Moody 2018: William of Ockham and his Milieu

From the 2nd to the 4th of March, the University of California Los Angeles will be hosting the yearly Moody Workshop in Medieval Philosophy. This meeting is named after Earnest Addison Moody, a former member of the Philosophy Department and a founding member of the UCLA Centre for Medieval and Renaissance Studies – which are jointly sponsoring the event.

Professor Moody was one of the the pioneers of Medieval Philosophy in North America and one of the first scholars to approach the study of medieval philosophical theories in their own right, without subordinating them to theological views. But for those who have even a passing interest in the history of logic, E. A. Moody is first and foremost the author of  Truth and Consequence in Medieval Logic (19531), one of the most influential volumes in the historiography of medieval logic and of medieval philosophy as a whole.

A Williams College graduate (class 1924), E. A. Moody obtained his PhD from Columbia in 1936, with a thesis on William of Auvergne’s Treatise De anima. While teaching at Columbia, he developed an interest in the history of medieval logic and science. Having retired for a few years to a ranch in Texas, in 1958 he joined the Department of Philosophy at UCLA; there he found a department not only already traditionally strong in logic and language but that was undergoing further changes toward that direction as well – in other words, the perfect fit for Moody’s own research interests.

Above all, those research interest left a significant imprint on the way we look at medieval philosophy in general and at the history of medieval logic in particular, especially in North America. Since the 19th century, the history of the study of medieval philosophy had been almost entirely shaped by quasi-nationalistic and quasi-theological concerns. Leo XIII’s Aeterni Patris encyclical (1879), by restoring “Christian Philosophy in Catholic Schools in the spirit of the Angelic Doctor, St. Thomas Aquinas”, was pivotal in determining a dominant picture of medieval philosophy that had both the kind of uniformity that scholars like Maurice De Wulf ascribed to terms like “scholasticism” and Aquinas as the central figure. True enough, this picture of medieval philosophy as fundamentally homogenous began to break down when Étienne Gilson and others started to realise that it couldn’t manage to account for roughly a thousand years of philosophical speculations. But even so, after Aeterni Patris typically there was still an idea that medieval philosophy had seemingly emerged out of the wreckage of the Roman Empire, grown slowly to a peak with Aquinas, and then began to decay – Gilson, for example, thought that the decay culminated in Descartes. Various people had slightly different pictures, but it was always as a curve and Aquinas was typically at its peak. Now, Moody had a different agenda and a different set of thoughts: he pursued his interests in medieval logic, language and science in connection to the contemporary discussions in logic and language – an whatever Aquinas was up to, an emphasis on logic and language wasn’t really that. This pushed Moody’s interests later, well into the 14th century, and had the consequence that the people who where interested in what Moody was interested in started to look more closely and seriously at the later middle ages, finding in 14th century philosophy a veritable goldmine, while it simultaneously became a common practice to develop those interests in the history of science, logic and language in connection with analogous contemporary endeavours. That ultimately set the tone for Medieval Philosophy on this side of the Pond. E. A. Moody remained at UCLA until his retirement in 1969 and in 1972 was succeeded by Marilyn McCord Adams. Even if McCord Adams later on became much more interested in philosophical theology, when she was at UCLA her major work was on Ockham – and it wasn’t really a theological work at all, rather it focused on Ockham’s logic. Overall, what Moody’s influence in North America amounted to was creating a climate in which Medieval Philosophy could be moved out of theology and toward philosophical issues relevant for contemporary discussions; from that kind of point of view, the 14th century was one of the most interesting things one could study, and in many ways, still is. Nobody else among the major figures who were doing medieval philosophy in Moody’s generation had anything like that on their agenda or achieved similar results.

The Moody Workshop was instituted by Calvin Normore, when he took over the mantle of Medieval Philosophy at UCLA in 1998. The first speaker in the first Moody Workshop was Martin Tweedale, Moody’s last student at UCLA. Since then a small group of scholars meets every year to discuss a particular topic in medieval philosophy, usually among those that would have met Moody’s interest. This year’s meeting, on William of Ockham and his Milieu, is dedicated to the memory of Marilyn McCord Adams.



3:30 PM Peter King (Toronto)
Mental Without the Mind: Ockham’s Radical Revolution


10:00 AM Jenny Pelletier (Leuven)
What is Dominium? Ockham and the Ontology of Lordship

11:30 AM Mikko Yrjönsuuri (Jyväskylä)
Valid on Formal Ground: Burley, Ockham and Buridan

1:00 PM Lunch

2:00 PM Magali Roques (Helskinki)
Ockham’s Theory of Real Definitions

3:30 PM Graziana Ciola (UCLA)
Relativa grammaticalia and the Regimentation of Latin in 14th Century Logic


10:00 AM André Martin (McGill)
What Can the Ockham/Chatton Debate on Self‐Awareness Tell us About Medieval Accounts of Consciousness?

11:30 AM Josh Blander (The King’s College)
Does Ockham Have Priorities?

1:00 PM Lunch

2:00 PM Tom Ward (Baylor)
Ockham on Omnipotence, ‘LogicalImpossibility’, and Hating God

3:30 PM Christopher Martin (Auckland)
Suppose God did not Exist, or that the Eye Were an Animal: Impossible Positio and its use by Scotus, Ockham and Chatton


If you happen to be around, come and join us!

