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S 1229 elements in Suhrawardı¯’s writings. This last approach led Secondary Sources to a better grasp of the importance of Suhrawardı¯’s logical Amin Razavi M (1997) Suhrawardi and the school of illumination. Curzon Press, Richmond theories (it is interesting to note that only the parts on Corbin H (1971) En Islam iranien. Aspects spirituels et philosophiques. metaphysics were included in Corbin’s edition of the Tome II: Sohrawardıˆ et les Platoniciens de Perse. Gallimard, Paris Talwı¯h:a¯t, Muqa¯wama¯t, and Masha¯ri‘, and that his transla- Ibra¯hı¯mı¯Dı¯na¯nı¯Gh H (1985) Shu‘a‘-i andisha va shuhu¯d dar falsafah-yi tion of the Kita¯bHikmat al-Ishra¯qı¯ skips over the first part Suhrawardı¯. Hikmat Tehran ˙ ˙ on general questions regarding and epistemology). Ha’iri Yazdi M. (1992) The principles of epistemology in Islamic philos- ophy: knowledge by presence. State University of New York Press, A few scholars have also pointed to other intellectual Albany traditions, which may have contributed to Suhrawardı¯’s Marcotte R (2001) Suhrawardı¯ al-maqtu¯l, the martyr of Aleppo. system, such as Isma¯ʿ¯lıı ¯ thought, opening new perspectives al-Qantara 22:395–419 still to be explored. Walbridge J (2000) The leaven of the ancients: Suhrawardi and the heritage of the Greeks. State University of New York Press, Albany See also: ▶ Ibn Sı¯na¯, Abu¯ ʿAlı¯(Avicenna) ▶ Isma¯ʿ¯lıı ¯ Phil- Walbridge J (2001) The wisdom of the mystic East: Suhrawardi and Platonic orientalism. State University of New York Press, Albany osophical Tradition ▶ Logic in the Arabic and Islamic Ziai H (1990) Knowledge and illumination: a study of Suhrawardi’s World ▶ Philosophy, Arabic ▶ al-Shahrazu¯rı¯, Muh:ammad Hikmat al-Ishraq. Scholars Press, Atlanta ibn Mah:mu¯d Shams al-Dı¯n

Bibliography

Primary Sources Supposition Theory Suhrawardı¯(1334/1955) Mant:iq al-Talwı¯h:a¯t, ed. Fayyad ‘A-A. Intisha¯rat-i Da¯nishga¯h-i Tihra¯n, Tehran CATARINA DUTILH NOVAES Suhrawardı¯ (1397/1977) Sih risa¯la al Shaykh-i Ishra¯q: al-Alwa¯h: ILLC and Department of Philosophy al-‘Ima¯diyya. Kalima¯t al-tas:awwuf. al-Lamah:a¯t, ed. Habı¯bı¯ N.-G. University of Amsterdam ¯ ˙ Anjuman-i Sha¯hansha¯hı¯-’i Falsafah-’i Ira¯n, Tehran Amsterdam Suhrawardı¯(1935) Kohlhammer W, Three treatises on mysticism, ed. and trans. Spies O., Khatak SK. Stuttgart (contains Lughat-i-Mu¯ran; The Netherlands Safı¯r-i Sı¯murgh; Risa¯lat al-t:ayr) ˙ Suhrawardı¯ (1945–1970) Opera metaphysica et mystica I–III, ed. Corbin H. (repr. (1993) oeuvres philosophiques et mystiques. Anjuman-i Abstract Shahanshahı¯-’i Falsafah-’i¯ Iran, Tehran) (t. I contains the metaphysical ¯ ¯ ¯ Supposition theory is one of the most important later part of al-Talwı¯h:a¯t, al-Muqa¯wama¯t, and al-Masha¯ri‘wa-l-mut:a¯rah:a¯t; t. II contains Kita¯bHikmat al-ishra¯q; Risa¯la fı¯i‘tiqa¯d al-hukama¯’; medieval semantic theories (in the Latin tradition). Sup- ˙ : Qis:s:at al-g˙urba al-g˙arbı¯ya; t. III contains the following short treatises position is the of terms (occurring in proposi- in Persian: Partow Na¯me, Haya¯kil al-nu¯r, Alwa¯h:-i ‘Ima¯dı¯ya, Risa¯lat tions) of standing for things, so that these things can be al-t:ayr, ‘Aql-i sorkh, Ru¯zı¯ba¯ jama¯‘at-i s:u¯fı¯ya¯n, Fı¯h:a¯lat al-t:ufu¯lı¯ya, talked about by means of , and supposition Fı¯h:aqı¯qat al-‘ishq, Lughat-i mu¯ra¯n, Safı¯r-i Sı¯murgh, Busta¯n al-qulu¯b, ˙ theory (in its different versions) is a theory codifying the Yazda¯n shinakht, al-Kalima¯tal-dhawqı¯ya aw Risa¯lat al-abra¯j) Suhrawardı¯(1976) L’archange empourpre´: quinze traite´setre´cits mys- different uses of terms in propositions, based on the idea tiques, trans. Corbin H. Fayard, Paris (French translation of most of that one and the same term can stand for different things the treatises in Opera metaphysica et mystica, t. III, plus a few others) when occurring in different propositional contexts. The S Suhrawardı¯(1982) The mystical and visionary treatises of Shihabuddin different kinds of supposition are attempts to capture the Yahya Suhrawardi, trans. Thackston W.M. Octagon Press, London phenomenon of semantic variation prompted by different (repr. (1999) The philosophical allegories and mystical treatises. A parallel Persian-English text. Costa Mazda Publishers) (the intro- propositional contexts. The theory emerged in the twelfth duction and translation are misleading on several counts. See century, and the two main traditions contributing to its H. Landolt’s (1987) review in J Am Orient Soc 107(3):475–486) development were the tradition of commentaries on Suhrawardı¯(1986) Le livre de la sagesse orientale. KitaˆbHikmat al-Ishraˆq. ˙ ’s and the tradition Commentaires de Qotboddıˆn Shıˆraˆzıˆ et Mollaˆ Sadraˆ Shıˆraˆzıˆ, trans. : commenting on the fourth-century grammarian Priscian. Corbin H. intro. Jambet C. Verdier (transl: Hikmat al-ishraˆq, Intro- ˙ duction and Part 2, with commentaries) Supposition theory acquired its first mature form in the Suhrawardı¯ (1996) Temples of lights, trans. Kuspinar B. ISTAC, thirteenth century, with the terminist/summulist tradition Kuala Lumpur (in the works of , , Suhrawardı¯ (1998) The book of radiance (Partow Na¯meh). A parallel , and Lambert of Lagny/Auxerre), and was English-Persian text, ed. and trans. Ziai H. Costa Mazda Publishers further developed in the fourteenth century by authors Suhrawardı¯(1999) The philosophy of illumination. A new critical edition of the text of Hikmat al-ishraq, ed. and trans. Walbridge J., Ziai H. such as Walter Burley, , and John ˙ Brigham Young University Press, Provo Buridan. 1230 S Supposition Theory

