Late medieval logicPaul Vincent SpadeIMedieval logic encompassed more than what we call logic today. Itincluded semantics, philosophy of language, parts of physics, ofphilosophy of mind and of epistemology.Late medieval logic began around 1300 and lasted through at leastthe fifteenth century. With some noteworthy exceptions, its mostoriginal contributions were made by 1350, particularly at Oxford.Hence the focus of this chapter will be on the period 1300–1500, withspecial emphasis on Oxford before 1350.But first some background concerning the earlier period. The logicalwritings of Aristotle were all available in Latin by the mid-twelfthcentury.1In addition, except for the theory of ‘proofs of propositions’2(see section VIII below), the characteristic new ingredients of medievallogic were already in place or at least in progress by the end of thetwelfth century or the beginning of the thirteenth.The theory of inference or ‘consequence’, for example, was studiedas early as Peter Abelard (1079–1142). Again, after about 1120 thecirculation of Aristotle’sSophistical Refutationsin Latin stimulated astudy of fallacies and the many features of language that produce them.Out of this investigation there arose twelfth- and thirteenth-centurywritings on semantic ‘properties of terms’, like ‘supposition’ and‘ampliation’ (see section VI below).3At the same time, treatises onsophismataor puzzle-sentences in logic, theology or philosophy ofnature began to be produced. (A good analogy for this literature maybe found in modern discussions of Frege’s ‘The morning star is theevening star’.) Likewise, studies were written about the logical effectsof words like ‘only’, ‘except’, ‘begins’ and ‘ceases’ that offer manyopportunities for fallacies and involve complications going far beyondsyllogistic or the theory of topical inferences.4Treatises on ‘insolubles’or semantic paradoxes began to appear late in the twelfth century([17.42], [17.49]).Simultaneously, a literature developed on a newkind of disputation called ‘obligations’.5Collectively, these new logicalgenres are known as ‘terminist’ logic because of the important roleplayed 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 Williamof Sherwood were writing summary treatises(summulae)covering thewhole of logic, including the material in Aristotle’s writings as well asnew terminist developments.6Then, after about 1270, something odd happened, both in Englandand on the Continent. In France, terminism was eclipsed by an entirelydifferent theory called ‘speculative grammar’, which appealed to thenotion of ‘modes of signifying’ and is therefore sometimes called‘modism’. This theory prevailed in France until the 1320s, when JohnBuridan (b.c.1295/1300, d. after 1358) suddenly restored the theoryof supposition and associated terminist doctrines. After Buridan,supposition theory was the leading vehicle for semantic (as distinctfrom grammatical) analysis until the end of the Middle Ages.Modism never dominated England as it did elsewhere; terminismsurvived there during its period of neglect on the Continent. Still,few innovations in supposition theory or its satellite doctrines weremade in England during the last quarter of the thirteenth century.But then, in the very early fourteenth century, Walter Burley (orBurleigh, b.c.1275, d. 1344/5) began to do new work in the terministtradition.This temporary decline of terminism on both sides of the Channelat the end of the thirteenth century, and its sudden revival shortly after1300, are mysterious events. But, whatever the underlying causes, whensupposition theory and related doctrines re-emerged in the earlyfourteenth century, they were importantly different from how they hadbeen earlier.7IIThis section will survey the main stages of late medieval logic, andintroduce important names. Later sections will focus on particulartheoretical topics.8In England,9logic 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. Bothmade important contributions to supposition theory, and Ockham inparticular 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 (earlyfourteenth century, d. 1361) and William Heytesbury (b. before 1313,d. 1372/3), among others, applied the techniques ofsophismatatoquestions in natural philosophy, epistemic logic and other fields.Thomas Bradwardine (c.1295–1349) wrote anInsolublesthat wasperhaps the most influential treatise on semantic paradoxesthroughout the Middle Ages. Around 1330–2, Adam Wodehamdevised an important theory of ‘complexly significables’(complexesignificabilia),the closest medieval equivalent to the modern notionof ‘proposition’. Richard Billingham (fl. 1340s or 1350s) seems tohave originated the important theory of ‘proofs of propositions’. HistreatiseSpeculum puerorumorYouths’ Mirrorwill be discussed insection VIII below.The second stage of English logic after 1300 lasted from 1350 to1400. This was a time of consolidation, of sophisticated but no longerespecially original work. The period has not yet been well researched,but at least three trends can be distinguished. First, there was aremarkable number of school-manuals written in logic, compilationsof standard doctrine with little innovation. Works of Richard Lavenham(d. 1399 or after) provide a good example. Gradually, certain of theseschool-texts congealed into two collections called theLibellisophistarum (Little Books for Arguers),one for Oxford and one forCambridge. These were printed in several editions around 1500.Second, English logic from 1350 to 1400 had a special interest inthe doctrine of ‘proofs of propositions’ associated with Billingham. Astime passed, the labour devoted to this topic grew enormously. JohnWyclif dedicated a large part of hisLogic(before 1368) and especiallyof hisContinuation of the Logic(1371–4) to this theory. So did RalphStrode, a contemporary of Wyclif s, in his ownLogic.John Huntmanwrote aLogicsometime near the end of the century, showing thecontinued expansion of the Billingham tradition.A third concern of English logic in this period was the significationof propositions. The most influential work here was probablyOn theTruth and Falsehood of Propositionsby Henry Hopton (fl. 1357).There Hopton discussed and rejected several previous views beforesetting 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 RichardFeribrigge (fl. probably 1360s), author of an importantConsequencesand aLogic or Treatise on the Truth of Propositions. Of lesserimportance are: Robert Fland (fl. 1335–60); Richard Brinkley, theauthor of aSummaof logic probably between 1360 and 1373; ThomasManlevelt (or Mauvelt), who wrote several treatises around