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Three-year lectureship in medieval philosophy, Charles University, Prague

Boosting the signal:

Job offer: Lecturer in philosophy
Department of Philosophy and Religious Studies
Faculty of Arts, Charles University

The Department of Philosophy and Religious Studies, Faculty of Arts, Charles University invites applications for one full-time three-year position at the lecturer level (starting at AP2 in the Czech scale), beginning October 1st 2018.

Info about the department:

The area of specialization for the position will be medieval philosophy possibly with another area of specialisation.

Responsibilities for the position include:

  • teaching philosophy courses at the undergraduate as well as graduate level: 7 courses (course = 90 min per week) in one academic year (academic year = two terms), i.e. 3 courses in one term, four courses in the other term
  • supervising students
  • student’s examination
  • contributing to the curriculum development as appropriate
  • establishing and maintaining independent research
  • participating in the academic life of the department


  • PhD in philosophy or a related field
  • teaching experience
  • publication record
  • working knowledge of Latin (the curriculum includes Latin reading classes)
  • excellent command of English (or Czech) both in writing and speaking; knowledge of Czech is not required but working knowledge of it is expected after two years (in the case the contract should be prolonged); good knowledge of one other language (preferably German or French)

Conditions of employment

The Faculty of Arts offers a salary up to 30 000 CZK with possibility of further increase depending on the research outcomes of the employee. The Faculty covers social and medical insurance according to EU regulations. According to the university rules the contract can be prolonged after three years; the prolongation is either for another period of three years or tenure. The probationary period is three months.

Starting date: 1st October 2018


You may apply for this position until 15th March 23:59h / before 16th March 2018 Prague local time. Submission by mail or in person: the application with all its attachments can be sent by mail or delivered in person to the following address: Hana Vamberská, Human Resources Dept., FF UK, nám. Jana Palacha 1/2, 116 38 Praha, Czech Republic

Submission by e-mail: the application with all its attachments can be sent by e-mail to the address

The application must include the following:

  1. a cover letter containing your motivation for the position
  2. cv and list of publications
  3. the names and contact details of two referees and an indication whether we can contact them at this stage
  4. a sample of a written work that is relevant to this position, not more than 10 000 words; it may be a published or unpublished sample and may be an extract from a longer piece
  5. teaching evaluation (if available)
  6. suggestion of a syllabus for an undergraduate course on medieval philosophy (two terms, 20-24 lectures (one lecture = 90 min); the aim of the course should be introduction to medieval philosophy (possibly its sources and impacts on later tradition) for philosophy students on BA level

The application process will be in two rounds. The committee appointed by the dean of the Faculty of Arts decides in the first round on the basis of submitted materials. The candidates invited for the second round will be asked to (a) deliver a public lecture in the Department of Philosophy and Religious Studies, Faculty of Arts, Charles University and (d) be available for an interview with the committee.

The shortlist of candidates for the second round will be available by early April 2018; lectures and interviews are scheduled for late April and early May 2018.


For additional information you can contact:
Dr. Jakub Jirsa, Head of department, (job profile and academic matters)

Hana Vamberská, (application procedures)

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Brill’s “Investigating Medieval Philosophy” series

In case any of our readers don’t already know about it, Brill has a book series “Investigating Medieval Philosophy”, edited by John Marenbon and with an editor board: consisting of Margaret Cameron, Simo Knuuttila, Christopher J. Martin, and our very own Martin Lenz. The series aims to publish two volumes a year, and:

The series aims to provide a peer-reviewed forum for high-quality monographs and coherent collective volumes on medieval philosophy, written in such a way as to make them comprehensible and interesting to mainstream philosophers and historians of philosophy in Anglophone philosophy departments. Volumes in the series are not required to use medieval philosophy to make a direct contribution to debates in contemporary analytical philosophy (although this is one possibility), but the manner in which the medieval texts are treated should reflect, in an historically sensitive way, the methods and the language of contemporary analytical philosophy – in especial, its ideals of clarity and unpretentiousness. There are many different varieties of this general ‘analytical’ approach, and the series is open to any of them. The scope of medieval philosophy is taken widely, to include the Arabic, Greek and Jewish traditions, as well as the Latin one, and to run from c.500 to c.1500; works which go on even so far as 1700 may be considered, if they are at least equally concerned with the period before 1500.

For more information, including titles in the series, see here.

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John Trevisa on the rational soul

Earlier this week I picked up John Trevisa’s Middle English translation of Bartholomeus Anglicus’s De Proprietatibus Rerum ‘On the Properties of Things’, for reasons entirely unrelated to logic and philosophy (mostly because I wanted to learn things like “why do you never seen angels’ thighs when they are depicted by painters in corporeal form?” and “what does the shape of your soul say about you?” and “why is the stomach ridged and ribbed instead of smooth?” and other such important questions). But what Anglicus/Trevisa has to say about ‘rationality’ is interesting.

Bartholomeus Anglicus was a 13th-century English Franciscan who studied at the university of Paris. His compendium De Proprietatibus Rerum, an early forerunner of the modern encyclopedia, was written around 1240 at Magdeburg, and draws upon a tremendous wealth of resources, classic and medieval, western and eastern, dipping into philosophy, theology, medicine, natural sciences, biology, astronomy, geography, etymology, etc. What I’ve found fascinating about it so far is how many of his sources he cited by name, far, far more than the usual “some say” that you often get in medieval texts.

John Trevisa, a Cornishman who was educated at Exeter College, Oxford, and worked in the circle of Wyclif at Queen’s College, translated De Proprietatibus Rerum into Middle English while he lived and worked in Berkeley, Gloucestershire, around 1397-1399. The first printed edition of the Middle English text was produced by Wynkyn De Worde, around 1495, attesting to its importance.

