novaes.
- 3.
Green-Pedersen (1984) provides a full reconstruction of the medieval approaches to loci , from the earliest texts to the 14th century. The first works considered were published before the year 1000 and are connected with the Swiss Monastery of St. Gall (see Green-Pedersen 1984: 139). Green-Pedersen comments that at the end of the time span he is considering, the treatises on loci are less numerous: “The works dealing with the topics in the 14th century are fewer than in the earlier periods” (Green-Pedersen 1984: 301).
- 4.
- 5.
The notion of habitudo becomes misinterpreted and forgotten after the medieval tradition, despite its plain applicability to the definition of loci (see Chap. 6). At the end of the fifteen century, in his De inventione dialectica, the otherwise important contributor to the study of loci Agricola (see Chap. 4) misunderstands habitudo; he does not see that this Latin term is used in the sense of “relation” and interprets it as “se habere”, i.e. “to be in a certain way” (Rigotti 2014a). The refusal of the notion of habitudo (and of other medieval concepts such as that of maxim) is partly due to Agricola’s polemical attitude towards the medieval contributors (“qui post Boethium scripsere”, as he puts it, “those who have been writing after Boethius”, without bothering to mention their names) and its predilection for the classical tradition. We shall present a more detailed analysis of these aspects in Chap. 4.
- 6.
The same concept of locus as vis inferentiae is present in Buridan’s Summulae de dialectica (henceforth, abbreviated with BSD. See Klima 2001). When talking about locus from genus and species, Buridan explains how habitudines are the sources of the maxims’ truthfulness and (persuasive) efficacy by stating the following (BSD 6.2.2.): “Quidquid vere affirmatur de genere vere affirmatur de specie’ sit locus maxima, isti termini ‘species’ et ‘genus’ sunt locus-diffrentia maximae: ex habitudine enim speciei ad suum genus maxima habet veritatem et efficaciam” (“Be ‘Whatever is affirmed truthfully of the genus is truthfully affirmed of the species’ the maxim, these terms ‘species’ and ‘genus’ are the difference of the maximal proposition: in fact, the maxim assumes its truthfulness and effectiveness from the relation (habitudo) of a species to its genus”, our translation).
- 7.
This and the following translations in this section, unless otherwise stated, are the authors’ translations. When we cite the original Latin texts, we report them as they are written in the editions we are considering. In particular, for the letters /v/ and /u/ in Latin, we use both variants, depending on the edition that we refer to.
- 8.
These examples have been elaborated by the authors of this volume.
- 9.
See Footnote 8.
- 10.
The reconstruction of Garlandus’ life and work is controversial. In his introduction to the first edition of the two extant manuscripts of the Dialectica (which we have adopted as a basis for our discussion in this section), De Rijk (1959) proposes an accurate reconstruction of Garlandus’ life (Green-Pedersen 1984 also uses De Rijk’s biographical reconstruction as a basis for his account of Garlandus). In what follows, we report the final summary of Garlandus’ life, which we take from De Rijk’s (1959) accurate reconstruction: “(1) he was born around 1015, presumably in the surroundings of Liége. (2) He went to England under the reign of Harald I (1036-1040), and stayed there until 1066. He wrote his Compotus in this period. (3) He was magister scholarum in his later years at Besançon […]. The Candela was written in this period. (4) He died between 1084 and 1102 in Besançon or in its surroundings” (De Rijk 1959: xlii). According to De Rijk (1959: xlix), Garlandus must have written the Dialectica on the continent after his return from England (1066), and before the beginning of his stay at Besançon (before 1075), when living at Liége. Eleonore Stump (1989: 67–68) generally refers to De Rijk for the reconstruction of Garlandus’ life. She stresses that Garlandus’ work is ancient, supposing that it “may have been written before 1040” (ibid.). In an article published in 1992, Iwakuma Yukio (1992) questions the attribution of Dialectica to Garlandus the Compotist, suggesting instead that it was most likely compiled by another, younger, author, Garlandus of Besançon, who on this hypothesis should have lived and taught in Besançon several decades later. Thus, the Dialectica would have been written between 1120 and 1130. More recently, Marenbon (2011) compares the hypotheses by De Rijk and Iwakuma, concluding that “it seems wisest to leave the identification of the author of the Dialectica open and to accept that it could date from the 1080s or even earlier, or from as late as the 1120s, or from sometime between” (Marenbon 2011: 195). For De Rijk and others, the surname “Compotist” potentially identifies the author of the Dialectica. “Compotist” comes from Compotus, the title of one of the works associated to Garlandus Compotista. Compotus is a medieval variant of Latin computus, which means “calculation”. In fact, this work presented a system for a particular application of computing. In the medieval tradition, compotus was indeed a branch of astronomical science whose object was “to calculate the year of Grace and the date of movable feasts of the Church especially of Easter by the motions of the sun and the moon” (De Rijk 1959: XXII ff.).