Introduction Indeed, theories of supposition deal with four main Supposition is one of the properties treated within the kinds of semantic variation: doctrine of the properties of terms, a doctrine whose 1. Whether a term is taken literally or metaphorically. development started in the twelfth century and which 2. The different ontological kinds of the things that one then became the cornerstone of later medieval and the same term can stand for – the supposita: (see Read 2006, and the entry on Terms, Properties of (extra-mental) individual entities, universal entities, in this volume). In fact, the development of this doctrine mental entities, or linguistic entities. from the twelfth century onward consists precisely in 3. The different temporal and modal statuses of the ‘‘the growing dominance of just one of the properties of supposita: present, past, future, actual, or possible. terms, supposition’’ (De Rijk 1982:161). Indeed, by the 4. The different quantities of entities required to verify or fourteenth century the of supposition had falsify a . almost entirely superseded or absorbed the other prop- erties of terms for the purposes of . (1) The first kind of variation is usually codified by means Asection(oftenseveralchapters)specificallyonsuppo- of the distinction of proper vs. improper supposition. For sition is to be found in every single logical textbook of reasons of space, though, improper supposition will not be the thirteenth and fourteenth centuries (not to mention analyzed in any detail here, and we shall concentrate on the several De suppositionibus treatises in the fourteenth proper supposition. (2) The second kind of variation is century). accounted for by means of the distinction of the main Very generally put, supposition is the property of kinds of proper supposition, usually personal, simple, and terms (occurring in propositions) of standing for things, material supposition (such as in Ockham’s Summa so that these things can be talked about by means of logicae). The contextual element usually thought to pro- propositions. Thus described, it may appear to be the voke this kind of variation is the ontological kind(s) of the medieval counterpart of the modern concept of refer- things of which the other term in the proposition is ence, and indeed such a comparison has often been put correctly predicated, as suggested by an oft-repeated forward. But there are also significant dissimilarities motto (Ebbesen 1981:41): ‘‘subjects are such as the pred- between medieval theories of supposition and modern icates permit’’ (see Sherwood 1966:113). (3) The third theories of , and in fact this comparison can be kind of variation is addressed by the of quite misleading (see Dutilh Novaes 2007: chap. 1). ampliation and restriction, originally independent prop- Rather, it seems more appropriate to view medieval the- erties of terms that in later developments were absorbed by ories of supposition as having no exact modern counter- the supposition machinery. The contextual element usu- part – one must attempt to understand them in their own ally (though not always) thought to provoke this kind of terms. Moreover, throughout the centuries the concept variation is the tense (past, present, future) and the mode of supposition ‘‘developed in response to a variety of (actual, possible, necessary) of the verb in the proposition. needs, and one mistake of modern attempts at interpre- (4) The fourth kind of variation is dealt with by means of tation is to seek a unique rationale’’ for its various for- the distinction of the modes of (common) personal sup- mulations at different stages of its development (Read position, whose main modes are confused and distribu- 2006: Introduction). tive, merely confused, and determinate supposition (such Nevertheless, a fairly accurate general characterization as in Ockham’s Summa logicae). The contextual element of the different versions of supposition theory is as usually thought to provoke this kind of variation is the a theory codifying the different uses of terms in proposi- presence or absence of syncategorematic terms (i.e., terms tions; such variations of uses are important as such, but such as ‘‘every,’’ ‘‘some,’’ ‘‘no,’’ ‘‘not’’) and word order. they are also crucial for key logical concepts such as truth, (This last distinction is treated elsewhere in this volume; (fallacious or valid) inference, and propositional con- see the entry on Quantification.) tent. In other words, a trait common to the different Among the other early properties of terms, the only formulations of the theory is the idea that one and the one having resisted total absorption by supposition in the same term can stand for different things when occurring long run is the property of signification. Indeed, while the in different propositional contexts, thus having distinct notion of supposition implies that a given term does not semantic contributions to the content of a proposition at have a stable, general , but rather that its semantic each