I’m finding Trevisa’s Middle English somewhat more accessible than Chaucer’s; most of the words are easily identifiable as their modern counterparts, though archaic forms of the being verb like ‘buþ’ and ‘beþ’ threw me at first until I figured them out. One verb which turns up quite a bit that I was not familiar with previously is fongen, which has proven to be quite a useful and versatile word and I’m sorry it has fallen out of common currency in English. (I also lament the loss of the variant ‘noseþirl’ for ‘nostril’.)

All that by means of introduction. I thought it would be interesting and semi-relevant for the topic of this blog to say something about Anglicus/Trevisa’s view of rationality and the rational soul, which is not the typical view I’m used to.

First, in Book III, Chapter 6 Trevisa (or rather Trevisa-translating-Anglicus, but I’m just going to say “Trevisa” from here on out) notes that there “fyue maner myȝtes and vertues” that the soul has: (1) “felinge”, (2) “bodiliche wit”, (3) “ymaginacioun”, (4) “racio ‘reason'”, and (5) “intellectus ‘vndirstondinge and inwit'”. Reason is glossed as the power to “demeþ betwene gode and euel and soþ and fals”. The first three powers are common to both men and other beasts, and depend upon a composite of body and soul. But the latter two powers are found in men alone, and do not require a body; for they “beþ in þe soule, in þat he may be departid from þe body and abide departid as an aungel.” The power in such a disembodied soul which “biholdeþ þe ouer þinges” is intellectus, and the power which “beholdiþ þe neþer þinges” is racio.

When we consider the ends of the soul, three properties or virtues of the soul can be distinguished, namely (1) “racionalis, þerby he takeþ hede to þing þat is soþ and trewe”, (2) “concupissibilis and þerby he takeþ hede to þing þat is good”, and (3) “irascibilis and þerby he takeþ hede to þing þat is grete and huge and to þing þat is euerlastinge”. We’ll ignore (2) and (3) for now; but of (1), Trevisa says that “in þe racional is knowinge [soþ].”

However, if we consider the soul with respect to its workings (and this is the topic of Chapter 7), we can distinguish three virtues that are found in the soul:

  1. vegetabilis þat ȝeueþ lif”
  2. sensibilis þat ȝeueþ felinge”
  3. racionalis þat ȝeueþ resoun”

Whatever has a sensible soul also has a vegetative soul, and whatever has a rational soul also has a sensible one.

For Trevisa and Anglicus, the only reason to exercise reason is to become closer to God. I’m kind of disappointed that there is no more explicit discussion of reasoning, of logic, of dialectics, or argument, or anything of how one can use reason to know what is “soþ and trewe” — because surely isn’t that the interesting bit? Maybe this topic will come up again — the work does have, after all, nineteen books each of which is divided up into many chapters — so there’s still hope that I can revisit the topic again!

In the meantime, I’m live-tweeting my way through the book under the hash-tag #PropThings, if you want to follow along!

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Syllogism Mnemonics

The other day a colleague of mine asked if I had anything I could send him regarding the medieval syllogism mnemonics. I told him there was some info in the textbook I’m writing, but it’s rather idiosyncratic to the way I present the syllogistic, and that instead I’d write up something specific for him. When he protested, I told him it’d be a useful thing to have on the Medieval Logic blog, which we hope to update every Thursday. It’s this sort of thing precisely that blogging is good for! I may not need this collected information now, but I’m sure I’ll use it sometime in the future.

Syllogisms are characterised by their figure — the relative arrangement of the terms — and their mood — the triple of copulae that connect the terms.

Figure 1 Figure 2 Figure 3
P__M M__P P__M
M__S M__S S__M
P__S P__S P__S

(where P is the predicate of the conclusion (the major term), S is the subject of the conclusion (the minor term), and M is the middle term).

William of Sherwood in his Introduction to Logic (c1240, [1]) provides his students with a mnemonic verse to remember which figure is which:

The difference of the figures is retained in this verse: Sub pre prima bis pre secunda tertia bis sub (66).

That is, in the fist figure, the middle term is first the subject and then the predicate; in the second, it is the predicate twice; in the third, it is the subject twice. (This same verse occurs in Roger Bacon [5, ∥ 290], and Lambert of Auxerre, their contemporary, has the same content in a much more verbose form [5, 139].)

Following this, he then says:

The moods and their reductions, on the other hand, are retained in these verses:

Barbara celarent darii ferio baralipton
Celantes dabitis fapesmo frisesomorum
Cesare camestres festino baroco
Darapti felapton disamis datisi bocardo ferison

Kretzmann notes that this is “the oldest known surviving version of these famous mnemonic verses, and Sherwood may have been the inventor of them…However, there were earlier attempts at the same sort of device in the thirteenth century, and the word ‘Festino’ appears ‘in a MS dating at the latest from 1200′” [citing Bochenski] (66-67), though later in the same footnote he compares Sherwood’s verses to those in Peter of Spain and concludes that the differences between the two “strongly suggest at least one earlier version on which both men were drawing” (67).

Sherwood explains the mnemonic names as follows:

In these lines ‘a’ signifies a universal affirmative proposition, ‘e’ a universal negative, ‘i’ a particular affirmative, ‘o’ a particular negative, ‘s’ simple conversion [conversio simplex], ‘p’ conversion by limitation [conversio per accidens], ‘m’ transposition of the premisses, and ‘b’ and ‘r’ when they are in the same word signify reduction per impossibile. The first two lines are devoted to the first figure, the four words of the third line to the second figure, and all the other words to the third figure (67).