mid-centurythat 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 centurywas 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 toItaly, he taught at Padua and elsewhere, and was an important conduitthrough which English logic became known in Italy in the fifteenthcentury. His writings include a widely circulatedLittle Logic (Logicaparva)and the enormousBig Logic (Logica magna).The third stage of late medieval English logic includes the wholefifteenth century. This was a period of shocking decline. Except for afew insignificant figures around 1400, not even second-rate authorsare known. The manuscripts from this period—and by 1500, earlyprinted books—offer little hope that further research will change thisassessment. The Oxford and CambridgeLittle Books for Arguers,already mentioned, testify to the deterioration of logic during thisperiod. Medieval logic was effectively dead in England after 1400.Logic on the Continent during these same two centuries cannot beso neatly divided into stages. Still, there as in England, the mostimportant work was done before about 1350. The pre-eminent figurewas doubtless Buridan. His writings include aConsequences,aSophismataand aSummulae of Dialectic. Buridan’s students includedmany influential logicians of the next generation, among them: Albertof Saxony (d. 1390), the author of aSophismataandA Very UsefulLogic,and the first rector of the University of Vienna; and Marsilius ofInghen (c.1330–96), the first rector of the University of Heidelbergand the author of anInsolublesand of treatises on ‘properties of terms’.On many points, Buridan’s logical views were like Burley’s orespecially Ockham’s in England. There are differences, but thesimilarities are more striking, especially when contrasted with logic oneither side of the Channel before 1300. The extent of Ockham’s owninfluence on Buridan is doubtful, but Ockham’s confrère AdamWodeham was instrumental in transmitting much English learning toParis. In particular, Wodeham’s theory of ‘complexly significables’ wasadopted by Gregory of Rimini (c.1300–58).The Parisian Peter of Ailly (1350–1420/1) wrote several interestinglogical works, including:Concepts and Insolubles,a pair of treatiseson ‘mental language’ and the Liar Paradox;Destructions of the Modesof Signifying,against ‘modism’;Treatise on Exponibles(see sectionVIII below); andTreatise on the Art of ‘Obligating’(perhaps byMarsilius of Inghen instead).Before 1400, the Italian Peter of Mantua (fl. 1387–1400) wrote aLogicthat already shows knowledge of earlier English work,particularly that stemming from Billingham. Around 1400 Angelo ofFossombrone, who taught at Bologna (1395–1400) and Padua (1400–2), wrote anInsolublesmaintaining an elaborated version ofHeytesbury’s theory. About the same time, the newly returned Paul ofVenice spread the gospel of Oxford logic further in Italy. Among hisstudents, Paul of Pergula (d. 1451/5) wrote aLogicand a treatiseOnthe Composite and the Divided Sense(on the scope of certain logicaloperators) based on Heytesbury’s own work of that name, and Gaetanoof Thiene (1387–1465) wrote detailed commentaries on works byHeytesbury and Strode. Other authors in Italy and elsewhere continuedto write on logic to the end of the Middle Ages and beyond.11Even these few names will suffice to show that the logical landscapeafter about 1400 was by no means so desolate on the Continent as inEngland. Still, on either side of the Channel logical work after 1350was largely derivative and, while sometimes very sophisticated, notvery innovative. There was certainly no one, for example, with thestature of Burley, Ockham or Buridan.IIIThis and the following sections will concentrate on five important topicsin late medieval logic: (a) the theory of ‘mental language’, (b) thesignification of propositions, (c) developments in supposition-theory,(d) semantic paradoxes, and (e) connotation-theory and the ‘proofs ofpropositions’.InOn Interpretation,16a3–4, Aristotle stated that ‘spoken soundsare symbols of affections in the soul, and written marks symbols ofspoken sounds’. These words were translated by Boethius andinterpreted as implying three levels of language: spoken, written andmental. Through Boethius this three-level hierarchy of language becamea commonplace in medieval logical literature.Of the three, mental language was regarded as the most basic. Itssemantic properties are natural ones;12they do not originate from anyconvention or custom, and cannot be changed at will. Unlike spokenand 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 ‘inFrench’. Thus a public speaker might rehearse a speech by runningthrough silently the words he will later utter aloud. What goes on thereis a kind of ‘let’s pretend’ speaking that takes place in imagination andis in that sense ‘mental’. But it is not what most authors meant by‘mental language’. Since silent recitation varies with the spoken languageone is rehearsing, it is not the same for everyone. Proper mental languageis different. It includes, for example, what happens when one suddenly‘sees’ the force of a mathematical proof; in that case there is a ‘flash ofinsight’, an understanding or judgement that need not yet be put intowords, even silently. This kind of mental language, the theory goes,isthe same for everyone.13Spoken language, by contrast, has its semantic function parasitically,through a conventional correlation between its expressions and mentalones. The arbitrariness of this convention is what allows the multitudeof spoken languages. Written language plays an even more derivativerole, through a conventional correlation between its inscriptions andthe sounds of spoken language. The arbitrariness of this conventiontoo allows for different scripts among written languages. Only throughthe mediation of spoken language, the theory went, are inscriptionscorrelated with thoughts in mental language. This view implies thatone cannot read a language one does not know how to speak. Mostmedieval authors accepted this consequence.Following Boethius, the correlations between written and spokenlanguage and between spoken and mental language were often regardedas relations of ‘signification’. This claim had theoretical consequences,since signification was a well-defined notion in the Middle Ages. Aterm ‘signifies’ what it makes one think of (‘establishes an understandingof’=constituit intellectum+genitive).14While there was dispute aboutwhat occupies the object-pole of this relation, there was agreementover the criterion. Signification is thus a special case of causality, andso transitive. (Certain authors added to signification in general