Late medieval logic

Late medieval logic
Late medieval logic Paul Vincent Spade I Medieval logic encompassed more than what we call logic today. It included semantics, philosophy of language, parts of physics, of philosophy of mind and of epistemology. Late medieval logic began around 1300 and lasted through at least the fifteenth century. With some noteworthy exceptions, its most original contributions were made by 1350, particularly at Oxford. Hence the focus of this chapter will be on the period 1300–1500, with special emphasis on Oxford before 1350. But first some background concerning the earlier period. The logical writings of Aristotle were all available in Latin by the mid-twelfth century.1 In addition, except for the theory of ‘proofs of propositions’2 (see section VIII below), the characteristic new ingredients of medieval logic were already in place or at least in progress by the end of the twelfth century or the beginning of the thirteenth. The theory of inference or ‘consequence’, for example, was studied as early as Peter Abelard (1079–1142). Again, after about 1120 the circulation of Aristotle’s Sophistical Refutations in Latin stimulated a study of fallacies and the many features of language that produce them. Out of this investigation there arose twelfth- and thirteenth-century writings on semantic ‘properties of terms’, like ‘supposition’ and ‘ampliation’ (see section VI below).3 At the same time, treatises on sophismata or puzzle-sentences in logic, theology or philosophy of nature began to be produced. (A good analogy for this literature may be found in modern discussions of Frege’s ‘The morning star is the evening star’.) Likewise, studies were written about the logical effects of words like ‘only’, ‘except’, ‘begins’ and ‘ceases’ that offer many opportunities for fallacies and involve complications going far beyond syllogistic or the theory of topical inferences.4 Treatises on ‘insolubles’ or semantic paradoxes began to appear late in the twelfth century ([17.42], [17.49]). Simultaneously, a literature developed on a new kind of disputation called ‘obligations’.5 Collectively, these new logical genres are known as ‘terminist’ logic because of the important role played in them by the ‘properties of terms’. These developments continued into the thirteenth century. By midcentury, authors such as Peter of Spain, Lambert of Auxerre and William of Sherwood were writing summary treatises (summulae) covering the whole of logic, including the material in Aristotle’s writings as well as new terminist developments.6 Then, after about 1270, something odd happened, both in England and on the Continent. In France, terminism was eclipsed by an entirely different theory called ‘speculative grammar’, which appealed to the notion of ‘modes of signifying’ and is therefore sometimes called ‘modism’. This theory prevailed in France until the 1320s, when John Buridan (b. c. 1295/1300, d. after 1358) suddenly restored the theory of supposition and associated terminist doctrines. After Buridan, supposition theory was the leading vehicle for semantic (as distinct from grammatical) analysis until the end of the Middle Ages. Modism never dominated England as it did elsewhere; terminism survived there during its period of neglect on the Continent. Still, few innovations in supposition theory or its satellite doctrines were made in England during the last quarter of the thirteenth century. But then, in the very early fourteenth century, Walter Burley (or Burleigh, b. c. 1275, d. 1344/5) began to do new work in the terminist tradition. This temporary decline of terminism on both sides of the Channel at the end of the thirteenth century, and its sudden revival shortly after 1300, are mysterious events. But, whatever the underlying causes, when supposition theory and related doctrines re-emerged in the early fourteenth century, they were importantly different from how they had been earlier.7 II This section will survey the main stages of late medieval logic, and introduce important names. Later sections will focus on particular theoretical topics.8 In England,9 logic after 1300 may be divided into three stages: first, 1300–50, when the best work was done. Burley and William of Ockham (c. 1285–1347) were the paramount figures during this period. Both made important contributions to supposition theory, and Ockham in particular developed sophisticated theories of ‘mental language’ and ‘connotation’. In the next generation, several men associated with Merton College, Oxford, were influential in specific areas. Richard Kilvington (early fourteenth century, d. 1361) and William Heytesbury (b. before 1313, d. 1372/3), among others, applied the techniques of sophismata to questions in natural philosophy, epistemic logic and other fields. Thomas Bradwardine (c. 1295–1349) wrote an Insolubles that was perhaps the most influential treatise on semantic paradoxes throughout the Middle Ages. Around 1330–2, Adam Wodeham devised an important theory of ‘complexly significables’ (complexe significabilia), the closest medieval equivalent to the modern notion of ‘proposition’. Richard Billingham (fl. 1340s or 1350s) seems to have originated the important theory of ‘proofs of propositions’. His treatise Speculum puerorum or Youths’ Mirror will be discussed in section VIII below. The second stage of English logic after 1300 lasted from 1350 to 1400. This was a time of consolidation, of sophisticated but no longer especially original work. The period has not yet been well researched, but at least three trends can be distinguished. First, there was a remarkable number of school-manuals written in logic, compilations of standard doctrine with little innovation. Works of Richard Lavenham (d. 1399 or after) provide a good example. Gradually, certain of these school-texts congealed into two collections called the Libelli sophistarum (Little Books for Arguers), one for Oxford and one for Cambridge. These were printed in several editions around 1500. Second, English logic from 1350 to 1400 had a special interest in the doctrine of ‘proofs of propositions’ associated with Billingham. As time passed, the labour devoted to this topic grew enormously. John Wyclif dedicated a large part of his Logic (before 1368) and especially of his Continuation of the Logic (1371–4) to this theory. So did Ralph Strode, a contemporary of Wyclif s, in his own Logic. John Huntman wrote a Logic sometime near the end of the century, showing the continued expansion of the Billingham tradition. A third concern of English logic in this period was the signification of propositions. The most influential work here was probably On the Truth and Falsehood of Propositions by Henry Hopton (fl. 1357). There Hopton discussed and rejected several previous views before setting out his own theory.10 (See section V below.) Several other English authors during this period should be mentioned, although their works are not yet fully understood. They include Richard Feribrigge (fl. probably 1360s), author of an important Consequences and a Logic or Treatise on the Truth of Propositions. Of lesser importance are: Robert Fland (fl. 1335–60); Richard Brinkley, the author of a Summa of logic probably between 1360 and 1373; Thomas Manlevelt (or Mauvelt), who wrote several treatises around mid-century that were influential on the Continent; and near the end of the century, Robert Alington, William Ware, Robert Stonham, and others. One of the most significant events in English logic late in the century was the arrival at Oxford in 1390 of the Italian Paul of Venice (c. 1369–1429). Paul studied there for some three years. On his return to Italy, he taught at Padua and elsewhere, and was an important conduit through which English logic became known in Italy in the fifteenth century. His writings include a widely circulated Little Logic (Logica parva) and