(Note that, conveniently, ‘a’ and ‘i’ are the first two vowels in Latin affirmo ‘I affirm’, and ‘e’ and ‘o’ are the two vowels in Latin nego ‘I deny’.) While the names that Sherwood introduces are typical/traditional, the explanation that he gives of the names is not. First, he doesn’t note that the first letter of the name indicates to which of the four basic syllogisms, Barbara, Celarent, Darii, and Ferio, the others can be reduced to. Second, his identification of ‘b’ and ‘r’ as the cues for reductio per impossibile are atypical (it’s not much of a mnemonic; why not, e.g., ‘r’ alone?)

Other roughly contemporary texts offer a slightly different version of the verses and explanation of the names. Roger Bacon in his Art and Science of Logic [5] has a verse for remembering the types of conversions (Maloney notes that similar verses also occur in the 12th-century Logica Ut Dicit and the Logic ‘cum sit nostra’la):

Simpliciter feci convertitur, eva per acci,
Acto per contra. Sic fit conversio tota (∥ 279)

and he notes that “‘E’ signifies a universal negative, ‘I’ a particular affirmative, ‘A’ a universal affirmative, and ‘O’ a particular negative” (∥ 279). The list of mnemonic names, identical to Sherwood’s, appears in ∥ 295, and is explained in ∥ 296; he corrects Sherwood’s apparent mistake and identifies ‘c’ as the code for reductio per impossibile. Lambert also has the same list of names (143), except that he names the second mood of the second figure “Campestres”; the addition of the ‘p’ is not warranted.

Peter of Spain in his Summaries of Logic, written shortly after Sherwood’s, [2] says:

Barbara Celarent Darii Ferio Baralipton
Celantes Dabitis Fapesmo Frisesomorum
Cesare Cambestres Festino Barocho Darapti
Felapto Disamis Datisi Bocardo Ferison

In these four verses are nineteen words representing the nineteen moods of the three figures, so that by the first word we understand the first mood of the first figure, by the second word the second mood, and so on for the others…

…By the vowel A we understand the universal affirmative, by E the universal negative, by I the particular affirmative, and by O the particular negative…

…It must be understood that all the moods indicated by a word beginning with ‘B’ are to be reduced to the first mood of the first figure, and ll the moods signified by a word beginning with C to the second mood, those beginning with D to the third, and those with F to the fourth. Also, wherever an S is put in these words, it signifies that the proposition understood by the immediately preceding vowel is to be converted simply. And by P it signifies that the proposition is to be converted accidentally [converti per accidens]. Wherever M is put, it signifies that a tranposition in premisses is to be done…Where C is put, however, it signifies that the mood understood by that word is to be confirmed by impossibility (191, 193).

Peter of Spain’s identification of “C” (by which we should understand NOT the “C” which begins the word) with reductio per impossibile is orthodox.

Copenhaver et al. also have a footnote, noting that “since the verses scan as Latin hexameters, Latin was almost certainly the language in which they were first written” (contra Prantl who “contends that the first mnemonic lines were Greek and formulated by Psellus (b. 1020)” [3, 519]), and that Sherwood’s verses “appear in the Dialectica monacensis and the Logica ‘cum sit nostra’, treatises dated before or around 1200 by de Rijk…note that de Rijk thinks that BARBARA CELARENT is a later interpolation in the Dialectica monacensis” (191). They also mention related material in the Ars burana and Ars emmerana, also edited by de Rijk, and some mnemonic verses found in a 9th C text [3]. These verses, appearing in Codex Sti. Galli 64, “though they do not contain the technical words, Barbara, etc., or their equivalent, yet served the purpose for which those words were afterwards invented” (519). (Because the verses are long and can be read in full, for free, on JSTOR, we do not quote them here.) Turner notes that

it would, of course, be idle to look for evidences of an original contribution to the science of logic. It belongs to an age in which originality was not a dominant characteristic of teachers of logic. It simply sums up what was to be found in the treatises of Apuleius, Martianus Capella, Cassiodorus, and Isidore. Its terminology does not vary essentially from that which was current in the schools of the ninth and tenth centuries (525).

In the few cases where the terminology used is not standard, this is due to the need to pick terms that fit the desired meter.

Let us return to the matter of the verses and material in the Dialectica monacensis, the Logica ‘cum sit nostra’, and the Artes burana et emmerana. De Rijk notes that “I have not been able to find these verses in twelfth century treatises. It should be noted, however, that the famous verses BARBARA, CELARENT had a few forerunners in two twelfth century tracts on syllogism” (401), namely the Ars emmerana and the Ars burana, which we will discuss below.

The Logica ‘cum sit nostra’ contains chapter on the syllogisms which in de Rijk’s edition [4] contains:

Barbara Celarent Darii Ferio
Baralipton Celantes Dabitis Fapesmo Frisesomorum
Cesare Campestres Festimo Baroco Drapti
Felaptdon Disamis Datisi Bocardo Ferison.

A notat universalem affirmativam, E notat universalem negativam, I particularem affirmativam, O particularem negativam…

…Consequenter dicendum est de reductione. Et sciendum quod omnes modi debent reduci in quatuor primos modos prime figure, quia omnes modi incipientes per B debent reduci in Barbara, per C in Celarent, per D in Darii, per F in Ferio.