time. The different kinds of supposition are contribution depends fundamentally on the propositional attempts to capture the phenomenon of semantic varia- context (and thus on specific uses), the property of tion prompted by different propositional contexts. signification is thought to be context-independent and Supposition Theory S 1231 pre-propositional. Signification concerns the first imposi- forthcoming) must also be taken into account to explain tion of what a term shall be used to talk about, whereas these developments. Furthermore, it is now believed that supposition concerns uses of a term that already has a more cautious timeframe for the seminal texts would be a signification, and the semantic variations that may be the very last decades of the twelfth century and the first prompted by the propositional context. decades of the thirteenth century, differing thus from De Another important point to bear in mind is that sup- Rijk’s earlier dating of these texts. Nonetheless, the signif- position theory was not simply a sterile exercise, devel- icance of these two traditions – the grammarian tradition oped for purely theoretical reasons. Much to the contrary, and the tradition on the fallacies – is beyond any doubt, so supposition theory was widely used as a semantic tool in let us examine how exactly the suppositional framework an ample range of fields, most notably theology (Brown may have emerged from them. 1993) and physics. Hence, besides the bare presentations At this early stage (second half of the twelfth century), of the theory that one encounters in medieval logical suppositio is often related to the syntactic act of putting textbooks, the theory actually put to practice is perhaps a term as the grammatical subject of a proposition (see even more fascinating. For reasons of space we shall not Kneepkens 1987). But it has been argued (Ebbesen 1981) deal with specific applications of supposition theory, but that even at this early stage, the suppositio terminology is one should bear in mind that supposition theory was used not only to refer to a syntactic act but also to the essentially developed to be used, to be put to practice as semantic relation between a term and what it stands for, a semantic tool for the analysis and interpretation of which was later to become the standard notion of discourse, and thus also to deal with matters of truth suppositio. In fact, these two apparently different accep- and inference in different fields of investigation. tations of the suppositio terminology (present, for exam- In what follows, I present a chronological account of ple, in the twelfth-century grammarian Peter Helias, the development of supposition theory in the twelfth, whose Summa super Priscianum is a key text for these thirteenth, and fourteenth centuries. Such a partition developments) – the syntactic one and the semantic one although obviously somewhat arbitrary is nonetheless – are not really dissimilar if one considers that the proto- supported by the significant coherence within each cen- typical subject of a proposition is a substantive noun and tury. Moreover, it should not be taken to imply that after that, according to the grammatical tradition following the fourteenth century no developments worth mention- Priscian, a noun signifies a substance together with ing took place: much to the contrary, in very late medieval a quality. Hence, by placing a noun as the subject of authors one finds sophisticated solutions to many of the a proposition, one also naturally invokes the substance issues left open by previous generations (see Dutilh that the noun signifies. The noun ‘‘man,’’ for example, Novaes 2008a; Ashworth 1974). Nevertheless, these three signifies the individual primary substances that are men centuries embody what we could call the ‘‘classical era’’ of insofar as they instantiate the universal nature humanity, supposition theory. and thus it may stand for men in a proposition. Moreover, following Aristotelian hylomorphism, universal natures Early Developments: Twelfth Century and qualities are usually viewed as corresponding to The historical emergence of supposition theory was forms, which are combined with matter to give rise to the topic of De Rijk’s groundbreaking study Logica individuals. Thus, in the twelfth century, to be S modernorum, published in three volumes (De Rijk 1962/ a suppositum is regularly used in the sense of being the 1967) and including the edition of a wide range of twelfth- bearer of a name or, equivalently, of a form/quality: and and thirteenth-century crucial (anonymous) texts. De Rijk indeed, the notion of ‘‘bearer of form’’ is (according to identified two main traditions contributing to the devel- Ebbesen 1981:38) crucial in the early development of opment of supposition theory: the tradition of commen- supposition theory. taries on Aristotle’s Sophistical Refutations and, more Unsurprisingly, in this period supposition is often generally, of theories of fallacies; and the tradition viewed as a property pertaining exclusively to the subject commenting on the fourth-century grammarian Priscian. term, the corresponding property for predicates being This account is still thought to be essentially correct, but copulation; but soon thereafter (e.g., in the first English since the publication of De Rijk’s study, some scholars texts of the thirteenth century – Logica ‘‘Cum sit nostra,’’ (e.g., Ebbesen 1981 have questioned certain aspects of De Logica ‘‘Ut dicit,’’ and Introductiones Parisienses), supposi- Rijk’s account. Also, it appears that other elements (such tion is seen as a property of predicates as well. as the theological tradition stemming from Gilbert of But even at this early stage, it is also widely acknowl- Poitiers’ writings; see Kneepkens 1987 and Valente edged that terms can be used to stand for things other than 1232 S Supposition Theory