the enormous Big Logic (Logica magna). The third stage of late medieval English logic includes the whole fifteenth century. This was a period of shocking decline. Except for a few insignificant figures around 1400, not even second-rate authors are known. The manuscripts from this period—and by 1500, early printed books—offer little hope that further research will change this assessment. The Oxford and Cambridge Little Books for Arguers, already mentioned, testify to the deterioration of logic during this period. Medieval logic was effectively dead in England after 1400. Logic on the Continent during these same two centuries cannot be so neatly divided into stages. Still, there as in England, the most important work was done before about 1350. The pre-eminent figure was doubtless Buridan. His writings include a Consequences, a Sophismata and a Summulae of Dialectic. Buridan’s students included many influential logicians of the next generation, among them: Albert of Saxony (d. 1390), the author of a Sophismata and A Very Useful Logic, and the first rector of the University of Vienna; and Marsilius of Inghen (c. 1330–96), the first rector of the University of Heidelberg and the author of an Insolubles and of treatises on ‘properties of terms’. On many points, Buridan’s logical views were like Burley’s or especially Ockham’s in England. There are differences, but the similarities are more striking, especially when contrasted with logic on either side of the Channel before 1300. The extent of Ockham’s own influence on Buridan is doubtful, but Ockham’s confrère Adam Wodeham was instrumental in transmitting much English learning to Paris. In particular, Wodeham’s theory of ‘complexly significables’ was adopted by Gregory of Rimini (c. 1300–58). The Parisian Peter of Ailly (1350–1420/1) wrote several interesting logical works, including: Concepts and Insolubles, a pair of treatises on ‘mental language’ and the Liar Paradox; Destructions of the Modes of Signifying, against ‘modism’; Treatise on Exponibles (see section VIII below); and Treatise on the Art of ‘Obligating’ (perhaps by Marsilius of Inghen instead). Before 1400, the Italian Peter of Mantua (fl. 1387–1400) wrote a Logic that already shows knowledge of earlier English work, particularly that stemming from Billingham. Around 1400 Angelo of Fossombrone, who taught at Bologna (1395–1400) and Padua (1400– 2), wrote an Insolubles maintaining an elaborated version of Heytesbury’s theory. About the same time, the newly returned Paul of Venice spread the gospel of Oxford logic further in Italy. Among his students, Paul of Pergula (d. 1451/5) wrote a Logic and a treatise On the Composite and the Divided Sense (on the scope of certain logical operators) based on Heytesbury’s own work of that name, and Gaetano of Thiene (1387–1465) wrote detailed commentaries on works by Heytesbury and Strode. Other authors in Italy and elsewhere continued to write on logic to the end of the Middle Ages and beyond.11 Even these few names will suffice to show that the logical landscape after about 1400 was by no means so desolate on the Continent as in England. Still, on either side of the Channel logical work after 1350 was largely derivative and, while sometimes very sophisticated, not very innovative. There was certainly no one, for example, with the stature of Burley, Ockham or Buridan. III This and the following sections will concentrate on five important topics in late medieval logic: (a) the theory of ‘mental language’, (b) the signification of propositions, (c) developments in supposition-theory, (d) semantic paradoxes, and (e) connotation-theory and the ‘proofs of propositions’. In On Interpretation, 16a3–4, Aristotle stated that ‘spoken sounds are symbols of affections in the soul, and written marks symbols of spoken sounds’. These words were translated by Boethius and interpreted as implying three levels of language: spoken, written and mental. Through Boethius this three-level hierarchy of language became a commonplace in medieval logical literature. Of the three, mental language was regarded as the most basic. Its semantic properties are natural ones;12 they do not originate from any convention or custom, and cannot be changed at will. Unlike spoken and written languages, mental language is the same for everyone. Careful authors sometimes distinguished ‘proper’ from ‘improper’ mental language. The latter occurs when we think ‘in English’ or ‘in French’. Thus a public speaker might rehearse a speech by running through silently the words he will later utter aloud. What goes on there is a kind of ‘let’s pretend’ speaking that takes place in imagination and is in that sense ‘mental’. But it is not what most authors meant by ‘mental language’. Since silent recitation varies with the spoken language one is rehearsing, it is not the same for everyone. Proper mental language is different. It includes, for example, what happens when one suddenly ‘sees’ the force of a mathematical proof; in that case there is a ‘flash of insight’, an understanding or judgement that need not yet be put into words, even silently. This kind of mental language, the theory goes, is the same for everyone.13 Spoken language, by contrast, has its semantic function parasitically, through a conventional correlation between its expressions and mental ones. The arbitrariness of this convention is what allows the multitude of spoken languages. Written language plays an even more derivative role, through a conventional correlation between its inscriptions and the sounds of spoken language. The arbitrariness of this convention too allows for different scripts among written languages. Only through the mediation of spoken language, the theory went, are inscriptions correlated with thoughts in mental language. This view implies that one cannot read a language one does not know how to speak. Most medieval authors accepted this consequence. Following Boethius, the correlations between written and spoken language and between spoken and mental language were often regarded as relations of ‘signification’. This claim had theoretical consequences, since signification was a well-defined notion in the Middle Ages. A term ‘signifies’ what it makes one think of (‘establishes an understanding of’=constituit intellectum+genitive).14 While there was dispute about what occupies the object-pole of this relation, there was agreement over the criterion. Signification is thus a special case of causality, and so transitive. (Certain authors added to signification in general the particular notions of immediate and ultimate signification. The general relation of signification thus became what modern logicians call the ‘ancestral’ of the relation of immediate signification;15 a term t then ultimately signifies x if and only if t signifies x and x does not signify anything else.) Terms in mental language signify (make one think of) external objects only in the degenerate sense that they are the thoughts of those external objects. According to this view, to say that expressions of spoken language immediately signify expressions of mental language is to say that the function of speech is to convey thoughts. Certain authors, e.g. Duns Scotus (c. 1265–1308), Burley and Ockham, regarded this as too restrictive. For them, spoken (and written) terms may be made to signify anything, not only the speaker’s thoughts. In fact spoken words do not always make us think of thoughts; sometimes we are made to think directly of external objects. For these authors, the relations between written and spoken language and between either of these and mental language are not relations of signification. Ockham described them neutrally as relations of ‘subordination’.16 IV Although authors since Boethius had recognized mental language, it was not until the fourteenth century that it began to be investigated in detail. Ockham