Et reducuntur per tria, scilicet per conversionem, per transpositionem, et per impossibile. Unde sciendum quod S denotat conversionem simplicem, P conversionem per accidens, M transpositionem propositionum, C reductionem per impossibile. Unde versus:

S simplx, P per acc.
M transpos., C notat impossibile (436).

In the Dialectia Monacensis, we have the following:

Hec omnia facilius possunt haberi per hos versus:

Barbara * Celarent * Darii * Ferio * Baralipton *
Celantes * Dabitis * Fapesmo * Frisesmomorum

In hiis versibus sunt novem dictiones novem modis prime figure deservientes, prima primo et secunda secundo, et sic deinceps. Horum autuem versuum triplex est utilitas. Prima est quia scitur quales et quante debeant esse propositiones in qualibet materia; et hoc per vocales istarum dictionem: per A intelligitur universalis affirmativa, per E universalis negativa, per I particularis affirmativa, per O particularis negativa…Secunda utilitas est quia scitur qui sillogismi in quos habeant reduci; et hoc per initiales litteras istarum dictionum. Tertia utilitas est quia scitur per quid unusquisque sillogismus reducator: hec enim littera S ubicumque inventiur est signum simplicis conversionis; B vero significant conversionem per accidens; M vero significat transpositionem premissarum, idest quod de maiore fiat minor et econverso (494).

Note the use of “B” to stand for accidental conversion; this cannot be correct since (a) it leaves Fapesmo and Baralipton wholly unexplained and (b) Dabitis cannot be proven if the major premise is accidentally converted.

A separate verse is given for the second and third figure syllogisms:

Et sciendum quod omnia que dicta sunt de secunda et tertia figura, faciliter possunt haberi per hos versus:

Cesare * Camestres * Festino * Baroco *
Darapti * Felapton * Disamis * Datisi * Bocardo * Feriso *

In hiis versibus sunt decem dictiones. Inter quas prime quatuor deserviunt secunde figure et alie que secuntur deserviunt tertie figure, ita quod prima primo, et ita deinceps (497-498).

Of these verses, de Rijk notes “something peculiar must be noticed” (413) about their placement; the verse concerning the first figure appears after the discussion of the first figure, but the verses discussing the second and third figure occur together after the discussion of the third figure. He says that “this peculiar arrangement of the mnemonic verses strongly suggests that they were interpolated in the original treatise” (413) and that there was insufficient margin space to add the verses at the end of the discussion of the second figure, which is why they were saved for a later space.

What about the early hints towards the later mnemonics that de Rijk found in the Ars Emmerana and the Ars Burana? We have no verses in AE, but there is a clear attempt to encode the relevant information of a mood in terms of letters:

Notandum quod universalis affirmative designantur his quatuor literis E I O U; universales negative his: L M N R; particularis affirmative tribus: A S T; particulares negative tribus: B C D.

Secundum hoc he novem voces designent novem modos prime figure:


he quatuor voces designant quatuor modos secunde figure:


sex modi tertie figure his sex designantur:

EVA * NEC * AUT * ESA * DUC * MAC (173).

Here, only the quality and the quantity of the propositions involved in the syllogisms are mentioned.

The mnemonic material in the Ars Burana is similar:

He littere E I O V significant universales affirmativas; et he littere L M N R significant universales negativas; et he A S T significant particulares affirmativas; et he B C D significant particulares negativas (199).

With this convention established, the author goes on to say that:

De modis igitur prime figure talis assignatur versus:


Each of these syllogisms is then exemplified; VIO is Barbara, NON is Celarent, etc. A similar verse is given for the second figure: “REN ERM RAC OBD” (203), and the third: “EVA NEC AVT ESA DVC NAC” (205).

So much for the period up through the 13th century. What about afterwards? I have fewer 14th-century treatises on my shelves, but Buridan has a chapter on syllogisms in his Summulae de Dialectica [7]. In that chapter, the mnemonic names are taken completely for granted; Buridan refers to Disamis and Bocardo before he even introduces the concepts of figure and mood, thus assuming that these are already familiar to the reader (310). The mnemonic verse itself doesn’t appear for another 10 pages or so, where he introduces the verse (320), explains how to form a syllogism from the names given (321), and then explains “the verse insofar as it indicates the reduction of imperfect to perfect syllogisms” (321). His explanation follows that of Peter, Bacon, Lambert, etc.

The final person I’d like to mention in this post is Paul of Venice, if for no other reason than that I’m in the process of editing and translating his chapter on syllogisms from the Logica Magna, written at the very end of the 14th century. Paul also assumes familiarity with the names in that he uses them before he explains them:

Having seen what is required for a syllogism in the first figure, it remains to show the moods which are syllogized in the same [figure]. And they are six, namely: Barbara, Celarent, Darii, Ferio, Fapesmo, Frisesomorum.

(Note that he omits Dabitis and Celantes). He says:

Whence it must be noted that in whatever mode, some of these four vowels, namely a, e, i, o, are put in. ‘a’ denotes the universal affirmative, implicitly or explicitly. ‘e’ [denotes] the universal negative, implicitly or explicitly, ‘i’ the particular, indefinite, or singular affirmative, implicitly or explicitly. ‘o’ denotes the particular, indefinite, or singular negative, implicitly or explicitly.

(Paul differs from earlier writers in explicitly including indefinites and singulars in his syllogistic, and he assimilates them to the particulars, rather than to the universals, as some other commentators did.)