what they signify depending on the specific context of use. theory seeks to codify. In the case of the example above, Particularly in the formulation of grammatical theories, supposition theory will allow the theorist to say that the one must often use a term to talk about the very term itself term ‘‘man’’ supposits for different things in the first and (for example, to say that ‘‘man’’ is a noun and that ‘‘to run’’ second premises (a common nature vs. an individual is a verb), and thus not to talk about the thing(s) they man), and thus that it has different kinds of supposition. usually stand for. Now, in order to indicate this autonymic Typically, the occurrence of ‘‘man’’ in the first premise is use of a term, twelfth-century authors belonging to the said to have simple supposition (insofar as the proposition grammatical tradition (such as in William of Conches, is true), whereas the occurrence of the same term in the Adelard of Bath and Peter Helias (De Rijk 1962:108– second premise is said to have personal supposition (inso- 109)) often spoke of terms being ‘‘materially imposed’’ far as the proposition is true). Indeed, in the fourteenth (materiale impositum) in such cases. The notion of century, with Ockham (Summa logicae I chap. 65) and materiale impositum is the forerunner of the later notion Burley (De puritate Longer Treatise }44), the distinction of material supposition (see Rosier-Catach 2003), to between personal, simple, and material supposition is still appear for the first time in William of Sherwood, which associated to the fallacy of equivocation. Now, for an again indicates the crucial role of the grammarian tradi- inference to be valid, the recurring terms must supposit tion for the development of supposition theory. for the same things in all premises, and thus must have the As for the fallacies tradition, it is immediately appar- same kind of supposition; in these early developments, ent why the fact that the very same term can be used in one encounters formulations of rules of the form ‘‘no different acceptations is of crucial importance for the inference is possible from supposition A to supposition diagnosis of fallacious arguments; Ebbesen (1981:39) B’’ (Ebbesen 1981:39). argues that in the twelfth century this might have been seen as the main purpose of supposition theory. Generally The Age of Terminism: Thirteenth Century speaking, fallacies are arguments that appear to be sound The first decades of the thirteenth century are character- in that they seem to display one of the forms usually ized by logical texts (several of which are edited in De Rijk associated with sound arguments (for example, a valid 1962/1967) still presenting supposition theory in its early syllogistic mood), but which are in fact unsound in that stages. Its first reasonably mature versions, where it they feature true premises leading to (what appears to be) acquires the more or less standard shape it was to retain a false conclusion. The challenge is to identify where the for many centuries, are to be found in the writings problem lies, i.e., what (semantic) phenomenon is behind of the thirteenth-century terminists, also known as the false appearance of validity. A standard example of ‘‘summulists’’ because they produced complete overviews a fallacy is: of logic (summa, ‘‘sum’’ or summula, ‘‘little sum’’) where the properties of terms, and supposition in particular, Homo est dignissima (Man is the worthiest of occupy a key position. The main authors of this genera- creaturarum creatures) tion are William of Sherwood, Peter of Spain, Roger Sortes est homo (Socrates is a man) Bacon, and Lambert of Auxerre/Lagny, each of them hav- Ergo Sortes est dignissima (So Socrates is the worthiest ing written at least one comprehensive logical text. creaturarum of creatures) Moreover, the thirteenth century is also the period This is an obvious fallacy because the premises are true but when the Oxford/Paris opposition becomes significant. the conclusion is false, and yet it does seem to present In effect, while in the twelfth century the development a valid (syllogistic) form. Intuitively, we immediately per- of supposition theory is restricted to the Parisian schools, ceive that the problem lies in the different uses of the the thirteenth century witnesses the emergence of a middle term ‘‘man’’ in the first and second premises: in distinctively Oxford school in logic, and concerning sup- the first one, ‘‘man’’ seems to stand for the nature common position in particular, even though there were many to all men, i.e., humanity, while in the second one it seems points of mutual influence between the two centers (see to stand for a particular man, i.e., an individual instanti- De Libera 1982). One distinctive characteristic of the ating the common nature. Parisian tradition is the importance of natural supposi- Traditionally, a fallacy such as this one is diagnosed as tion, which is usually construed as the non-contextual, a fallacy of equivocation, as ‘‘man’’ is used in equivocal stable supposition of a term (resembling thus the notion ways in the first premise and in the second premise. Now, of signification), as opposed to accident supposition, i.e., it is precisely this variation of uses of one and the same the supposition that a term actually acquires in a given term in different propositional contexts that supposition propositional context (such as in Peter of Spain and Supposition Theory S 1233