was the first to develop a full theory of mental language and put it to philosophical use. Shortly thereafter, Buridan began to work out his own view. His theory agrees with Ockham’s on the whole, although Ockham’s is the more detailed. In the early 1340s, Gregory of Rimini refined certain parts of the theory, and applied it to a solution to the Liar Paradox. In 1372, Peter of Ailly’s Concepts and Insolubles incorporated the work of both Ockham and Gregory.17 Other authors made contributions to the theory, but these were the major ones. The presentation below will follow Ockham’s account except as indicated. Terms in mental language are concepts; its propositions are judgements. The fact that mental language is the same for everyone explains how it is possible to translate one spoken (or written) language into another. A sentence in Spanish is a correct translation of a sentence in English if and only if the two are subordinated to the same mental sentence. More generally, any two spoken or written expressions— from the same or different languages—are synonymous if and only if they are subordinated to the same mental expression. Again, any spoken or written expression is equivocal if and only if it is subordinated to more than one mental expression. If mental language accounts for synonymy and equivocation in spoken and written languages, can there be synonymy or equivocation in mental language itself? The textual evidence is mixed. There are passages in Ockham (Summa logicae I, 3 = [17.7] OP 1:11; Summa logicae I, 13 = [17.7] OP 1:44) supporting a negative answer in both cases. Nevertheless other texts (Ordinatio, I, d. 3, q. 2 = [17.7] OT 2:405; Ordinatio I, d. 3, q. 3 = [17.7] OT 2:425; Quodlibet 5, q. 9 = [17.7] OT 9:513–18), where Ockham is discussing the semantics of certain connotative terms (see section VIII below), perhaps imply the existence of mental synonymy. As for equivocation, Ockham’s theory of tense and modality, as well as his theory of supposition (see section VI below), commits him outright to certain kinds of equivocation in mental language.18 But apart from textual considerations, there are philosophical reasons for saying that, given other features of Ockham’s theory, mental synonymy or equivocation makes no sense.19 What is included in mental language? In two passages (Summa logicae, I, 3 = [17.7] OP 1:11.1–26; Quodlibet 5, q. 8 = [17.7] OT 9:508– 13), Ockham remarks that, just as for spoken and written language, the vocabulary of mental language is divided into ‘parts of speech’. Thus there are mental nouns, verbs, prepositions, conjunctions, etc. But not all features of spoken and written language are found in mental language. Ockham acknowledges doubts about mental participles (their job could be performed by verbs) and pronouns (presumably ‘pronouns of laziness’, as for example in ‘Socrates is a man and he is an animal’). Moreover, not all characteristics of spoken and written syntax are found in mental language. While mental nouns and adjectives have case and number, and mental adjectives admit of positive, comparative and superlative degrees, they do not have gender and are not divided into grammatical declensions (like Latin’s five declensions). Mental verbs have person, number, tense, voice and mood, but are not divided into grammatical conjugations. Ockham’s mental language looks remarkably like Latin. This fact led some modern writers to reject the theory as a foolish attempt to ‘explain’ features of Latin by merely duplicating them in mental language, which is then regarded as somehow more ‘basic’ ([17.39] § 23). But more is involved than that. Ockham’s strategy is to admit into mental language exactly those features of spoken or written language that affect the truth-values of propositions. All other features of spoken and written language, Ockham says, are only for the sake of decorative style, or in the interest of brevity. They are not present in mental language.20 Mental language is thus a logically perspicuous language for describing the world. It has whatever is needed to distinguish truth from falsehood, nothing more. In this respect, mental language is reminiscent of the ‘ideal languages’ proposed by early twentieth-century philosophers ([17.51]). How are mental words combined in mental propositions? What is the difference, for example, between the true mental proposition ‘Every man is an animal’ and the false ‘Every animal is a man’? In written language, the difference is the spatial configuration of the words. But the mind does not take up space, so that there can be no such difference there. In speech the difference lies in the temporal sequence of the words. But since proper mental language at least sometimes involves a ‘flash of insight’ that happens all at once, neither can temporal word order account for the difference between the two mental propositions. Because of such difficulties, authors such as Gregory of Rimini and Peter of Ailly held that mental propositions (although not all of them for Peter) are simple mental acts not really composed of distinct mental words at all.21 Ockham too had considered such a theory (In Sententias II, qq. 12–13 = [17.7] OT 5:279; Exposition of ‘On Interpretation’, proem = [17.7] OP 2:356). It is hard to reconcile this view with the claim that mental vocabulary is divided into ‘parts of speech’; distinct mental words would appear to have no job to do if they do not enter into the structure of mental propositions. V Besides the disagreement over the immediate signification of spoken and written terms (see section III above), there was a dispute over ultimate signification. Metaphysical realists, such as Burley, maintained the traditional view that general terms ultimately signify universal entities, while nominalists (e.g. Ockham and Buridan) held that they ultimately signify only individuals. Some authors extended the notion of signification to ask not only about the signification of terms but also about the signification of whole propositions. Do they signify anything besides what their component terms signify separately? Do they signify, for example, states of affairs or facts? Ockham did not explicitly address this question. But Buridan did, and his answer was no. For him ([17.16] II, conclusion 5), a proposition—and in general any complex expression—signifies whatever its categorematic terms signify, nothing more. (‘Categorematic’ terms are those that can serve as subject or predicate in a proposition; they were regarded as having their own signification. Other words were called ‘syncategorematic’ and were regarded as not having any signification of their own; they are ‘logical particles’ used for combining categorematic terms into propositions and other complex expressions.) Thus in the spoken proposition ‘The cat is on the mat’, when I hear the word ‘cat’ I am, on Buridan’s account, made to think of all cats and when I hear ‘mat’ I am made to think of all mats. That is all the proposition makes me think of, and so all it signifies. Elsewhere Buridan maintained a different and incompatible theory ([17.16] II, sophism 5 and conclusions 3–7). The proposition ‘Socrates is sitting’, for example, signifies Socrates to be sitting. And what is that? Buridan held that if Socrates really is sitting, then Socrates to be sitting is just Socrates himself. But if he is not sitting, then Socrates to be sitting is nothing at all.22 This view bears some similarity to a theory held earlier at Oxford by Walter Chatton (1285–1344) and discussed as the first previous view in Henry Hopton’s On the Truth and Falsehood of Propositions. Similar views were defended by Richard Feribrigge and John Huntman. The details of their texts have not been thoroughly investigated, and there is much that is still obscure; it is not certain that all these authors maintained variants of the same doctrine. Still, the