theparticular notions of immediate and ultimate signification. The generalrelation of signification thus became what modern logicians call the‘ancestral’ of the relation of immediate signification;15a termtthenultimately signifiesxif and only iftsignifiesxandxdoes not signifyanything else.) Terms in mental language signify (make one think of)external objects only in the degenerate sense that theyarethe thoughtsof those external objects.According to this view, to say that expressions of spoken languageimmediately signify expressions of mental language is to say that thefunction of speech is to convey thoughts. Certain authors, e.g. DunsScotus (c.1265–1308), Burley and Ockham, regarded this as toorestrictive. For them, spoken (and written) terms may be made to signifyanything, not only the speaker’s thoughts. In fact spoken words donotalways make us think of thoughts; sometimes we are made to thinkdirectly of external objects. For these authors, the relations betweenwritten and spoken language and between either of these and mentallanguage are not relations of signification. Ockham described themneutrally as relations of ‘subordination’.16IVAlthough authors since Boethius had recognized mental language, itwas not until the fourteenth century that it began to be investigated indetail. Ockham was the first to develop a full theory of mental languageand put it to philosophical use. Shortly thereafter, Buridan began towork out his own view. His theory agrees with Ockham’s on the whole,although Ockham’s is the more detailed. In the early 1340s, Gregoryof Rimini refined certain parts of the theory, and applied it to a solutionto the Liar Paradox. In 1372, Peter of Ailly’sConcepts and Insolublesincorporated the work of both Ockham and Gregory.17Other authorsmade contributions to the theory, but these were the major ones. Thepresentation below will follow Ockham’s account except as indicated.Terms in mental language are concepts; its propositions arejudgements. The fact that mental language is the same for everyoneexplains how it is possible to translate one spoken (or written) languageinto another. A sentence in Spanish is a correct translation of a sentencein English if and only if the two are subordinated to the same mentalsentence. More generally, any two spoken or written expressions—from the same or different languages—are synonymous if and only ifthey are subordinated to the same mental expression. Again, any spokenor written expression is equivocal if and only if it is subordinated tomore than one mental expression.If mental language accounts for synonymy and equivocation inspoken and written languages, can there be synonymy or equivocationin mental language itself? The textual evidence is mixed. There arepassages in Ockham (Summa logicaeI, 3 = [17.7]OP1:11;SummalogicaeI, 13 = [17.7]OP1:44) supporting a negative answer in bothcases. Nevertheless other texts (Ordinatio,I, d. 3, q. 2 = [17.7]OT2:405;OrdinatioI, d. 3, q. 3 = [17.7]OT2:425;Quodlibet5, q. 9 = [17.7]OT9:513–18), where Ockham is discussing the semantics of certainconnotative terms (see section VIII below), perhaps imply the existenceof mental synonymy. As for equivocation, Ockham’s theory of tenseand modality, as well as his theory of supposition (see section VI below),commits him outright to certain kinds of equivocation in mentallanguage.18But apart from textual considerations, there arephilosophical reasons for saying that, given other features of Ockham’stheory, mental synonymy or equivocation makes no sense.19What is included in mental language? In two passages (Summalogicae,I, 3 = [17.7]OP1:11.1–26;Quodlibet5, q. 8 = [17.7]OT9:508–13), 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 mentallanguage. Ockham acknowledges doubts about mental participles (theirjob could be performed by verbs) and pronouns (presumably ‘pronounsof laziness’, as for example in ‘Socrates is a man andheis an animal’).Moreover, not all characteristics of spoken and written syntax are foundin mental language. While mental nouns and adjectives have case andnumber, and mental adjectives admit of positive, comparative andsuperlative degrees, they do not have gender and are not divided intogrammatical declensions (like Latin’s five declensions). Mental verbshave person, number, tense, voice and mood, but are not divided intogrammatical conjugations.Ockham’s mental language looks remarkably like Latin. This factled some modern writers to reject the theory as a foolish attempt to‘explain’ features of Latin by merely duplicating them in mentallanguage, which is then regarded as somehow more ‘basic’ ([17.39] §23). But more is involved than that. Ockham’s strategy is to admit intomental language exactly those features of spoken or written languagethat affect the truth-values of propositions. All other features of spokenand written language, Ockham says, are only for the sake of decorativestyle, or in the interest of brevity. They are not present in mentallanguage.20Mental language is thus a logically perspicuous language fordescribing the world. It has whatever is needed to distinguish truthfrom falsehood, nothing more. In this respect, mental language isreminiscent of the ‘ideal languages’ proposed by early twentieth-centuryphilosophers ([17.51]).How are mental words combined in mental propositions? What isthe difference, for example, between the true mental proposition‘Every man is an animal’ and the false ‘Every animal is a man’? Inwritten language, the difference is the spatial configuration of thewords. But the mind does not take up space, so that there can be nosuch difference there. In speech the difference lies in the temporalsequence of the words. But since proper mental language at leastsometimes involves a ‘flash of insight’ that happens all at once, neithercan temporal word order account for the difference between the twomental propositions.Because of such difficulties, authors such as Gregory of Rimini andPeter of Ailly held that mental propositions (although not all of themfor Peter) are simple mental acts not really composed of distinct mentalwords at all.21Ockham too had considered such a theory (In SententiasII, qq. 12–13 = [17.7]OT5:279;Exposition of ‘On Interpretation’,proem = [17.7]OP2:356). It is hard to reconcile this view with theclaim that mental vocabulary is divided into ‘parts of speech’; distinctmental words would appear to have no job to do if they do not enterinto the structure of mental propositions.VBesides the disagreement over the immediate signification of spokenand written terms (see section III above), there was a dispute overultimate signification. Metaphysical