Lambert of Auxerre/Lagny). Indeed, natural supposition is and especially material supposition make a resounding the only variation in the development of this concept that comeback in the fourteenth century. concerns terms out of a propositional context. Another division of formal supposition presented by The four authors just mentioned each offer a Sherwood is between common and discrete supposition. particular version of supposition theory, each with its It is unclear whether Sherwood intends it to be a own divisions and subdivisions (for trees representing subdivision of the simple-personal division or the other these divisions per author, see Spade 1996:272–276). In way round – or perhaps as an independent division fact, the different versions of the theory recognize different altogether. Either way, the subsequent tradition usually divisions and subdivisions of supposition, but they mostly treats this distinction as a subdivision of personal sup- agree on the definitions of the kinds of supposition that position: common supposition is the supposition of they do recognize. For the present purposes, let us exam- common terms, i.e., of terms not meant to designate ine the divisions and subdivisions presented by William of one specific individual, while discrete supposition is the Sherwood in his Introduction to Logic, as his theory supposition of singular terms such as proper names and contains all the kinds and modes of supposition that demonstrative pronouns, which pick out one specific remained influential throughout the fourteenth century individual. and beyond. For Sherwood, personal common supposition is fur- Sherwood’s first division of proper supposition is ther subdivided into determinate and confused supposi- between formal and material supposition. He defines for- tion; confused supposition is then divided into merely mal supposition as ‘‘when a word supposits what it sig- confused, and confused and distributive; and finally, the nifies’’ (William of Sherwood 1966:107), as signification is latter is divided into mobile and immobile. The divisions inherently related to forms: for Sherwood, the significa- of the modes of personal common supposition are then to tion of a common term is the universal form it corre- be found in virtually all subsequent texts (although the sponds to, e.g., humanity in the case of ‘‘man.’’ But mobile vs. immobile distinction tends to disappear), and formal supposition is of two kinds: simple supposition account for the different quantities of supposita that are is when a term supposits ‘‘for the signified form’’; per- required for the verification of different propositional sonal supposition is when a term supposits ‘‘for a thing contexts (variation (4) above, treated elsewhere in this bearing the form’’ (Sherwood 1966:107), that is, for the volume.) individuals instantiating the universal nature. Indeed, As for variation (3) above, it is usually accounted for these are the definitions of personal and simple supposi- by means of the concepts of ampliation and restriction, as tion that one generally encounters in writings of the in William of Sherwood, Peter of Spain, and Lambert of thirteenth and fourteenth centuries (with an important Auxerre/Lagny; Sherwood also discusses this kind of var- modification regarding simple supposition brought iation within the context of his theory of composite and about by Ockham, as we shall see). Material supposition divided senses of modal propositions. The idea is that is opposed to formal supposition in that it is not signif- some propositional contexts ampliate the range of icative; indeed, Sherwood continues the tradition of supposita being supposited for by a term, for example in referring to autonymic uses of a word (i.e., standing for a modal such as ‘‘A man can be white’’; in this itself) as ‘‘material,’’ as in the notion of materiale case, the supposition of ‘‘man’’ is not limited to the pres- S impositum discussed above. ently existing men, but also to possible men. A similar These three main kinds of proper supposition – phenomenon occurs with tensed propositions. Other con- personal, simple, and material – are in effect to be found texts restrict the range of supposition, for example, when in most fourteenth-century texts (except for those follow- an adjective modifies a noun, such as ‘‘white man.’’ But ing Buridan in his dismissal of simple supposition), and ampliation and restriction usually do not generate sub- account for the variation of ontological kinds of supposita kinds of supposition, rather it is usually said that the (variation (2) above). Interestingly, none of the other supposition of a given term is ampliated or restricted. thirteenth-century main texts has either formal or mate- In the last decades of the thirteenth century, there was rial supposition as kinds of supposition, but they all have a marked decline of the influence of terminist logic, in personal and simple supposition: for Roger Bacon and particular in Paris, where an alternative approach to Lambert of Auxerre, what Sherwood understood as mate- semantics became very influential, that of the modistae rial supposition, namely, the supposition of a term for (Ebbesen 1981, 1985). The modistae influence in Oxford itself or for other expressions qua expressions, becomes was less intense, but still felt. In any case, terminism did a variation of simple supposition. But formal supposition not go into total dormant state in this period, as is 1234 S Supposition Theory

sometimes thought: Roger Bacon’s De signis, where to the subdivisions of the modes of personal supposition, a sophisticated version of supposition theory is presented Ockham maintains the traditional divisions. (improving his own earlier theory presented in his After Ockham, one important tradition in the four- Summulae dialectices) was written in the last decades of teenth century (following Buridan) simply dispenses with the thirteenth century, in Oxford (see De Libera 1982). simple supposition altogether, maintaining only personal and material as the main kinds of proper supposition. The Later Developments: Fourteenth Century idea is this: if simple supposition is the supposition for and Beyond a mental term, as Ockham has it, then it is in fact a kind of In the fourteenth century, terminist logic somehow material supposition (Buridan, Summulae de dialectica reemerges as the chief doctrine for semantic analysis, 4.3.2). Like Ockham, Buridan rejects the existence of completely replacing the modistae theories. In the very extra-mental universals, so for him simple supposition first years of the century, at Oxford, Walter Burley writes becomes a superfluous concept. a De suppositionibus treatise, essentially taking over Another author writing in the Buridanian tradition, Sherwood’s distinctions of supposition. At the same , introduces another important inno- time, Burley seems to have been the first to introduce vation, namely that of applying the subdivisions tradi- quite a few innovations, which were to remain influential tionally reserved to personal supposition to material in the fourteenth century and beyond (see Brown 1972). supposition as well (see Marsilius of Inghen 1983 and Thus, one can say that Burley’s treatise inaugurates four- Dutilh Novaes 2008a:sect. 2). With this move, it becomes teenth-century-style supposition theory. possible to ‘‘quantify’’ over occurrences of spoken, written, The next important text in the development of sup- and mental terms being the material supposita of terms, position theory was composed in the 1320s by William of just as one quantifies over the extra-mental individuals Ockham, also an Englishman: his Summa logicae. that are typically (but not always) the personal supposita of Ockham’s Summa is revolutionary for many different rea- terms. sons, among which his purely extensional definition of All in all, in the fourteenth century supposition theory signification – for Ockham, a common term such as is widely applied to a variety of ; in fact, it becomes ‘‘man’’ signifies each and every man, not the universal an over-arching methodological tool. Ockham, for exam- humanity. Another important innovation developed by ple, makes extensive use of it for theological as well as Ockham (but with earlier in the thirteenth century, physical analyses. In effect, a significant application of for example, in Lambert of Auxerre/Lagny; see Read 2006: supposition theory in the fourteenth century is to the sect. 3) is the idea that the concept itself is a , just as issues surrounding the dogma of the Trinity (see the written and spoken terms. In fact, Ockham develops the entry on Trinitarian Logic in this volume). Moreover, idea of a mental functioning very much like the theory continues to develop well into the fifteenth written and spoken language, and thus equally apt to and sixteenth century. (The interested reader is urged to undergo semantic analysis; indeed, Ockham applies the consult the secondary literature on these developments, in supposition apparatus also to mental propositions (see particular the work of E.J. Ashworth.) Panaccio 1999), but with some paradoxical results (see Spade 1980). Conclusion While Ockham was clearly inspired by Burley’s treatise For reasons of space, this brief overview has touched upon (the section on the supposition of relatives is almost an only some of the important aspects in the development of exact copy of the same section in Burley’s treatise see supposition theory only. However, it seems that two gen- Brown 1972), he had to adjust the supposition machinery eral issues must still be addressed, concerning the very gist to the ontological and semantic modifications he had and purpose of the theory: (1) What is to determine the introduced. Thus, for Ockham simple supposition is no kind(s) of supposition that a term has in a given proposi- longer the supposition for an extra-mental universal, as tion? (2) Is