motivation is the same in each case: to find something to serve as the significate of a proposition in an ontology that does not allow anything like facts, states of affairs or ‘propositions’ in the modern sense. But there were other opinions. As early as Abelard, some authors held that what propositions signify falls outside the Aristotelian categories, and is something like the modern notion of ‘proposition’. Sometimes this new entity was called a ‘mode’, sometimes a dictum.23 In the fourteenth century, such theories continued to find their defenders. Perhaps a version of it may be seen in the early 1330s in William of Crathorn. Perhaps too Henry Hopton intended such a theory as the second previous view he considered, according to which a proposition signifies a ‘mode’ of a thing, where a ‘mode’ is not a something but a being-somehow (esse aliqualiter). But an unequivocal statement can be found in the theory of ‘complexly significables’ ([17.38]; see also [17.35] chs 14–15). According to this theory, complexly significables are the bearers of truth-value. They are not propositions in the medieval sense, not even mental propositions, but are what is expressed by propositions. They are the significates of propositions, and the objects of knowledge, belief and prepositional attitudes generally. Complexly significables do not exist in the way substances and accidents do. Before creation, for example, only God existed. But even then God knew that the world was going to exist. This complexly significable cannot be identified with God himself, since God is a necessary being but it was contingent that the world was going to exist. Yet as distinct from God, it cannot have existed before creation. Such extralogical considerations were an important motivation for the theory of complexly significables. Authors such as Buridan and Peter of Ailly rejected the theory; Peter, for example, claimed that the argument about God’s knowledge before creation is based on an illegitimate substitution of identicals in an opaque context involving necessity ([17.27] 62). All these theories offered a real entity (even if an odd one, like a ‘complexly significable’) as the correlate of a true proposition, and so as the ontological basis for a ‘correspondence’ theory of truth. Other authors took a different approach. They too maintained a correspondence theory, often expressed as: a proposition is true if and only if it ‘precisely signifies as is the case’, or if and only if ‘howsoever [the proposition] signifies, so it is the case’. For them, the proper question is not what but how a proposition signifies. This ‘adverbial’ notion of signification allowed a correspondence theory without being obliged to find any ontological correlate for a true proposition to correspond to. After rejecting earlier views, Henry Hopton’s own theory was like this. Heytesbury had earlier held a similar view, as did Peter of Ailly later ([17.22] 61–5; [17.27] 10, 48–54 and nn.). VI The theory of ‘supposition’ is a mystery. Although it is central to the theories of ‘properties of terms’ that developed from the twelfth century on, it is not clear what the theory was intended to accomplish, or indeed what the theory as a whole was about.24 Throughout its history, there were two main parts to supposition theory. One was a theory of the reference of terms in propositions, and how that reference is affected by syntactic and semantic features of propositions. The question this part of the theory was intended to answer is, ‘What does a term refer to (supposit for, stand for) in a proposition?’ That much is clear. But from the beginning, there was another part of supposition theory, an account of how one might validly ‘descend to singulars’ under a given occurrence of a term in a proposition, sometimes combined with a correlative account of ‘ascent from singulars’. The mystery surrounds this second part. Before the decline of terminism after 1270, there is some evidence that the second part of supposition theory, like the first, was intended to answer the question of what a term refers to in a proposition. The first part of the theory says what kind of thing a given term-occurrence refers to, while the second specifies how many such things it refers to (in much the way one finds even today accounts purporting to say whether the terms of a syllogism are about ‘all’ or ‘some’ of a class). The evidence for this is mixed, but even if this was the original intent of the second part of supposition theory, some authors quite early realized its theoretical difficulties. When supposition theory re-emerged with Burley in England and later with Buridan in France, the two parts of the theory had been separated once and for all. By that time the theory of descent and ascent clearly was not about what a term refers to in a proposition. What it was about instead is uncertain. The account below will mainly follow Ockham, although other authors will be mentioned. Their theories differed from his in detail, sometimes in important detail, but Ockham’s is fairly typical. The first part of supposition theory divided supposition or reference first into proper (literal) and improper (metaphorical). The latter is illustrated by ‘England fights’, where ‘England’ refers by metonymy to England’s inhabitants. Medieval logic, like modern logic, did not have an adequate theory of metaphor. Ockham, Burley and a few others list some haphazard subdivisions of improper supposition, but really mention it only to set it aside. Their emphasis is on proper supposition. Proper supposition was divided into three kinds: personal, simple and material. The origin of these names is unclear, although the term ‘personal’ suggests a connection with the theology of the Trinity and the Incarnation. But it should not be thought that personal supposition has anything especially to do with persons. Personal supposition occurs when a term refers to everything of which it is truly predicable. Thus in ‘Every man is running’, ‘man’ refers to all men and so is in personal supposition. But so too ‘running’ refers there to all things now running, and hence is likewise in personal supposition. It does not refer there only to some running things, for example, only to the running men. Again, in ‘Some man is running’, ‘man’ refers to all men, not just to running ones. A term has material supposition when it refers to a spoken or written word or expression and is not in personal supposition. Thus, ‘man’ in ‘Man has three letters’ has material supposition. Although there are obvious similarities, material supposition is not merely a medieval version of modern quotation marks. For in ‘It is possible for Socrates to run’, the phrase ‘for Socrates to run’ has material supposition. But it refers to the proposition ‘Socrates is running’, of which the phrase ‘for Socrates to run’ is not a quotation. (For Ockham, there are no states of affairs or complexly significables that can be said to be possible. Only propositions are possible in this sense.) The definition of simple supposition was a matter of dispute, depending in part on an author’s metaphysical views and in part on his theory about the role of language in general ([17.46]). As a paradigm, ‘man’ in ‘Man is a species’ has simple supposition. In general, terms in simple supposition refer to universals. But for nominalists like Ockham, there are no metaphysical universals; the only universals are universal terms in language, most properly universal concepts in mental language. Thus for Ockham terms in simple supposition refer to concepts. It is they that are properly said to be species or genera. To prevent the term ‘concept’ in ‘Every concept is a being’ from having simple supposition (it has personal supposition, since it refers to everything it signifies— to all concepts), Ockham added that a term in simple supposition must not be ‘taken