- 11.
Logica vetus is the name of that part of the Aristotelian logic, whose Latin translation was known before 1150. The sources of Logica vetus were Boethius’ translations, commentaries and monographs on logic, on syllogisms, both categorical and hypothetical, and, of course, on topics (see Chap. 2 of this volume).
- 12.
The acknowledgment of the foundational role played by Aristotle and Boethius within the tradition of logical studies is stressed by Garlandus, who frequently quotes these authors’ works using the phrase “the book” par excellence (Lat. liber).
- 13.
A concise list of the contents of the six booklets of the Dialectica includes the following: (1) predicables and categories in relation to simple voices; (2) propositions and their logical properties; (3) propositions and their constituents; (4) the doctrine of loci with its semantic and logical preliminaries; (5) figures and modes of categorical syllogisms; (6) hypothetical syllogisms.
- 14.
According to Garlandus, in this second meaning the quaestio is introduced by the Latin word utrum, which means “which of the two”.
- 15.
This use of the term argumentum refers to the traditional use of writing a short preface of theatrical pieces. This meaning of argumentum is mentioned by Quintilian (Institutionis oratoriae libri duodecim, VI, l. V, 25517-3565, see Winterbottom 1970) and Lorenzo Valla in his Dialecticae Disputationes (see Zippel (1982) and Chap. 4 in this volume). In contemporary Italian, this meaning of the word (It. argomento) has been maintained and widened to include the theme of a certain discourse. Thus, the polysemy of argumentum, which Garlandus rightly identifies, is still present in the Italian argomento, which oscillates between “reason” and “theme”, with the second meaning prevailing in everyday (non-scientific) use.
- 16.
When he gives this primacy to the inferential strength of syllogism, Garlandus is wholly in line with Aristotle and Boethius. Not coincidentally, Garlandus speaks about syllogism using Aristotle’s definition, as reported in Boethius’ translation into Latin.
- 17.
Stump (1989: 68) maintains that Garlandus’ treatise on loci is “plainly derivative” from Boethius’ De topicis differentiis. However, we believe that Garlandus, though closely following Boethius, often introduces comments and remarks which, generally, enrich and deepen the doctrine of loci. Some examples of his remarks have been given above in our brief reconstruction of the contents of the Dialectica.
- 18.
Concerning his classification of loci, Garlandus’ contribution is not particularly relevant, as he largely reproduces the list of loci proposed by Boethius. It might be said that Garlandus is not interested in designing a taxonomy of loci. Notably, he argues that one and the same locus can receive different denominations, thus substantially ‘emptying’ the classification of any relevance.
- 19.
Garlandus adopts locus instead of difference of the maximal proposition for the sake of simplicity, in line with the goal of his treatise to reach a broad public: “Differentias maximae propositionis simplices locos appellamus” (GLV IV31, in De Rijk 1959: 100).
- 20.