realists, such as Burley, maintainedthe traditional view that general terms ultimately signify universalentities, while nominalists (e.g. Ockham and Buridan) held that theyultimately signify only individuals.Some authors extended the notion of signification to ask not onlyabout the signification of terms but also about the signification of wholepropositions. Do they signify anything besides what their componentterms signify separately? Do they signify, for example, states of affairsor facts?Ockham did not explicitly address this question. But Buridan did,and his answer was no. For him ([17.16] II, conclusion 5), aproposition—and in general any complex expression—signifieswhatever 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 wordswere called ‘syncategorematic’ and were regarded as not having anysignification of their own; they are ‘logical particles’ used for combiningcategorematic terms into propositions and other complex expressions.)Thus in the spoken proposition ‘The cat is on the mat’, when I hear theword ‘cat’ I am, on Buridan’s account, made to think of all cats andwhen I hear ‘mat’ I am made to think of all mats. That is all theproposition 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 ‘Socratesis sitting’, for example, signifiesSocrates to be sitting. And what is that?Buridan held that if Socrates really is sitting, thenSocrates to be sittingis just Socrates himself. But if he is not sitting, thenSocrates to be sittingis nothing at all.22This view bears some similarity to a theory heldearlier at Oxford by Walter Chatton (1285–1344) and discussed as thefirst previous view in Henry Hopton’sOn the Truth and Falsehood ofPropositions. Similar views were defended by Richard Feribrigge andJohn Huntman. The details of their texts have not been thoroughlyinvestigated, and there is much that is still obscure; it is not certain thatall these authors maintained variants of the same doctrine. Still, themotivation is the same in each case: to find something to serve as thesignificate of a proposition in an ontology that does not allow anythinglike facts, states of affairs or ‘propositions’ in the modern sense.But there were other opinions. As early as Abelard, some authorsheld that what propositions signify falls outside the Aristoteliancategories, and is something like the modern notion of ‘proposition’.Sometimes this new entity was called a ‘mode’, sometimes adictum.23In the fourteenth century, such theories continued to find theirdefenders. Perhaps a version of it may be seen in the early 1330s inWilliam of Crathorn. Perhaps too Henry Hopton intended such a theoryas the second previous view he considered, according to which aproposition signifies a ‘mode’ of a thing, where a ‘mode’ is not asomethingbut abeing-somehow (esse aliqualiter). But an unequivocalstatement 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 notpropositions in the medieval sense, not even mental propositions, butare what is expressed by propositions. They are the significates ofpropositions, and the objects of knowledge, belief and prepositionalattitudes generally. Complexly significables do not exist in the waysubstances and accidents do. Before creation, for example, only Godexisted. But even then God knewthat the world was going to exist.This complexly significable cannot be identified with God himself, sinceGod is a necessary being but it was contingent that the world wasgoing to exist. Yet as distinct from God, it cannot have existed beforecreation. Such extralogical considerations were an important motivationfor the theory of complexly significables. Authors such as Buridan andPeter of Ailly rejected the theory; Peter, for example, claimed that theargument about God’s knowledge before creation is based on anillegitimate substitution of identicals in an opaque context involvingnecessity ([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 soas the ontological basis for a ‘correspondence’ theory of truth. Otherauthors took a different approach. They too maintained acorrespondence theory, often expressed as: a proposition is true if andonly 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 properquestion is notwhatbuthowa proposition signifies. This ‘adverbial’notion of signification allowed a correspondence theory without beingobliged to find any ontological correlate for a true proposition tocorrespond to. After rejecting earlier views, Henry Hopton’s own theorywas like this. Heytesbury had earlier held a similar view, as did Peter ofAilly later ([17.22] 61–5; [17.27] 10, 48–54 and nn.).VIThe theory of ‘supposition’ is a mystery. Although it is central to thetheories of ‘properties of terms’ that developed from the twelfth centuryon, it is not clear what the theory was intended to accomplish, or indeedwhat the theory as a whole was about.24Throughout its history, there were two main parts to suppositiontheory. One was a theory of the reference of terms in propositions, andhow that reference is affected by syntactic and semantic features ofpropositions. The question this part of the theory was intended toanswer is, ‘What does a term refer to (supposit for, stand for) in aproposition?’ That much is clear. But from the beginning, there wasanother part of supposition theory, an account of how one might validly‘descend to singulars’ under a given occurrence of a term in aproposition, sometimes combined with a correlative account of ‘ascentfrom singulars’. The mystery surrounds this second part.Before the decline of terminism after 1270, there is some evidencethat the second part of supposition theory, like the first, was intendedto answer the question of what a term refers to in a proposition. Thefirst part of the theory says what kind of thing a given term-occurrencerefers to, while the second specifies how many such things it refers to(in much the way one finds even today accounts purporting to saywhether 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 intentof the second part of supposition theory, some authors quite earlyrealized its theoretical difficulties.When supposition theory re-emerged with Burley in England andlater with Buridan in France, the two parts of the theory had beenseparated once and for all. By that time the theory of descent andascent 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 otherauthors 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 referencefirst into proper (literal) and improper (metaphorical). The latter isillustrated by ‘England fights’, where ‘England’ refers by metonymy toEngland’s inhabitants. Medieval logic, like modern logic, did not havean adequate theory