significatively’, i.e. that it not be in personal supposition. But for a realist like Burley, terms in simple supposition refer to real universals outside the mind. It is they that are species and genera. Furthermore, for Burley and certain others, general terms in language signify those extramental universals. Thus the term ‘man’ signifies universal human nature, not any one individual man or group of men, and not all men collectively. For Burley, therefore, it is in simple supposition that a term refers to what it signifies. For Ockham, general terms do not signify universals, not even universal concepts; they signify individuals. Even a term like ‘universal’ signifies individuals, since it signifies concepts, which are metaphysically individuals and are ‘universal’ only in the sense of being predicable of many things. Hence for Ockham, it is in personal supposition, not simple, that a term refers to what it signifies. Personal supposition is the default case. Any term in any proposition can be taken in personal supposition. It may alternatively be taken in simple or material supposition only if the other terms in the proposition provide a suitable context. In such cases, the proposition is strictly ambiguous and may be read in either sense.25 From this first part of supposition theory alone, certain authors, e.g. Ockham and Buridan, although not Burley, developed a theory of truth-conditions for categorical propositions on the square of opposition. Thus, a universal affirmative ‘Every A is B’ is true if and only if everything the subject term refers to the predicate term also refers to (although it may refer to other things as well). Truthconditions for other propositions on the square of opposition can be derived from this. Subordinated to this first part of supposition theory was a theory of ‘ampliation’, accounting for the effects of modality and tense on personal supposition. A term in personal supposition may always be taken to refer to the things of which it is presently predicable. But in the context of past or future tenses, the term may also be taken to refer to the things of which it was or will be predicable. Likewise, in a modal context (possibility, necessity), the term may also be taken to refer to the things of which it can be truly predicable. This expansion of the range of referents was called ‘ampliation’. Ockham and Burley regarded the new referents provided by ampliation as alternatives to the normal ones. Thus in the proposition ‘Every man was running’, ‘man’ may be taken as referring either to all presently existing men or to all men existing in the past. The proposition is thus equivocal. But on the Continent, Buridan and others regarded the new referents as additions to the normal ones. For them, in the proposition ‘Every man was running’ ‘man’ refers to all presently existing men and all past men as well.26 The second main part of supposition theory, the theory of descent and ascent, was a theory subdividing personal supposition only, into several kinds. First, there is discrete supposition, possessed by proper names, demonstrative pronouns or demonstrative phrases (e.g. ‘this man’). All other personal supposition is common, and was typically subdivided into: determinate (e.g. ‘man’ in ‘Some man is running’), confused and distributive (e.g. ‘man’ in ‘Every man is an animal’), and merely confused (e.g. ‘animal’ in ‘Every man is an animal’). The details varied with the author. Sometimes these subdivisions were described via the positions of terms in categorical propositions. Subjects and predicates of particular affirmatives, and subjects of particular negatives, have determinate supposition. Subjects of universal affirmatives and negatives, and predicates of universal and particular negatives, have confused and distributive supposition. Only predicates of universal affirmatives have merely confused supposition. More helpful is the description in terms of descent and ascent. For Ockham (Burley’s and Buridan’s theories are equivalent), a term has determinate supposition in a proposition if and only if it is possible to ‘descend’ under that term to a disjunction of singulars, and to ‘ascend’ to the original proposition from any singular. The exact specification of the notions of ‘descent’, ‘ascent’ and ‘singular’ is subtle, but an example should suffice. In ‘Some man is running’ one can ‘descend’ under ‘man’ to a disjunction: ‘Some man is running; therefore, this man is running or that man is running’, etc., for all men. Likewise one can ‘ascend’ to the original proposition from any singular: ‘This man is running; therefore, some man is running.’ Hence ‘man’ in the original proposition has determinate supposition. A term has confused and distributive supposition in a proposition if and only if it is possible to ‘descend’ under that term to a conjunction of singulars but not possible to ‘ascend’ to the original proposition from any singular. Thus in ‘Every man is running’ it is possible to descend under ‘man’: ‘Every man is running; therefore, this man is running and that man is running’, etc., for all men. But the ascent from any singular ‘This man is running; therefore, every man is running’ is invalid. Hence the term ‘man’ in the original proposition has confused and distributive supposition. A term has merely confused supposition in a proposition if and only if (a) it is not possible to descend under that term either to a disjunction or to a conjunction, but it is possible to descend to a disjoint term, and (b) it is possible to ascend to the original proposition from any singular. Thus in ‘Every man is an animal’ it is not possible to descend under ‘animal’ to either a disjunction or a conjunction, since if every man is an animal, it does not follow that every man is this animal or every man is that animal, etc. Much less does it follow that every man is this animal and every man is that animal, etc. But it does follow that every man is this animal or that animal or, etc. Again, if it happens that every man is this animal (i.e. there is only one man and he is an animal), then every man is an animal. Hence the term ‘animal’ in that proposition has merely confused supposition. It is hard to see what this doctrine was intended to accomplish, particularly with its appeal to odd ‘disjoint terms’ in merely confused supposition. At first, modern scholars thought it was an attempt to provide truth-conditions for quantified propositions in terms of (infinite) disjunctions or conjunctions. But if that was its purpose, the doctrine is a failure. The predicate of the particular negative ‘Some man is not a Greek’ has confused and distributive supposition according to the above definitions, but the conjunction to which one can descend under ‘Greek’ does not give the truth-conditions for the original proposition. Suppose Socrates and Plato are the only men. Then the conjunction ‘Some man is not this Greek [Socrates] and some man is not that Greek [Plato]’ is true, but the original proposition is false. The problem is that rules for ascent always concern ascent from any one singular, never from a conjunction. Certain later authors, e.g. Ralph Strode, Richard Brinkley and Paul of Venice, do explicitly discuss ascent from conjunctions.27 But earlier writers such as Burley, Ockham and Buridan conspicuously did not. Another attempt to explain this second part of supposition theory suggests that the rules for ascent and descent were used in detecting and diagnosing fallacies. This is doubtless correct as far as it goes, but does not account for the details in the theory as we actually find it. In the end, the exact function of this part of the theory in the early fourteenth century remains a mystery. VII Medieval discussions of ‘insolubles’ (semantic paradoxes like the Liar Paradox, ‘The sentence I am now saying is false’) began in the late twelfth century. By