As Kretzmann (1966: 4) argues, all of the philosophers who seem to have been directly influenced by Sherwood had lived in Paris during the time span he might have been lecturing there. Kretzmann includes, among such philosophers, Peter of Spain and Lambert D’Auxerre, as well as Thomas Aquinas (for his work on modality) and Albert the Great (for his logical writings). Brands and Kann (1995: XIII–XIV), however, also quoting De Rijk (1972), tend to exclude any direct influence by William on these authors; they also question the fact that he ever lived in Paris, thus criticizing Kretzmann’s view.
- 21.
- 22.
William mentions the term habitudo in relation to the locus called “proportion” (analogy).
- 23.
In the introduction to his edition, De Rijk (1972: ix) notes that the identity of Peter of Spain is controversial: “is the author identical with Peter of Spain (Petrus Hispanus) who in 1276 became Pope under the name of John XXI?” (ibid.). After analyzing the controversy (De Rijk 1972: ix–xix), De Rijk concludes that: “Generally speaking […], it should be remarked that, when all pieces of evidence in support of Pope John XXI’s authorship of the so-called Summule logicales are weighted out against those suggesting the author’s membership of the Dominican Order, the scales are far tipped in favour of the former view” (De Rijk 1972: xix). Degen and Pabst (2006: ix), in the introduction to their German edition of the Summulae Logicales, presuppose the identity of the author of the Summulae and Pope John XXI. If we accept the identity hypothesis, Peter of Spain must have been born in Portugal (De Rijk 1972: xxiv); according to Degen and Pabst (2006: ix), he was born between 1205 and 1215 in Lisbon. Peter might have partially studied in Lisbon, then he was certainly sent to “the famous center of logical, philosophical and theological learning of those days, the University of Paris” (De Rijk 1972: xxx). He presumably left Paris in 1229 (according to De Rijk 1972: xxxvii), settling down in different places, including Northern Spain, the South of France (Toulouse and Montpellier), then Siena, Viterbo, Orvieto, and again Lisbon (De Rijk 1972). He taught logic and studied and taught medicine (ibid.); in 1263, he was appointed magister scholarum of the Cathedral School of Lisbon (De Rijk 1972: xxxix). In 1273 he was elected Archbishop of Braga in Portugal and in the same year he became Cardinal Archbishop of Frascati in Italy (De Rijk 1972: xlii). Then, as De Rijk (1972: xl) explains, “Peter of Spain was elected Pope on September 15, 1276. He was erroneously crowned as Pope John XXI instead of John XX, as he should rightly have been”. He died on May 20, 1277 following an accident: the roof of his private apartment—which he used for study purposes—collapsed (De Rijk 1972: xl). From a cultural viewpoint, it is interesting to add that Peter of Spain is mentioned in Dante Alighieri’s Commedia (Paradiso) as the author of the Summulae logicales: “…and Peter the Spaniard/who casts light from his twelve books below” (original Italian: “…e Pietro Spano/lo qual giù luce in dodici libelli” (Dante, Div. Com., Paradiso, Canto XII, 134-135; the original and the translation have been taken from the online Princeton Dante Project, see http://etcweb.princeton.edu/cgi-bin/dante/campuscgi/mpb/GetCantoSection.pl, last visited March 2018). Amongst other things, the presence of Peter’s “twelve books” in the Commedia testifies to the wide distribution of the study of logic (including topics) in the Middle Ages, beyond the boundaries of scholarly discussion among logicians.
- 24.
The original name of this work was Tractatus, but Summulae logicales (or Summule logicales) has become a common name (see De Rijk 1972: xliii). We will use Summulae logicales.
- 25.
- 26.
Note that the diagram in Fig. 3.2 is ours—it is not present in the Summulae Logicales. Yet the rationale behind this diagram clearly surfaces from Peter’s discussion of the intrinsic loci.
- 27.
This type of “descriptive definition”, so to say, is very much used when one is only interested in identifying a specific entity in a closed domain rather than investigating what that entity is. For example, in a class of twenty students, we might say that Mary is “the only one wearing a green jumper”; we do not mean to describe Mary exhaustively but, if it is true that no other student is wearing a green jumper in that given moment, we have succeeded in identifying her exclusively (see the treatment of ἴδιον by Aristotle in Chap. 1).