There is one way in which Paul’s discussion of the mnemonics is utterly unlike anything that I have seen preceding him. He says:

It is considered whether in a mood there are four such letters by the multiplication of one, or not…However, if this is so [that you have four letters rather than three, e.g., Barbarai], it will happen that you know the conclusion is able to follow according to the third or fourth denotation. Hence in Barbara is ‘a’ triplicated, and a simple solitary ‘i’ for that reason may be denoted by such mood that the premisses are implicitly or explicitly universals according to a two-fold precession of that term ‘a’, that is, because of their position. The conclusion which is able to be inferred either implicitly or explicitly is denoted by the third vowel, but because there is a final ‘i’, for this reason it may be denoted by the particular, indefinite, or affirmative itself, it is possible to infer either explicitly or implicitly, just as is stated in the example.

What’s going on in this section is not entirely clear, though it became clearer when we worked through my draft translation in the St Andrews medieval logic/Latin reading group a year or two ago. What we think is going on is that Paul is explicitly noting the validity of “Barbari”, a syllogism which has otherwise not been mentioned at all in any of the mnemonics above.

It is not until Paul introduces Fapesmo, the first non-perfect syllogism in hist list above, that he explains the other letters in the names:

Whereby any mood beginning with ‘B’ is able to be reduced to Barbara, everyone beginning with ‘C’ to Celarent, and everyone beginning with ‘D’ to Darii. And everyone beginning with ‘F’ to Ferio: But, as this is able to done, you ought to note that whenever ‘S’ is put down in these words, it signifies that the proposition indicated by the vowel immediately preceding ought to be converted simply. Wherever a ‘P’ is put down it signifies that the proposition indicated before the ‘P’ ought to be converted per accidens, and wherever an ‘M’, it is denoted that a transposition of the premises ought to be made, that is, to make the minor of the major and conversely. However, where ‘C’ is put down, it is denoted that this mood or a syllogism formed in the same should be reduced per impossibile.

He then gives this verse:

Simpliciter verti universaliter, ‘S’, ‘P’ vero per accidens, ‘M’ vult transponi, ‘C’ per impossibile duci.

I had intended in this post to also write about the verses relating to the square of opposition, especially the modal one; but I think that this point, that’s best saved for another post! One other aspect that I haven’t mentioned at all here is the mnemonic tradition in commentaries on the Prior Analytics, and that is because I have no idea what such a tradition is, or if it even existed. Again, a topic for another post! One final topic for another post, if only because I am running out of time, is how long these syllogism mnemonics persisted as pedagogical tools; in particular, I’d like to look at these and other 16th-century logic textbooks to see if the syllogism mnemonics show up in them.


[1] William of Sherwood, Introduction to Logic, translated with an introduction and notes by Norman Kretzmann (University of MN Press: 1966).

[2] Peter of Spain, Summaries of Logic, text, translation, introduction, and notes by Brian P. Copenhaver with Calvin Normore and Terence Parsons (OUP: 2014).

[3] William Turner, “Mnemonic Verses in a Ninth Century MS.: A Contribution to the History of Logic”, The Philosophical Review Vol. 16, No. 5 (Sep., 1907), pp. 519-526, JSTOR link

[4] L. M. de Rijk, ed., Logica Modernorum: A Contribution to the History of Early Terminist Logic vol. II, parts one & two (Van Gorcum, 1967).

[5] Roger Bacon, Art and Science of Logic, trans. Thomas S. Maloney, (PIMS 2009).

[6] Lambert of Auxerre, Logica or Summa Lamberti, T. S. Maloney, trans., (University of Notre Dame, 2015).

[7] John Buridan, Summulae de Dialectica, trans. with an introduction by Gyula Klima (Yale University Press, 2001).

[8] Paul of Venice, Logica Magna (Venice, 1499).

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The Historian (of Logic)’s Craft – A conversation with Calvin Normore

Today, rummaging through my files, I stumbled upon the transcript of a very informal interview I had several months ago with Calvin Normore, for an issue of The Reasoner that I guest edited.

Since it might be of interests for the readers of our blog, I am sharing it here too.


Graziana Ciola:           Did you begin as a medievalist?

Calvin Normore:         In a way, I did. As an undergraduate – I think I was in the beginning  of my senior year –, at McGill we had a new professor, John Trentman, who had come from the University of Minnesota, where he had been a track star, actually. John gave a seminar on Buridan’s Sophismata, which had just come out in the T.K. Scott’s translation – there was no text –, and I got very interested in this. I had gone up to university wanting to be Bertrand Russell, so I wanted to do both math and philosophy. I was not as good at Math as I guess I was at Philosophy. In Math, I like more to have done it than – I discovered – to actually doing it. So, I was switching over into Philosophy and John’s seminar was really interesting. He got me interested. It was just at the moment when Arthur Prior was still at Oxford – I think he died the next year – and so there was question of what to do. I thought we were going to study with him. He had suggested that if one were interested in modal and tense logic, then there was lots to be learned from the medievals. And I was very interested in modal and tense logic. In the event, I went to Toronto, because that was the place to do medieval things in those days, and certainly if you were an Anglophone and a Canadian – but I think in general. So I went there but, frankly, I found the medieval atmosphere somewhat boring, so I fell in with people in the Philosophy Department who were more interested in contemporary things. Hans Herzberger, who was working on truth, became my supervisor; Bas van Fraassen had just come to Toronto as well, so I took courses from him; David Gauthier was there, and John Woods, who was a good logician. I worked really more with them at the beginning, but I did the things one did at the Institute. When I had been thinking of going up to Toronto, I had gone to the city and I talked with Father Ed Synon, because the question was: “should I apply to come to the Pontifical Institute or should I go to the Philosophy Department?”. And Father Synon said: “Oh, you should go to the Philosophy Department, because you can do everything you like at the Institute if you are in the Philosophy Department. And what’s more you’ll get a job, which you wouldn’t do if you came to the Institute”. So I got into the Philosophy Department, but I continued to do all these things at the Institute: I took their first year programme, the palaeography courses and so on. But I was working mostly with Hans, actually. I got interested in Ockham because… one could. This was 1968, when I went up. It was just at the moment when Saul Kripke and Charles Chastain were working on the causal theory of names. It was actually Chastain whose work I encountered first; and he came to Toronto and gave a talk. I had been reading Ockham at the same time when I realised “ah! this is a very similar view! let me explore it further…”. And that’s really what got me into Ockham.