around 1200, theories on how to solve them can be distinguished. Thereafter, three periods in the medieval insolubles literature can be distinguished: (1) c. 1200–c. 1320, (2) c. 1320– c. 1350 and (3) everything after that. The earliest known medieval theory of insolubles (cassatio or cancelling) maintained that one who utters an insoluble is simply ‘not saying anything’, in the sense that his words do not succeed in making a claim. This view, although it has its supporters today, quickly disappeared in the Middle Ages. Other early theories rejected some or all self-reference; these too have their modern counterparts. Still other early theories sound less familiar to modern ears. A few authors argued that, despite the surface grammar, the reference in insolubles is always to some previous proposition. For example, ‘What I am saying is false’ really amounts to ‘What I said a moment ago is false’. The insoluble is true or false depending on whether I did in fact say something false a moment ago. Others, e.g. Duns Scotus, appealed to a distinction between signified acts and exercised acts. This is the distinction between what the speaker of an insoluble proposition says he is doing (the signified act) and what he is really doing (the exercised act). Although the distinction is suggestive, it is far from clear how it solves the paradoxes. Many of these early views are cast in the framework of Aristotle’s fallacy of what is said ‘absolutely’ and what is said ‘in a certain respect’. Discussing that fallacy in his Sophistical Refutations, Aristotle made some enigmatic remarks (180a38–b3) that suggested the Liar Paradox [17.42]. Consequently, many medieval authors tried to treat insolubles as instances of that fallacy, although there was little agreement on the details. Some held that insoluble propositions are true ‘absolutely’ but false ‘in a certain respect’. Some had it the other way around. Others said they were both true and false, each ‘in a certain respect’. Still others applied the Aristotelian distinction not to truth but to supposition, so that they distinguished between supposition absolutely and supposition in a certain respect. Long after the early period in the medieval literature, the fallacy absolutely/in a certain respect was retained as an authoritative framework for many authors’ discussions, even when the real point of their theories was elsewhere. These early theories predominated until about 1320; some of them survived much longer. Burley and Ockham offered nothing new here. Both maintained a theory that merely rejected problematic cases of self-reference without being able to identify which those problematic cases were. The first to break new ground was Thomas Bradwardine, in the early 1320s. Bradwardine’s theory was based on a view linking signification with consequence. He appears to have been the first to hold that a proposition signifies exactly what follows from it.28 Since he was also committed to saying that every proposition implies its own truth (e.g. Socrates is running, therefore ‘Socrates is running’ is true), this means that the insoluble ‘This proposition is false’ signifies that it itself is true. Since it also signifies that it is false, it signifies a contradiction, and so is simply false. The paradox is broken.29 Bradwardine’s view was enormously influential. Buridan later maintained a broadly similar theory, and others held variants of it to the end of the Middle Ages; it was one of the predominant theories. Shortly after Bradwardine, Roger Swyneshed (fl. before 1335, d. c. 1365), an Englishman associated with Merton College, proposed a theory in which truth is distinguished from correspondence with reality. For a proposition to be true, it must not only correspond with reality (‘signify principally as is the case’), it must also not ‘falsify itself, i.e. not be ‘relevant to inferring that it is false’. (This notion of ‘relevance’ is not well understood.) Swyneshed drew three famous conclusions from his theory: (1) There are false propositions (namely, insolubles) that nevertheless correspond with reality. (2) Valid inference sometimes lead from truth to falsehood. Validity does not necessarily preserve truth, although it does preserve correspondence with reality. (3) Sometimes, two contradictory propositions are both false. The insoluble ‘This proposition is false’ is false because it ‘falsifies’ itself. But its contradictory ‘That proposition is true’ (referring to the previous proposition) is also false, since it fails to correspond with reality—the previous proposition is not true. These conclusions generated much discussion in the later literature. Swyneshed’s theory did not have many followers, but it had at least one important one: Paul of Venice maintained a version of Swyneshed’s theory in his Big Logic. In 1335, William Heytesbury proposed a theory that rivalled and may have surpassed Bradwardine’s in influence. He maintained that in circumstances that would make a proposition insoluble if it signified just as it normally does (‘precisely as its terms pretend’), it cannot signify that way only, but must signify some other way too. Thus ‘Socrates is uttering a falsehood’, if Socrates himself utters it and nothing else, cannot on pain of contradiction signify only that Socrates is uttering a falsehood, but must signify that and more. Depending on what else it signifies, and how it is related to the ordinary signification of the proposition, different verdicts about the insoluble are appropriate. Heytesbury himself refused to say what else an insoluble might signify besides its ordinary signification; that could not be predicted. But some late authors went on to fill in Heytesbury’s silence. They stipulated that insolubles in addition signify that they are true, thus linking Heytesbury’s theory with Bradwardine’s. Heytesbury’s view has an important consequence. Since signification in mental language is fixed by nature, not by voluntary convention, mental propositions can never signify otherwise than they ordinarily do. Given Heytesbury’s account of insolubility, this means that there can be no insolubles in mental language. Heytesbury himself did not draw this conclusion, but it is there none the less. All important developments concerning insolubles between 1320 and 1350 originated with Englishmen and are associated in one way or another with Merton College. Later writers, in the third and last stage of the medieval insolubles literature, sometimes developed this English material in interesting new ways. Thus Gregory of Rimini and Peter of Ailly took the above consequence of Heytesbury’s theory to heart. They maintained that there are no insolubles in mental language, and that insolubles arise in spoken and written language only because they correspond (are subordinated) to two propositions in the mind, one true and the other false. Apart from these developments of earlier views, there seem to be no radically original theories of insolubles in the Middle Ages after about 1350. VIII Ockham’s theory of connotation has antecedents in Aristotle’s remarks on paronymy (Categories, 1a12–15). It is the most highly developed such theory in the Middle Ages. For Ockham, some categorematic terms are absolute; others are connotative. ‘Bravery’ is absolute since it signifies only bravery, a quality in the soul. But ‘brave’ is connotative since it signifies certain persons (brave ones), but only by making an oblique reference to (‘connoting’) their bravery. Connotative terms have nominal definitions; absolute terms do not. The notion of a nominal definition is difficult to state exactly ([17.44]), but all nominal definitions of a connotative term are ‘equivalent’ for Ockham in a sense that is perhaps as strong as synonymy. Furthermore, it appears that the connotative term itself is synonymous with each of its nominal definitions, and