of metaphor. Ockham, Burley and a few others listsome haphazard subdivisions of improper supposition, but reallymention it only to set it aside. Their emphasis is on proper supposition.Proper supposition was divided into three kinds: personal, simpleand material. The origin of these names is unclear, although the term‘personal’ suggests a connection with the theology of the Trinity andthe Incarnation. But it should not be thought that personal suppositionhas anything especially to do with persons.Personal supposition occurs when a term refers to everything of whichit is truly predicable. Thus in ‘Every man is running’, ‘man’ refers to allmen and so is in personal supposition. But so too ‘running’ refers thereto all things now running, and hence is likewise in personal supposition.It does not refer there only to some running things, for example, onlyto the running men. Again, in ‘Some man is running’, ‘man’ refers toall men, not just to running ones.A term has material supposition when it refers to a spoken or writtenword or expression and is not in personal supposition. Thus, ‘man’ in‘Man has three letters’ has material supposition. Although there areobvious similarities, material supposition is not merely a medievalversion of modern quotation marks. For in ‘It is possible for Socratesto run’, the phrase ‘for Socrates to run’ has material supposition. But itrefers to the proposition ‘Socrates is running’, of which the phrase ‘forSocrates to run’ is not a quotation. (For Ockham, there are no states ofaffairs or complexly significables that can be said to be possible. Onlypropositions 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 onhis 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 insimple supposition refer to universals. But for nominalists like Ockham,there are no metaphysical universals; the only universals are universalterms in language, most properly universal concepts in mental language.Thus for Ockham terms in simple supposition refer to concepts. It isthey 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 mustnot be ‘taken significatively’, i.e. that it not be in personal supposition.But for a realist like Burley, terms in simple supposition refer to realuniversals outside the mind. It is they that are species and genera.Furthermore, for Burley and certain others, general terms in languagesignify those extramental universals. Thus the term ‘man’ signifiesuniversal human nature, not any one individual man or group of men,and not all men collectively. For Burley, therefore, it is in simplesupposition that a term refers to what it signifies. For Ockham, generalterms do not signify universals, not even universal concepts; they signifyindividuals. Even a term like ‘universal’ signifies individuals, since itsignifies concepts, which are metaphysically individuals and are‘universal’ only in the sense of being predicable of many things. Hencefor Ockham, it is in personal supposition, not simple, that a term refersto what it signifies.Personal supposition is the default case. Any term in any propositioncan be taken in personal supposition. It may alternatively be taken insimple or material supposition only if the other terms in the propositionprovide a suitable context. In such cases, the proposition is strictlyambiguous and may be read in either sense.25From this first part of supposition theory alone, certain authors,e.g. Ockham and Buridan, although not Burley, developed a theoryof truth-conditions for categorical propositions on the square ofopposition. Thus, a universal affirmative ‘EveryAisB’ is true if andonly if everything the subject term refers to the predicate term alsorefers to (although it may refer to other things as well). Truthconditionsfor other propositions on the square of opposition can bederived from this.Subordinated to this first part of supposition theory was a theory of‘ampliation’, accounting for the effects of modality and tense onpersonal supposition. A term in personal supposition may always betaken to refer to the things of which it is presently predicable. But inthe context of past or future tenses, the term may also be taken to referto the things of which it was or will be predicable. Likewise, in a modalcontext (possibility, necessity), the term may also be taken to refer tothe things of which itcanbe truly predicable. This expansion of therange of referents was called ‘ampliation’.Ockham and Burley regarded the new referents provided byampliation as alternatives to the normal ones. Thus in the proposition‘Every man was running’, ‘man’ may be taken as referring either to allpresently existing men or to all men existing in the past. The propositionis thus equivocal. But on the Continent, Buridan and others regardedthe new referents as additions to the normal ones. For them, in theproposition ‘Every man was running’ ‘man’ refers to all presentlyexisting men and all past men as well.26The second main part of supposition theory, the theory of descentand ascent, was a theory subdividing personal supposition only, intoseveral kinds. First, there is discrete supposition, possessed by propernames, demonstrative pronouns or demonstrative phrases (e.g. ‘thisman’). All other personal supposition iscommon,and was typicallysubdivided into: determinate (e.g. ‘man’ in ‘Some man is running’),confused and distributive (e.g. ‘man’ in ‘Every man is an animal’), andmerely confused (e.g. ‘animal’ in ‘Every man is an animal’). The detailsvaried with the author.Sometimes these subdivisions were described via the positions ofterms in categorical propositions. Subjects and predicates of particularaffirmatives, and subjects of particular negatives, have determinatesupposition. Subjects of universal affirmatives and negatives, andpredicates of universal and particular negatives, have confused anddistributive supposition. Only predicates of universal affirmatives havemerely confused supposition.More helpful is the description in terms of descent and ascent. ForOckham (Burley’s and Buridan’s theories are equivalent), a term hasdeterminate 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 specificationof the notions of ‘descent’, ‘ascent’ and ‘singular’ is subtle, but anexample should suffice. In ‘Some man is running’ one can ‘descend’under ‘man’ to a disjunction: ‘Some man is running; therefore, thisman is running or that man is running’, etc., for all men. Likewise onecan ‘ascend’ to the original proposition from any singular: ‘This manis running; therefore, some man is running.’ Hence ‘man’ in the originalproposition has determinate supposition.A term has confused and distributive supposition in a proposition ifand only if it is possible to ‘descend’ under that term to a conjunctionof singulars butnotpossible to ‘ascend’ to the original propositionfrom any singular. Thus in ‘Every man is running’ it is possible todescend under ‘man’: ‘Every man is running; therefore, this man isrunning and that man is running’, etc., for all men. But the ascent fromany singular ‘This man is running; therefore, every man is running’ isinvalid. Hence the term ‘man’ in the original proposition has confusedand distributive supposition.A term has merely confused supposition in a proposition if and onlyif (a) it is not possible to descend under that term either to a disjunctionor to a conjunction, but it is possible to descend to adisjoint 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 isan animal, it does not follow that every man is this animal or everyman is that animal, etc. Much less does it follow that every man is thisanimalandevery man is that animal, etc. But it does follow that everyman isthis animal or that animal or,etc. Again, if it happens that everyman is this animal (i.e. there is only one man and he is an animal), thenevery man is an animal. Hence the term ‘animal’ in that propositionhas 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 confusedsupposition. At first, modern scholars thought it was an attempt toprovide 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 ‘Someman is not a Greek’ has confused and distributive suppositionaccording to the above definitions, but the conjunction to which onecan descend under ‘Greek’ does not give the truth-conditions for theoriginal proposition. Suppose Socrates and Plato are the only men.Then the conjunction ‘Some man is not this Greek [Socrates] andsome man is not that Greek [Plato]’ is true, but the original propositionis false.The problem is that rules for ascent always concern ascent from anyone singular, never from a conjunction. Certain later authors, e.g. RalphStrode, Richard Brinkley and Paul of Venice, do explicitly discuss ascentfrom conjunctions.27But earlier writers such as Burley, Ockham andBuridan conspicuously did not.Another attempt to explain this second part of supposition theorysuggests that the rules for ascent and descent were used in detectingand diagnosing fallacies. This is doubtless correct as far as it goes, butdoes not account for the details in the theory as we actually find it. Inthe end, the exact function of this part of the theory in the earlyfourteenth century remains a mystery.VIIMedieval discussions of ‘insolubles’ (semantic paradoxes like the LiarParadox, ‘The sentence I am now saying is false’) began in the latetwelfth century. By around 1200, theories on how to solve them canbe distinguished. Thereafter, three periods in the medieval insolublesliterature 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 (cassatioorcancelling) maintained that one who utters an insoluble is simply ‘notsaying anything’, in the sense that his words do not succeed in makinga claim. This view, although it has its supporters today, quicklydisappeared in the Middle Ages. Other early theories rejected some orall self-reference; these too have their modern counterparts. Still otherearly theories sound less familiar to modern ears. A few authors arguedthat, despite the surface grammar, the reference in insolubles is alwaysto somepreviousproposition. For example, ‘What I am saying is false’really amounts to ‘What I said a moment ago is false’. The insoluble istrue or false depending on whether I did in fact say something false amoment ago. Others, e.g. Duns Scotus, appealed to a distinctionbetween signified acts and exercised acts. This is the distinction betweenwhat the speaker of an insoluble proposition says he is doing (thesignified act) and what he is really doing (the exercised act). Althoughthe distinction is suggestive, it is far from clear how it solves theparadoxes.Many of these early views are cast in the framework of Aristotle’sfallacy of what is said ‘absolutely’ and what is said ‘in a certain respect’.Discussing that fallacy in hisSophistical Refutations,Aristotle madesome enigmatic remarks (180a38–b3) that suggested the Liar Paradox[17.42]. Consequently, many medieval authors tried to treat insolublesas instances of that fallacy, although there was little agreement on thedetails. Some held that insoluble propositions are true ‘absolutely’ butfalse ‘in a certain respect’. Some had it the other way around. Otherssaid they were both true and false, each ‘in a certain respect’. Stillothers applied the Aristotelian distinction not to truth but tosupposition, so that they distinguished between supposition absolutelyand supposition in a certain respect. Long after the early period in themedieval literature, the fallacyabsolutely/in a certain respectwasretained 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 themsurvived much longer. Burley and Ockham offered nothing new here.Both maintained a theory that merely rejected problematic cases ofself-reference without being able to identify which those problematiccases were.The first to break new ground was Thomas Bradwardine, in theearly 1320s. Bradwardine’s theory was based on a view linkingsignification with consequence. He appears to have been the first tohold that a proposition signifies exactly what follows from it.28Sincehe was also committed to saying thateveryproposition implies itsown truth (e.g. Socrates is running, therefore ‘Socrates is running’ istrue), this means that the insoluble ‘This proposition is false’ signifiesthat it itself is true. Since it also signifies that it is false, it signifies acontradiction, and so is simply false. The paradox is broken.29Bradwardine’s view was enormously influential. Buridan latermaintained a broadly similar theory, and others held variants of it tothe 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 atheory 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 conclusionsfrom his theory: (1) There are false propositions (namely, insolubles)that nevertheless correspond with reality. (2) Valid inference sometimeslead from truth to falsehood. Validity does not necessarily preservetruth, 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 itscontradictory ‘That proposition is true’ (referring to the previousproposition) is also false, since it fails to correspond with reality—theprevious proposition isnottrue. These conclusions generated muchdiscussion in the later literature. Swyneshed’s theory did not have manyfollowers, but it had at least one important one: Paul of Venicemaintained a version of Swyneshed’s theory in hisBig