- 28.
The original text in Latin is “Remota causa materiali removetur eius effectus”. William of Sherwood’s formulation of the same maxim was more incisive: “Deficiente materia deficit et materiatum” (see Sect. 3.4).
- 29.
We propose alternative translations to clarify the concepts. Corruption, in particular, is intended here as “termination” or “destruction”.
- 30.
Peter’s original example is the dichotomy “healthy/ill” in animals. Animals are said to be either ill or healthy, without possible intermediate statuses. Yet this example is not easy to maintain in view of current medical developments.
- 31.
To situate Abelard’s work in his historical context, we include some biographical data, which we largely report from De Rijk (1959), adding some additional comments. According to De Rijk (1959: ix–xi), Peter Abelard might have been born in Le Pallet—whose Latin form Palatium will suggest the appellation “magister Palatinus” for Abelard (see also Jolivet 1994: 2)—close to Nantes, in Brittany, in 1079. As De Rijk (1959: ix) observes, in Abelard’s autobiography (the renowned Historia calamitatum, see Monfrin 1962), Abelard reports that he journeyed through all the districts of France, wherever he heard that studies in logic flourished, in search of training (De Rijk 1959: xix). He eventually arrived in Paris, where logic was particularly advanced thanks to the teachings of William of Champeaux, certainly the most famous logician of the time in France (De Rijk 1959: ix). Green-Pedersen (1984: 165ff) discusses how much Abelard has taken from William and how much he has elaborated a different doctrine of loci. Abelard’s strongly critical attitude soon induced him (at about 1104) to abandon William of Champeaux and to set up a school of his own, first at Melun and then at Corbeil. His nature, characterized by independence of thought and a passionate search of truth, and always prone to a subtle and rigorous analysis of the interlocutor’s viewpoint, was also inclined to a polemical attitude. This was plainly one of the causes of a very turbulent biography, as emerges from his Historia calamitatum (Monfrin 1962). Abelard left Paris for Melun and then for Corbeil, before returning to Paris where he attended William of Champeaux’s lectures on rhetoric . He set up a school on Mont S.te Geneviève and thereafter went to Brittany (1113) for a short stay, before moving on to study theology with Anselm and his brother Ralph, as reported by De Rijk (1959: ix). But he then became a rival of these two famous masters (ibid.). He was forced to leave Laon and returned to Paris, where he obtained a chair at the cathedral school of Notre-Dame. His career, however, was seriously compromised by his dramatic love story with Héloise (Gilson 1960; see also the reconstruction in Jolivet 1994). In the meantime, his increasing interest in theological matters led him to take part in sharp debates with (and against) influential theologians. In 1121, his first theological work (De Unitate et Trinitate Divina) was condemned at the Council of Soissons. Later, in 1140, he was condemned again at the Council of Sens, mainly under the pressure of Bernard of Clairvaux, who was his personal enemy at the time. Abelard was also excommunicated in the same year by Pope Innocent II (De Rijk 1959: xi). While trying to reach Rome to lay his case before the Pope, he arrived at Cluny where the abbot Peter the Venerable invited him to rest in his abbey, advising him to make peace with Bernard of Clairvaux (ibid.). Having done so, Abelard could receive a mansio perpetua in the Abbey of Cluny (ibid.). Considering the state of his health, Peter the Venerable sent him to Châlons-sur-Sâone. There, as Peter the Venerable wrote to Héloise, he restarted his studies, totally devoting himself to reading, writing and praying, ibid.). At the end of his life, he compiled his Apology, a Monitum (recommendation) devoted to his son (Carmen ad Astralabium) and a Dialogue between a Philosopher, a Christian, and a Jew (ibid.).
- 32.