there always only one (correct) kind of suppo- such things simply do not exist in his ontology. Rather, he sition for a term in a given propositional context? These reformulates simple supposition as the supposition for the are difficult questions with no single answer; different mental term corresponding to the spoken or written term authors seem to have held different views. in question. Similarly, personal supposition becomes the Concerning (1), most authors seem to hold that the supposition for the thing(s) that the term signifies, given propositional context is indeed the main determining his reformulation of the notion of signification (Summa element, as suggested by the maxim ‘‘subjects are such as logicae I, chap. 64). For the rest, in particular with respect the predicates permit.’’ Some authors (such as Paul of Supposition Theory S 1235

Venice, at the end of the fourteenth century; see his Logica Helias Peter (1993) Summa super Priscianum, 2 vols, ed. Reilly L. parva, p 27), however, maintain that the desired truth of Pontifical Institute of Mediaeval Studies, Toronto Lambert of Auxerre (Lagny) (1971) Logica (Summa Lamberti), ed. the proposition, or in any case its intended meaning, is Alessio F. La nuova Italia Editrice, Florence what governs the kinds of supposition allowed for its Marsilius of Inghen (1983) Treatises on the properties of terms, a terms. Others, such as Buridan, seem to think that ulti- first critical edition of the Suppositiones, Ampliationes, mately the agreed-upon interpretation of a by Appellationes, Restrictiones and Alienationes, ed. Bos EP. Reidel, the speakers involved in the situation is what really deter- Dordrecht Paul of Venice (2002) Logica parva: first critical edition from the manu- mines the supposition of a term. Yet other authors, in scripts with introduction and commentary, ed. and trans. Perreiah particular Ockham, present rules for the determination AR. Brill, Leiden of the supposition of the terms in a given propositional Peter of Spain (1972) Tractatus, ed. De Rijk LM. Van Gorcum, Assen context that seem to function almost algorithmically (see William of Ockham (1974) Opera philosophica I, ed. Boehner Ph et al. Dutilh Novaes 2008b). Franciscan Institute, St. Bonaventure William of Sherwood (1995) Einfu¨hrung in die Logik, ed. and German As for the second issue, Ockham (like Burley and trans. Brands H, Kann C. Felix Meiner, Hamburg many other fourteenth-century authors) in fact allows English for multiple possibilities of kinds of supposition for Buridan John (2001) Summulae de Dialectica, trans. Klima G. Yale a term in one and the same propositional context, University Press, New Haven entailing thus that the context does not always uniquely Burley Walter (2000) On the purity of the art of logic, trans. Spade PV. Yale University Press, New Haven determine the supposition of a term. For Ockham, sup- Lambert of Auxerre (Lagny) (1988) Properties of terms. In: Cambridge position theory is an important device for the generation translations of medieval philosophical texts, trans. Kretzmann N, of the (often multiple) possible readings of propositions Stump E. Cambridge University Press, Cambridge, pp 102–162 (corresponding to the different kinds of supposition Marsilius of Inghen (1983) Treatises on the properties of terms, a first permitted by a given propositional context), what in the critical edition of the Suppositiones, Ampliationes, Appellationes, Restrictiones and Alienationes, ed. Bos EP. Reidel, Dordrecht fourteenth century is known as ‘‘distinguishing’’ proposi- Peter of Spain (1945) The Summulae logicales of Peter of Spain, ed. and tions. But not all authors insist on the possibility of trans. Mullally JP. University of Notre Dame Press, South Bend generating the multiple readings of propositions by William of Ockham (1998) Summa Logicae Part I, trans. Loux M. St. means of supposition theory: in earlier developments, Augustine’s Press, South Bend the underlying idea seems to be that there should be a William of Sherwood (1966) Introduction to logic, trans. Kretzmann N. University of Minnesota, Minneapolis unique correct kind of supposition for a term in a given propositional context. However, in both cases supposition Secondary Sources theory is essentially a theory for semantic analysis and Ashworth EJ (1974) Language and logic in the post-medieval period. interpretation. Reidel, Dordrecht Brown S (1972) Walter Burleigh’s treatise De suppositionibus and its influence on William of Ockham. Francisc Stud 32:15–64 See also: ▶ Gilbert of Poitiers ▶ John Buridan ▶ Lambert Brown S (1993) Medieval supposition theory in its theological context. of Lagny ▶ Logic ▶ Marsilius of Inghen ▶ Mental Lan- Mediev Philos Theol 3:121–157 guage ▶ Modal Theories and Modal Logic ▶ Modistae De Libera A (1982) The Oxford and Paris traditions in logic. In: ▶ Paul of Venice ▶ Peter Helias ▶ Peter of Spain Kretzmann N, Kenny A, Pinborg J (eds) The Cambridge history of ▶ Quantification ▶ Roger Bacon ▶ Terms, Properties of later . Cambridge University Press, Cambridge, S pp 147–187 ▶ Trinitarian Logic ▶ Truth, Theories of ▶ Walter Burley De Rijk LM (1962/1967) Logica modernorum. Van Gorcum, Assen ▶ William of Ockham ▶ William of Sherwood De Rijk LM (1982) The origins of the theory of properties of terms. In: Kretzmann