Logic.In 1335, William Heytesbury proposed a theory that rivalled andmay have surpassed Bradwardine’s in influence. He maintained that incircumstances that would make a proposition insoluble if it signifiedjust as it normally does (‘precisely as its terms pretend’), itcannotsignifythat way only, but must signify some other way too. Thus ‘Socrates isuttering a falsehood’, if Socrates himself utters it and nothing else,cannot on pain of contradiction signify only that Socrates is uttering afalsehood, but must signify that and more. Depending on what else itsignifies, and how it is related to the ordinary signification of theproposition, different verdicts about the insoluble are appropriate.Heytesbury himself refused to say what else an insoluble might signifybesides its ordinary signification; that could not be predicted. But somelate authors went on to fill in Heytesbury’s silence. They stipulatedthat insolubles in addition signify thatthey are true,thus linkingHeytesbury’s theory with Bradwardine’s.Heytesbury’s view has an important consequence. Since significationin mental language is fixed by nature, not by voluntary convention,mental propositions can never signify otherwise than they ordinarilydo. Given Heytesbury’s account of insolubility, this means thattherecan be no insolubles in mental language. Heytesbury himself did notdraw this conclusion, but it is there none the less.All important developments concerning insolubles between 1320and 1350 originated with Englishmen and are associated in one wayor another with Merton College. Later writers, in the third and laststage of the medieval insolubles literature, sometimes developed thisEnglish material in interesting new ways. Thus Gregory of Rimini andPeter of Ailly took the above consequence of Heytesbury’s theory toheart. They maintained that there are no insolubles in mental language,and that insolubles arise in spoken and written language only becausethey correspond (are subordinated) totwopropositions in the mind,one true and the other false. Apart from these developments of earlierviews, there seem to be no radically original theories of insolubles inthe Middle Ages after about 1350.VIIIOckham’s theory of connotation has antecedents in Aristotle’s remarkson paronymy (Categories,1a12–15). It is the most highly developedsuch theory in the Middle Ages.For Ockham, some categorematic terms are absolute; others areconnotative. ‘Bravery’ is absolute since it signifies only bravery, a qualityin 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; absoluteterms do not. The notion of a nominal definition is difficult to stateexactly ([17.44]), but all nominal definitions of a connotative term are‘equivalent’ for Ockham in a sense that is perhaps as strong assynonymy. Furthermore, it appears that the connotative term itself issynonymous with each of its nominal definitions, and may be viewedin fact as a kind of shorthand abbreviation for them. Thus the adjective‘white’ is a connotative term having the nominal definition ‘somethinghaving a whiteness’ or ‘something informed by a whiteness’. All threeexpressions 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 absoluteterm ‘whiteness’ and syntactical devices to form nominal definitionslike those above. But it does not, on pain of synonymy, contain a distinctmental adjective ‘white’. (But see section IV, above.)All primitive categorematic mental terms are thus absolute. Thishas important consequences for Ockham’s philosophy. For (barringmiracles) the mind has simple concepts only for things of which it hashad direct experience (‘intuitive cognition’). The supply of absoluteconcepts is therefore a guide to ontology.There is a related theory in Ockham, the theory of ‘exposition’ oranalysis (see [17.34] 412–27). The outlines of this theory wereestablished by the mid-thirteenth century. In brief, an exponibleproposition is one containing a word (the ‘exponible term’) thatobscures 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 isbeginning 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 isan attractive move, since whereas the theory of connotation providesexplicit nominal definitions for connotative terms, it is plausible toview exposition theory as providing contextual definitions of exponibleterms treated as incomplete symbols. Hence, just as the absence ofsynonymy in mental language means that it contains no simpleconnotative terms, so too it would mean that mental language containsno exponible propositions, but only their exponents. Since contextualdefinitions provide the more general approach, it is not surprising thatconnotation theory quickly declined after Ockham, and is treated onlyperfunctorily in Strode and Wyclif. Its place is taken there by muchmore elaborate treatments of exponibles. Buridan does retain a fairlyfull theory of connotation, but it is not so detailed as Ockham’s.30Although the theory of exposition continued to have a life of itsown, by mid-century it had also been incorporated into the theory of‘proofs of propositions’.31Billingham’sYouth’s Mirrorwas a seminalwork here.The notion of ‘proof’ involved in this literature was broader thanthe Aristotelian demonstration of thePosterior Analytics. It meant anyargument showing that a certain proposition is true. Not allpropositions can be ‘proved’. Some of them serve as ultimate premissesof all proofs; they must be learned another way. Such elementarypropositions 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 immediatepropositions. Billingham recognized three methods for such proofs:exposition, ‘resolution’ and proof using an ‘auxiliary’(officialis)term.Exposition has already been explained. Resolution amounts to proofby 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 aproblem. The premisses of this inference are not immediate, since theirpredicates are not immediate terms. And there appears to be no way toreduce them to yet more basic propositions by any of the three waysBillingham recognizes.