The first complete edition of the unique extant manuscript—MS. Lat.14.614 of the Bibliothèque Nationale in Paris—is due to the renowned Dutch philologist L. M. De Rijk. We follow his second revised edition (De Rijk 1970). The translation from Latin into English is our own, unless otherwise stated.
- 33.
Modes of meaning (modi significandi) are understood by Abelard as semiotic-semantic properties of different kinds of signs; the notion of dictio is a fundamental construct of the classical grammar, which is close to the modern notion of word-form (see Priscian’s definition of oratio “constructio dictionum congrua perfectam sententiam demonstrans”, which is only partially reported by Abelard). Abelard defines dictio as a non-complex (incomposita) voice which is meaningful according to an arbitrary convention (ad placitum), corresponding to the pronunciation of a single word, i.e. like ‘man’ and ‘runs’ is meaningful in its whole, not through its constituents, (“Est autem dictio singuli vocabuli nuncupatio, idest vox totaliter, non per partes, significativa, ut ‘homo’ vel ‘currit’.” Dial. I, 11433-1151-2). These aspects are the foundation of the study of inference , but are beyond the scope of this volume.
- 34.
The whole first volume and the initial part of the second volume of the Dialectica are lost, and the scheme of their content has been established by De Rijk on the basis of references provided in the body of the extant text (De Rijk 1970: XXVIII).
- 35.
De Rijk reports a quotation from John of Salisbury who refers to the Topica as an autonomous work.
- 36.
We refer to the edition in the Patrologia Latina, which is provided in the reference list.
- 37.
Abelard highlights Boethius’ emphasis (see Chap. 2) on the expression “per ea ipsa” (i.e. “in virtue of these things themselves”, namely of the things laid down and agreed upon) (Dial. III, 254 24-26).
- 38.
Boethius’ definition, as recalled in Chap. 2, closely follows Aristotle’s (Topica 100 a 25-27).
- 39.
The Latin text is as follows: “Argumentationes quaedam sunt locales, quaedam vero complexionales. <Complexionales> quidem sunt <quae> ex ipsa complexione, id est ex ipsorum teminorum dispositione firmitudinem contrahunt; locales vero sunt quibus convenienter potest assignari locus, idest evidentia conferri ex aliquo eventu rerum vel proprietate sermonis”.
- 40.
We are grateful to an anonymous reviewer who suggested this point.
- 41.
Because it includes many consequences, a maximal proposition becomes “a sort of multiple consequence” (tamquam multiplex consequentia).
- 42.
One example of such a rule reported by Abelard may be expressed in the following (revised) form, which corresponds to the transitive propriety: “if every A is a B and every B is a C, then every A is a C”.
- 43.
This conclusion would be acceptable if the issue were: “provided that you are a man, are you an animal or not?”. But this is not our case.
- 44.
The properties of definitions are considered in detail in the second book of the Topica. (Dial. III, 414-466).
- 45.
Both in the sense of collection of species building one genus, where the substance of genus exists in all its species (like animal vs man or horse) and of collection of individuals building one species (like man vs. Socrates or Plato).
- 46.
We are grateful to an anonymous reviewer for having suggested this remark.
- 47.
Boethius called mutually incompatible terms disparates (De hypotheticis syllogismis I, 834 C14-D1, see Orbetello 1969).
- 48.
According to Abelard, if one adopted the less strict definition proposed by Boethius (“Efficient cause is that which makes any thing, preceding it not as for the time, but as for the property of its nature”—De top. diff. III, 1199), the sun could be defined as a natural efficient causeEfficient cause of the day, which is obviously incorrect.
- 49.
Change in quantity (increase or decrease) is connected to the three spatial dimensions and to the numbering. Change in quality (also named alteration, Dial. III, 432-434) evokes an intricate dispute because quality is a vague term. Change in place coincides with the movement from one place to another.
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Rigotti, E., Greco, S. (2019). The Richness and Originality of Medieval Contributions. In: Inference in Argumentation. Argumentation Library, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-04568-5_3
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