GC:                             So, when you started working on these topics in Ockham’s philosophy, were you already more focused on the history of logic rather than philosophy?

CN:                             I didn’t see a distinction. Remember: Prior had claimed – quite correctly, I thought – that if you wanted to do modal and tense logic you could learn a lot from the medievals. And he was right! So I thought of working on these 14th century people as very much a contemporary project. I did never see it as a different issue at all. Later on, partly under the influence of Michael Frede, I came to think that there might be a subject – the History of Philosophy as a subject. But I am sure that when I was a graduate student I didn’t think of them as distinct subjects at all.

GC:                             There are some strong reasons for a philosopher to be interested in the History of Philosophy – same for a logician to be interested in the History of Logic. Your thoughts? How did your outlook evolve? How did it change over time?

CN:                             There is this famous quote of Quine that “logic is an old subject and since 1879 it has been a great one”, referring to Frege’s Begriffsschrift. This, I think, is just a mistake. What Frege was trying to do was to develop an adequate foundation for mathematics and to show that you could develop an adequate foundation for mathematics that relied only on concepts that would be uncontroversially thought of as logical. But, of course, that presupposes already that one had a conception of what was logical, right? Otherwise it would make no sense – and you might ask “well, where did that conception of logical come from?”. I think that is a part historical project. If you go back to Aristotle, something that, for example, Chris Martin has emphasised (and it’s true), is that Aristotle doesn’t have a propositional logic at all: he’s got a logic of terms, that explores relations among certain expressions we would call quantifiers. The Stoics developed a theory, which explores the relations among certain words – let’s suppose – or concepts that we would regard as propositional connectives. And medieval theorists inherited both: more obviously, Aristotle; but they inherited a good deal of Stoic material as well. What you find throughout the Middle Ages is an exploration of a number of these items (quantifiers, connectives, and so on) under the general heading of “syncategorematic expressions” – and also some “partially” syncategorematic expressions, as they thought, that is: expressions that when you analyse them turn out to have a syncategorematic component. The medievals were working to explore the structure of these syncategorematic terms. About the time you get to Frege a lot of that could simply be taken for granted. The logic that has been developed since 1879 is just, as I see it, a continuation. If you teach Introductory Logic these days, you teach your students, typically, a propositional logic – and what do you do? You explore the structure of conjunction, negation, disjunction, sometimes a conditional; you go on to explore the structure of some quantifiers; you worry, at some point, about how to give a translation of this into a mathematical framework –that is new: that wasn’t done much, before Frege. But the idea that you are going to explore the core of some syncategorematic terms, that has been the core of the subject. I don’t see it as a different subject now.

GC:                             I agree with you. However in many Departments, both in Europe and in the US, it is still common to find a split between historians of Philosophy and philosophers “in a proper sense”, as if the former were not as much philosophers as the the latter. And that seems very wrong to me.

CN:                             I think it’s wrong. When I went to Princeton, in the late ’70s, that split was very much there. Gil Harman is a wonderful philosopher but really did not think that the History of Philosophy belonged in a Philosophy Department. Now, interestingly, I don’t think that Michael Frede would have agreed exactly that it didn’t belong in a Philosophy Department, but Michael thought of it as a distinct subject. And the reason he thought of it as a distinct subject was that he thought that, unlike Philosophy, the History of Philosophy, as he saw it, was also a branch of History – and he thought of Philosophy and History as two distinct disciplines. So the History of Philosophy had two masters; because it had two masters, it had a master that wasn’t just Philosophy. How you lodge these people institutionally, that’s just an institutional accident. But the thought that a historian of philosophy had to be a good historian, as well as a good philosopher, meant that it was an open question whether the History of Philosophy would be best done in a Philosophy Department. Now, my own view is that Michael is right: there is a way in which a historian of Philosophy has answerable to the discipline of History, but also to the discipline of Philosophy. You have to be doing Philosophy: you can’t even understand the history, typically, unless you do the philosophy well. There’s something quite exciting about encountering ideas that are not part of the current philosophical landscape but you realise could be, as well as what got me into it – encountering ideas that were part of the contemporary philosophical landscape, but really hadn’t been explored yet very much. I don’t see any particular problem in housing a historian of Philosophy in a History Department, but I don’t see any reason to think that a historian of Philosophy couldn’t just as well be in a Philosophy Department. Nor do I see any problem in thinking that contemporary Philosophy can be informed by ideas that come from doing the History of Philosophy.

GC:                             Many historians have chosen to formalise medieval logical theories to make them intelligible and interesting for contemporary readers. What do you think about formalisation in approaching the History of Logic?