‘Auxiliary’ terms govern indirect discourse. They include epistemicverbs such as ‘knows’, ‘believes’, etc., and modal terms such as ‘it iscontingent’. To ‘prove’ a proposition containing an auxiliary term is toprovide an argument spelling out the role of the auxiliary term. One ofthe premisses of this argument states how the proposition referred to inindirect discourse ‘precisely signifies’. Thus ‘It is contingent for him torun’ is proved by: ‘“He runs” is contingent; and “He runs” preciselysignifies for him to run; therefore, it is contingent for him to run.’There are still many obscurities in the theory of ‘proofs ofpropositions’. But it was very widespread.IXOur knowledge of late medieval logic has advanced enormously sincethe 1960s. The availability of previously unpublished texts has shedgreat light on this fertile period. Yet, as this chapter shows, there is stillmuch that is unknown. The general reader should regard the claims inthis chapter as tentative. Readers with specialized training or interestshould regard them as an invitation to further research.NOTES1CHLMP,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 isexpressed by a sentence(-token). I shall use ‘proposition’ in its medieval sensethroughout this chapter except where indicated.3 De Rijk [17.29], especially vol. 1. Onconsequentiaein the twelfth century, seeChapter 7 above, pp. 157–8, 175–6.4CHLMP,ch. 11.5CHLMP,ch. 16. Despite the name, these disputations had nothing to do withethics or morality. They were not about deontic logic. Their exact purpose is stilluncertain.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, andreferences there. See alsoCHLMP,chs 12 and 16B.8 For information on authors mentioned in this section, seeCHLMP,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 toHeytesbury himself.11 On Angelo, see Spade [17.45] 49–52. For other authors mentioned in thisparagraph, 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 orthe ‘language’ ofPrincipia Mathematica. In medieval usage, the latter wouldlikewise count as ‘artificial’ languages, but so would English; the only truly naturallanguage 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 Somethingabears the ancestral of relationRtozif and only ifabearsRtosomethingbthat bearsRto somethingcthat…that bearsRtoz.16 With this section, seeCHLMP,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 forsupposition.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 doxasticcontexts. SeeSophismata[17.16], IV, sophisms 9–14. With the remainder of thissection, 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], andCHLMP,ch. 9.25 Spade [17.43]. In so far as such contexts can arise in mental language, this viewrequires 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 isappellatioor ‘appellation’ (Sophismata,IV).31 With this last part of section VIII, see Ashworth and Spade [17.28] and referencesthere.BIBLIOGRAPHYOriginal Language Editions17.1 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 compositeet diviso,St Bonaventure, NY, Franciscan Institute, 1961.17.6 De Rijk, L.M. (ed.)Peter of Spain: Tractatus, Called Afterwards SummuleLogicales,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=Operatheologica; 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, inseveral fascicles. Editors and translators vary.)17.9 Grabmann, M. (ed.)Die Introductions in logicam des Wilhelm vanShyreswood,Munich, Verlag der Bayerischen Adademie derWissenschaften, 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.) ‘LoSpeculum puerorum sive Terminus est in quemdi RiccardoBillingham’,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 Translations17.17John Buridan’s Logic: The Treatise on Supposition, the Treatise onConsequences,trans. P.King, Dordrecht, Reidel, 1985.17.18John Buridan: Sophisms on Meaning and Truth,trans. T.K.Scott, New York,Appleton-Century-Crofts, 1966. (translation of [17.16])17.19John 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. (Thepaperback edition omits the Latin text, and has different pagination andsubtitle.)17.20Paul of Venice: Logica parva,trans. A.R.Perreiah, Washington, DC, CatholicUniversity of America Press, and Munich, Philosophia Verlag, 1984.(translation of [17.14])17.21Peter of Spain: Language in Dispute,trans. F.P.Dinneen, Amsterdam, J.Benjamins, 1990. (translation of [17.6])17.22William Heytesbury, On ‘Insoluble’ Sentences: Chapter One of His Rules forSolving Sophisms,trans. P.V.Spade, Toronto, Pontifical Institute ofMediaeval Studies, 1979. (translated from [17.11])17.23William of Ockham: Ockham’s Theory of Propositions: Part II of the Summalogicae,trans. A.J.Freddoso and H.Schuurman, Notre Dame, Ind.,University of Notre Dame Press, 1980.17.24William 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, 1974.17.25William of Ockham: Predestination, God’s Foreknowledge, and FutureContingents,trans. M.M.Adams and N.Kretzmann, New York, Appleton-Century-Crofts, 1969; 2nd edn, Indianapolis, Ind., Hackett, 1983.17.26William of Sherwood’s Introduction to Logic,trans. N.Kretzmann,Minneapolis, Minn., University of Minnesota Press, 1966. (translation of[17.9])17.27Peter 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 Surveys17.28 Ashworth, E.J. and Spade, P.V. ‘Logic in Late Medieval Oxford’, inThe Historyof the University of Oxford,vol. II, Oxford, Clarendon Press, 1992.17.29 De Rijk, L.M.Logica Modernorum,vol. I,On the Twelfth Century Theoriesof Fallacy,Assen, Van Gorcum, 1962; vol. II,The Origin and EarlyDevelopment 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 andindices.)17.30CHLMP.17.31 Kretzmann, N. (ed.)Meaning and Inference in Medieval Philosophy: Studiesin Memory of Jan Pinborg,Dordrecht, Kluwer, 1988.17.32 Lewry, P.O. (ed.)The Rise of British Logic: Acts of the Sixth EuropeanSymposium 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: Actsof 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 MedievalConceptions of the Bearers of Truth and Falsity,Amsterdam, NorthHolland, 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 Symposiumon Medieval Logic and Semantics, Copenhagen, 16–21 November 1975,Copenhagen, Museum Tusculanum, 1976.Studies of Particular Topics17.38 Gál, G. ‘Adam of Wodeham’s question on the ‘complexe significabile’ as theimmediate object of scientific knowledge’,Franciscan Studies37 (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 thePropositio’, Journalof Philosophy67 (1970):767–87.17.41 Pinborg, J. ‘The English contribution to logic before Ockham’,Synthese40(1979): 19–42.17.42 Spade, P.V. ‘The origin of the mediaevalinsolubilialiterature’,FranciscanStudies33 (1973): 292–309.17.43 ——‘Ockham’s rule of supposition: two conflicts in his theory’,Vivarium12(1974): 63–73.17.44 ——‘Ockham’s distinction between absolute and connotative terms’,Vivarium13 (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 Studies35 (1975): 212–22.17.47 ——‘Synonymy and equivocation in Ockham’s mental language’,Journal ofthe History of Philosophy18 (1980): 9–22.17.48 ——‘Insolubiliaand Bradwardine’s theory of signification’,Medioevo: Rivistadi storia della filosofia medievale7 (1981): 115–34.17.49 ——‘Five early theories in the mediaevalinsolubilialiterature’,Vivarium25(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’,Mind79 (1970): 586–90.