N, Kenny A, Pinborg J (eds) The Cambridge history of Bibliography later medieval philosophy. Cambridge University Press, Cambridge, pp 161–173 Primary Sources Dutilh Novaes C (2007) Formalizing medieval logical theories. Latin Suppositio, Consequentiae and Obligationes. Springer, Berlin The anonymous texts edited in De Rijk (1962/1967) Dutilh Novaes C (2008a) 14th century logic after Ockham. In: Gabbay D, Bacon Roger (1986/1987) Summulae dialectics, ed. de Libera A. Woods J (eds) The handbook of the , vol 2. Elsevier, Les Summulae dialectics de Roger Bacon. Archives d’Histoire Amsterdam, pp 433–504 Doctrinale et Litteraire du Moyen Age 53:139–289 (1986); 54:171– Dutilh Novaes C (2008b) An intensional interpretation of Ockham’s 278 (1987) theory of supposition. J Hist Philos 46(3):365–393 Buridan John (1998) Summulae de suppositionibus, ed. van der Lecq R. Ebbesen S (1981) Early supposition theory (12th–13th century). Histoire, Ingenium, Nijmegen E´ piste´mologie, Langage 3/1:35–48 Burley Walter (1955) De puritate artis logicae Tractatus Longior, ed. Ebbesen S (1985) OXYNAT: a theory about the origins of British logic. In: Boehner P. Franciscan Institute, St. Bonaventure Osmund P, Lewry OP (ed) The rise of British logic. Papers in 1236 S Swineshead, Richard

mediaeval studies, vol 7. Pontifical Institute of Mediaeval Studies, changed. The theory of the modal was at Toronto, pp 1–17 a completely different stage of completion in the Prior Kneepkens CH (1987) Suppositio and supponere in 12th century gram- mar. In: Jolivet J, de Libera A (eds) Gilbert de Poitiers et ses Analytics, and in the hands of the medievals it went contemporains. Aux origines de la ‘‘Logica modernorum.’’ through a remarkable development. Bibliopolis, Naples, pp 325–351 Panaccio C (1999) Semantics and mental language. In: Spade PV (ed) The In the Aristotle presents the first logical Cambridge companion to Ockham. Cambridge University Press, system, that is, the theory of the syllogism. A syllogism is Cambridge, pp 53–75 Read S (2006) Medieval theories: properties of terms. In: Zalta E (ed) a deduction consisting of three sentences – two premises Stanford encyclopedia of philosophy. http://www.science.uva.nl/ and a conclusion. Syllogistic sentences are categorical seop/entries/medieval-terms/ sentences involving a predicate and a subject connected  Rosier-Catach I (2003) La suppositio materialis et la question de by a copula (verb) and they are divided into four different l’autonymie au Moyen Age. In: Authier-Revuz J, Doury M, Reboul- classes, namely universal affirmative (A), particular affir- Toure´ S (eds) Parler des mots, Le fait autonymique en discours. Presses de la Sorbonne nouvelle, Paris, pp 21–55 mative (I), universal negative (E), and particular negative Spade PV (1980) Synonymy and equivocation in Ockham’s mental lan- (O) sentences. Aristotle writes them as follows: guage. J Hist Philos 18:9–22 Spade PV (1996) Thoughts, words and things. http://www.pvspade.com A–‘‘A belongs to all B’’ (AaB). Valente L (forthcoming) Supposition theory and Porretan theology. In: E–‘‘A does not belong to any B’’ (AeB). Bos EP (ed) Proceedings of the 17th European symposium on medi- I–‘‘A belongs to some B’’ (AiB). eval logic and semantics O–‘‘A does not belong to some B’’ (AoB). For an extensive bibliography on supposition theory, see http://www. formalontology.it/supposition.htm The subject and predicate in the categorical sentences used in a syllogism are called terms (horoi) by Aristotle. There are three terms in a syllogism, a major, a minor, and a middle term. The major and the minor terms are called the extremes (akra), respectively major extreme (meizon Swineshead, Richard akron) and minor extreme (elatton akron), and they are the predicate and the subject of the conclusion. The mid- ▶ Richard Swineshead dle (meson) term is what joins the two premises. These three terms can be combined in different ways to form three figures (skheˆmata). Aristotle presents the following three in the Prior Analytics (A is the major, B the middle, Syllogism, Theories of and C the minor term): When the four categorical sentences are placed into HENRIK LAGERLUND these three figures Aristotle ends up with the following 14 Department of Philosophy valid moods (in parenthesis are the medieval mnemonic The University of Western Ontario names for the valid moods). London, ON A fourth figure was discussed in ancient times as well as Canada during the . In the Aristotelian syllogistic it had the following form: By treating this figure we derive additional valid moods, Abstract which are all mentioned by Aristotle in different parts of the Aristotle’s theory of the syllogism is one of the most influential theories ever developed. The theory of the syllogism for assertoric sentences was a remarkable Syllogism, Theories of. Table 1 The three Aristotelian figures achievement by Aristotle and it was virtually complete of the already from the beginning. Medieval logicians could gen- erally not add much to it. Small changes were made and it I II III was systematized in different ways. It was not until John A – BB– AA– B Buridan in the mid-fourteenth century reworked logic in B–C B–C C–B general and placed the theory in a context of a wider logic A – CA– CA– C of consequences that the picture of syllogistics also