may be viewed in fact as a kind of shorthand abbreviation for them. Thus the adjective ‘white’ is a connotative term having the nominal definition ‘something having a whiteness’ or ‘something informed by a whiteness’. All three expressions are synonymous for Ockham. Since Ockham’s ‘better doctrine’ is that there is no mental synonymy, the elementary vocabulary of mental language (simple concepts) includes no connotative terms. Mental language contains the absolute term ‘whiteness’ and syntactical devices to form nominal definitions like those above. But it does not, on pain of synonymy, contain a distinct mental adjective ‘white’. (But see section IV, above.) All primitive categorematic mental terms are thus absolute. This has important consequences for Ockham’s philosophy. For (barring miracles) the mind has simple concepts only for things of which it has had direct experience (‘intuitive cognition’). The supply of absolute concepts is therefore a guide to ontology. There is a related theory in Ockham, the theory of ‘exposition’ or analysis (see [17.34] 412–27). The outlines of this theory were established by the mid-thirteenth century. In brief, an exponible proposition is one containing a word (the ‘exponible term’) that obscures the sense of the whole proposition. It is to be analysed or ‘expounded’ into a plurality of simpler propositions, called ‘exponents’, that together capture the sense of the original. Thus ‘Socrates is beginning to run’ might be expounded by ‘Socrates is not running’ and ‘Immediately hereafter Socrates will be running’. Ockham’s own theory of exposition is not especially innovative, except that he explicitly links it with the theory of connotation. This is an attractive move, since whereas the theory of connotation provides explicit nominal definitions for connotative terms, it is plausible to view exposition theory as providing contextual definitions of exponible terms treated as incomplete symbols. Hence, just as the absence of synonymy in mental language means that it contains no simple connotative terms, so too it would mean that mental language contains no exponible propositions, but only their exponents. Since contextual definitions provide the more general approach, it is not surprising that connotation theory quickly declined after Ockham, and is treated only perfunctorily in Strode and Wyclif. Its place is taken there by much more elaborate treatments of exponibles. Buridan does retain a fairly full theory of connotation, but it is not so detailed as Ockham’s.30 Although the theory of exposition continued to have a life of its own, by mid-century it had also been incorporated into the theory of ‘proofs of propositions’.31 Billingham’s Youth’s Mirror was a seminal work here. The notion of ‘proof’ involved in this literature was broader than the Aristotelian demonstration of the Posterior Analytics. It meant any argument showing that a certain proposition is true. Not all propositions can be ‘proved’. Some of them serve as ultimate premisses of all proofs; they must be learned another way. Such elementary propositions Billingham calls ‘immediate’ propositions, containing only ‘immediate’ terms that cannot be ‘resolved’ into more elementary terms. Immediate terms include indexicals such as ‘I’, ‘he’, ‘this’, ‘here’ and ‘now’, and very general verbs such as ‘is’ and ‘can’ and their tenses. Hence a proposition like ‘This is now here’ is immediate. Other propositions can ultimately be ‘proved’ from immediate propositions. Billingham recognized three methods for such proofs: exposition, ‘resolution’ and proof using an ‘auxiliary’ (officialis) term. Exposition has already been explained. Resolution amounts to proof by expository syllogism. Thus ‘A man runs’ is ‘proved’ by the inference ‘This runs and this is a man; therefore, a man runs’. But there is a problem. The premisses of this inference are not immediate, since their predicates are not immediate terms. And there appears to be no way to reduce them to yet more basic propositions by any of the three ways Billingham recognizes. ‘Auxiliary’ terms govern indirect discourse. They include epistemic verbs such as ‘knows’, ‘believes’, etc., and modal terms such as ‘it is contingent’. To ‘prove’ a proposition containing an auxiliary term is to provide an argument spelling out the role of the auxiliary term. One of the premisses of this argument states how the proposition referred to in indirect discourse ‘precisely signifies’. Thus ‘It is contingent for him to run’ is proved by: ‘“He runs” is contingent; and “He runs” precisely signifies for him to run; therefore, it is contingent for him to run.’ There are still many obscurities in the theory of ‘proofs of propositions’. But it was very widespread. IX Our knowledge of late medieval logic has advanced enormously since the 1960s. The availability of previously unpublished texts has shed great light on this fertile period. Yet, as this chapter shows, there is still much that is unknown. The general reader should regard the claims in this chapter as tentative. Readers with specialized training or interest should regard them as an invitation to further research. NOTES 1 CHLMP, pp. 46, 74–5. See also Chapter 7 above, p. 176. 2 In medieval terminology, a ‘proposition’ is a declarative sentence, often a sentencetoken. The term was not typically used in its modern sense, to mean what is expressed by a sentence(-token). I shall use ‘proposition’ in its medieval sense throughout this chapter except where indicated. 3 De Rijk [17.29], especially vol. 1. On consequentiae in the twelfth century, see Chapter 7 above, pp. 157–8, 175–6. 4 CHLMP, ch. 11. 5 CHLMP, ch. 16. Despite the name, these disputations had nothing to do with ethics or morality. They were not about deontic logic. Their exact purpose is still uncertain. 6 There were also anonymous works of this kind, dating back to the twelfth century. See De Rijk [17.29]. 7 With these last three paragraphs, see Spade [17.50], especially pp. 187–8, and references there. See also CHLMP, chs 12 and 16B. 8 For information on authors mentioned in this section, see CHLMP, pp. 855–92 (‘Biographies’). 9 On English logic as discussed in this section, see Ashworth and Spade [17.28] and references there. 10 In the 1494 edition of Heytesbury, Hopton’s treatise is wrongly attributed to Heytesbury himself. 11 On Angelo, see Spade [17.45] 49–52. For other authors mentioned in this paragraph, see Maierù [17.34], 34–6. 12 There is potential for confusion here. In twentieth-century philosophy, a ‘natural’ language is one like English, in contrast to ‘artificial’ languages like Esperanto or the ‘language’ of Principia Mathematica. In medieval usage, the latter would likewise count as ‘artificial’ languages, but so would English; the only truly natural language is mental language. 13 See Peter of Ailly [17.27] 9, 19–21, 36–7, and references there. 14 See Aristotle, De interpretatione, 16b 19–21. 15 Something a bears the ancestral of relation R to z if and only if a bears R to something b that bears R to something c that…that bears R to z. 16 With this section, see CHLMP, ch. 9. 17 For Gregory and Peter, see Peter of Ailly [17.27]. 18 Buridan’s theory does not imply this, and Peter of Ailly flatly denies it for supposition. 19 With these last two paragraphs, see Spade [17.47]. 20 See the reply to Geach in Trentman [17.51]. For a critique of Ockham’s strategy, see Spade [17.47]. 21 See Peter of Ailly [17.27] 9 and 37–44, and references there. 22 A similar approach is used in Buridan’s discussion of opaque epistemic and doxastic contexts. See Sophismata [17.16], IV, sophisms 9–14. With the remainder of this section, see Ashworth and Spade [17.28]. 23 Kretzmann [17.40]. See also Chapter 7 above, pp. 157–8. 24 With this section, see Spade [17.50], and CHLMP, ch. 9. 25 Spade [17.43]. In so far as such contexts can arise in mental language, this view requires equivocation there. See Spade [17.47]. 26 [17.47]. See also n. 18, above. 27 Spade [17.50] n. 78 and the Appendix. For Brinkley I am grateful to M.J. Fitzgerald. 28 In the ‘adverbial’ sense of prepositional signification, described in section V above. 29 For qualifications and complications, see Spade [17.48]. 30 Buridan’s name for connotation is appellatio or ‘appellation’ (Sophismata, IV). 31 With this last part of section VIII, see Ashworth and Spade [17.28] and references there. BIBLIOGRAPHY Original Language Editions 17.1 Albert of Saxony, Perutilis logica, Venice, 1522; repr.Olms, Hildesheim, 1974. 17.2 ——Sophismata, Paris, 1502; repr. Olms, Hildesheim, 1975. 17.3 Alessio, F. (ed.) Lamberto d’Auxerre: Logica (Summa Lamberti), Florence, La nuova Italia editrice, 1971. 17.4 Boehner, B. (ed.) Walter Burley: De puritate artis logicae tractatus longior, with a Revised Edition of the Tractatus Brevior, St Bonaventure, NY, Franciscan Institute, 1955. 17.5 Brown, M.A. (ed.) Paul of Pergula: Logica and Tractatus de sensu composite et diviso, St Bonaventure, NY, Franciscan Institute, 1961. 17.6 De Rijk, L.M. (ed.) Peter of Spain: Tractatus, Called Afterwards Summule Logicales, Assen, Van Gorcum, 1972. (translated in [17.21]) 17.7 Gál, G. et al. (eds) Guillelmi de Ockham: Opera philosophica et theologica, 17 vols, St Bonaventure, NY, Franciscan Institute, 1967–88. (OT=Opera theologica; OP=Opera philosophica.) 17.8 Geach, P. and Kneale, W. (general editors) Pauli Veneti logica magna, Oxford, Oxford University Press, 1978–. (Latin edition and English translation, in several fascicles. Editors and translators vary.) 17.9 Grabmann, M. (ed.) Die Introductions in logicam des Wilhelm van Shyreswood, Munich, Verlag der Bayerischen Adademie der Wissenschaften, 1937. (translated in [17.26]) 17.10 Gregory of Rimini, Super primum et secundum Sententiarum, Venice, 1522; repr. Franciscan Institute, St Bonaventure, NY, 1955. 17.11 Heytesbury, W. Tractatus guilelmi Hentisberi de sensu composito et diviso, Regulae ejusdem cum sophismatibus…, Venice, 1494. 17.12 Hubien, H. (ed.) Johannis Buridani Tractatus de consequentiis, Louvain, Publications Universitaires, 1976. (translated in [17.17]) 17.13 Maierù, A. (ed.) ‘Lo Speculum puerorum sive Terminus est in quem di Riccardo Billingham’, Studi Medievali (3rd series) 10.3 (1969): 297–397. 17.14 Paul of Venice, Logica (=Logica parva), Venice, 1484; repr. Olms, Hildesheim, 1970. (translated in [17.20]) 17.15 Peter of Ailly, Conceptus et insolubilia, Paris, c. 1495. (translated in [17.27]) 17.16 Scott, T.K. (ed.) Johannes Buridanus: Sophismata, Stuttgart, Fromman- Holzboog, 1977. (translated in [17.18]) See also [17.19], [17.29] II, pt 2. English Translations 17.17 John Buridan’s Logic: The Treatise on Supposition, the Treatise on Consequences, trans. P.King, Dordrecht, Reidel, 1985. 17.18 John Buridan: Sophisms on Meaning and Truth, trans. T.K.Scott, New York, Appleton-Century-Crofts, 1966. (translation of [17.16]) 17.19 John Buridan on Self-Reference: Chapter Eight of Buridan’s ‘Sophismata’, with a Translation, an Introduction, and a Philosophical Commentary, trans. G. E.Hughes, Cambridge, Cambridge University Press, 1982. (The paperback edition omits the Latin text, and has different pagination and subtitle.) 17.20 Paul of Venice: Logica parva, trans. A.R.Perreiah, Washington, DC, Catholic University of America Press, and Munich, Philosophia Verlag, 1984. (translation of [17.14]) 17.21 Peter of Spain: Language in Dispute, trans. F.P.Dinneen, Amsterdam, J. Benjamins, 1990. (translation of [17.6]) 17.22 William Heytesbury, On ‘Insoluble’ Sentences: Chapter One of His Rules for Solving Sophisms, trans. P.V.Spade, Toronto, Pontifical Institute of Mediaeval Studies, 1979. (translated from [17.11]) 17.23 William of Ockham: Ockham’s Theory of Propositions: Part II of the Summa logicae, trans. A.J.Freddoso and H.Schuurman, Notre Dame, Ind., University of Notre Dame Press, 1980. 17.24 William of Ockham: Ockham’s Theory of Terms: Part 1 of the Summa logicae, trans. M.J.Loux, Notre Dame, Ind., University of Notre Dame Press, 1974. 17.25 William of Ockham: Predestination, God’s Foreknowledge, and Future Contingents, trans. M.M.Adams and N.Kretzmann, New York, Appleton- Century-Crofts, 1969; 2nd edn, Indianapolis, Ind., Hackett, 1983. 17.26 William of Sherwood’s Introduction to Logic, trans. N.Kretzmann, Minneapolis, Minn., University of Minnesota Press, 1966. (translation of [17.9]) 17.27 Peter of Ailly: Concepts and Insolubles, an Annotated Translation, trans. P.V. Spade, Dordrecht, Reidel, 1980. (translation of [17.15]) See also [17.8]. Collections of Articles, General Studies and Surveys 17.28 Ashworth, E.J. and Spade, P.V. ‘Logic in Late Medieval Oxford’, in The History of the University of Oxford, vol. II, Oxford, Clarendon Press, 1992. 17.29 De Rijk, L.M. Logica Modernorum, vol. I, On the Twelfth Century Theories of Fallacy, Assen, Van Gorcum, 1962; vol. II, The Origin and Early Development of the Theory of Supposition, Assen, Van Gorcum, 1967. (Vol. II is bound in 2 parts: 1, De Rijk’s own discussion; 2, Latin texts and indices.) 17.30 CHLMP. 17.31 Kretzmann, N. (ed.) Meaning and Inference in Medieval Philosophy: Studies in Memory of Jan Pinborg, Dordrecht, Kluwer, 1988. 17.32 Lewry, P.O. (ed.) The Rise of British Logic: Acts of the Sixth European Symposium on Medieval Logic and Semantics, Balliol College, Oxford, 19–24 June 1983, Toronto, Pontifical Institute of Mediaeval Studies, 1983. 17.33 Maierù, A. (ed.) English Logic in Italy in the 14th and 15th Centuries: Acts of the Fifth European Symposium on Medieval Logic and Semantics, Rome, 10–14 November 1980, Naples, Bibliopolis, 1982. 17.34 ——Terminologia logica della tarda scolastica, Rome, Edizioni dell’Ateneo, 1972. 17.35 Nuchelmans, G. Theories of the Proposition: Ancient and Medieval Conceptions of the Bearers of Truth and Falsity, Amsterdam, North Holland, 1973. 17.36 Pinborg, J. Die Entwicklung der Sprachtheorie im Mittelalter, Münster: Aschendorff, 1967. 17.37 ——(ed.) The Logic of John Buridan: Acts of the Third European Symposium on Medieval Logic and Semantics, Copenhagen, 16–21 November 1975, Copenhagen, Museum Tusculanum, 1976. Studies of Particular Topics 17.38 Gál, G. ‘Adam of Wodeham’s question on the ‘complexe significabile’ as the immediate object of scientific knowledge’, Franciscan Studies 37 (1977): 66–102. 17.39 Geach, P. Mental Acts: Their Content and Their Objects, London, Routledge & Kegan Paul, 1957. (Section 23 is on mental language.) 17.40 Kretzmann, N. ‘Medieval logicians on the meaning of the Propositio’, Journal of Philosophy 67 (1970):767–87. 17.41 Pinborg, J. ‘The English contribution to logic before Ockham’, Synthese 40 (1979): 19–42. 17.42 Spade, P.V. ‘The origin of the mediaeval insolubilia literature’, Franciscan Studies 33 (1973): 292–309. 17.43 ——‘Ockham’s rule of supposition: two conflicts in his theory’, Vivarium 12 (1974): 63–73. 17.44 ——‘Ockham’s distinction between absolute and connotative terms’, Vivarium 13 (1975): 55–75. 17.45 ——The Mediaeval Liar: A Catalogue of the Insolubilia Literature, Toronto, Pontifical Institute of Mediaeval Studies, 1975. 17.46 ——‘Some epistemological implications of the Burley-Ockham dispute’, Franciscan Studies 35 (1975): 212–22. 17.47 ——‘Synonymy and equivocation in Ockham’s mental language’, Journal of the History of Philosophy 18 (1980): 9–22. 17.48 ——‘Insolubilia and Bradwardine’s theory of signification’, Medioevo: Rivista di storia della filosofia medievale 7 (1981): 115–34. 17.49 ——‘Five early theories in the mediaeval insolubilia literature’, Vivarium 25 (1987): 24–46. 17.50 ——‘The logic of the categorical: the medieval theory of descent and ascent’, in [17.31] 187–224. 17.51 Trentman, J. ‘Ockham on mental’, Mind 79 (1970): 586–90.

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