CN:                             Formal tools are very old: Aristotle used schematic letters to represent things in the syllogistics; the Stoics used analogous things – they had “the first”, “the second” and various kinds of expressions like that. I don’t think of formalisation as distinct in kind from regimentation. What does happen more recently is the development of a formal semantics. You have a formal semantics when you take a symbol that doesn’t have any natural language meaning – if you like, just a letter of the alphabet or something – and you assign it something in your semantics. And of course if the formal semantics itself is something presented in set theory, then it’s going to look rather different from if your formal semantics is a fragment of natural language. But when you teach Introductory Logic, typically, before you dwell upon any formal semantics, what you do is you present an interpretation of the symbols you use, in ordinary natural language: it’s just a schematic way of presenting a fragment of the natural language. I think the big shift is not with introducing symbols and letters: the big shift is presenting something like a set-theoretic semantics. That’s of course new, because Set Theory is new, but the idea of schematic representation is not new – in Leibniz, Aristotle, etc.

CG:                             Where do you think the discipline is going?

CN:                             Here’s something that’s important, I think: what’s important is that Logic itself is becoming an orphan. My mathematician friends who do Logic say it’s less and less a standard part of Mathematics; philosophers think of it as less and less a standard part of Philosophy. It’s becoming an orphan. I don’t think this is anything special about the History of Logic, here: it’s that Logic itself is loosing the central place that it has had both in Philosophy and in Math. Now, you might ask why. This is an interesting question. In the first half of the 20th century, there were some extraordinarily exciting results in Logic, which gave us reason to think that the whole project of presenting a theoretical picture of the world was different from the way we had previously thought it was. The limitative results that Gödel and Turing and others showed were just mind-blowing or earth-shaking. Now there has been nothing like that since. And what’s more, the techniques that have been developed for exploring parts of Set Theory, in particular, have become very recondite: ever since Cohen’s works on forcing, and the beginnings of the development of large cardinal axioms and things like that, the technical side of contemporary Logic had less to do with anything other than itself than it ever had before. In Mathematics there’s a project, which Harvey Friedman and others have, of what they call “reverse Mathematics”, which is to take Mathematics as it currently stands and try to see what sort of logical foundation you need for it; it turns out that you don’t need most of the stuff that has been developed since 1964, for example. In Philosophy we teach our students how to read the symbolism; on a good day, we teach them something about Gödel’s results, for example. But we don’t take it very seriously and people don’t think hard about it anymore; that has just made Logic itself less and less central in the field – and, of course, the History of Logic follows. But some of that is just a plain mistake, because people haven’t appreciated the significance of the results that were developed throughout the 20th century. There’s also this other thing, which is reasoning. Logic is not a theory of reasoning, because what Logic can tell you is what follows from what, but it doesn’t tell you what to do once you discovered that. There’s much more to Reasoning than Logic. And so Reasoning, the theory of reasoning, is a lively part of the contemporary scene; it just presupposes a lot of the logic that people have taken for granted. What’s interesting is that, if you look at the History of Logic, the History of Logic is often in part a History of Reasoning, so it’s a wider subject than Logic once Frege, and eventually Russell and Whitehead, tried to use it as a basis for Mathematics. Because of that, in some sense, there’s perhaps more to be learned from earlier logical developments about what’s currently relevant than from the Frege or Russell project.

CG:                             I completely agree. So, what would you tell a student who’s becoming interested in the History of Logic?

CN:                             I would recommend to remember that the History of Philosophy has two masters – and so they have to be good at Philosophy and they have to be a good historian. I would urge not to forget that: you won’t understand what you are doing, if you haven’t thought hard about what philosophical issues are involved; and you won’t know what to do, if you haven’t thought about the historical context. I think that’s all true. From a purely sociological point of view, there’s no good reason not to get into this stuff. I point out to my students that a couple of years ago in North America there was one dedicated job in the Philosophy of Language and four in Medieval Philosophy. So if you are thinking just of an academic career, there’s no particular reason to prefer doing the Philosophy of Language to Medieval Philosophy. But if you are thinking of the subject, the key thing is to not be too narrow.

GC:                             Thank you, Calvin.

CN:                             My pleasure.

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What is a lie?

All right, so this isn’t quite logic per se, but it is what I’ve been thinking quite a bit about lately, and it certainly has its connections to logic.

Typical modern definitions of lying run along these lines: “A lie is a (known/believed) falsehood told with the intent to deceive”. Both components are considered necessary: If you tell someone something false that you genuinely believe is true, then you haven’t lied (you were simply mistaken). If you don’t intend to deceive someone with your statement, then you haven’t lied (perhaps you were being sarcastic).

Augustine writing at the end of the 4th C is happy to agree that the assertion of a known falsehood with the intent to deceive is certainly sufficient for someone to be guilty of lying — but he rejects that these are necessary conditions. In De Mendacio (see the Logic Museum for Latin and English) he discusses two problematic cases in &sec; 4. First, consider:

the case that a person shall speak a false thing, which he esteems to be false, on the ground that he thinks he is not believed, to the intent, that in that way falsifying his faith he may deter the person to whom he speaks, which person he perceives does not choose to believe him.

That is, suppose Alice knows that Bob will always believe the opposite of what she says; because she desires that he not be deceived, she will then always speak what she knows to be false. (Alas, Augustine does not go on to consider what happens if Bob knows that Alice knows that he will always believe the opposite of what she says, nor how Bob would respond then to Alice’s assertions!)

Next, consider:

this opposite case, the case of a person saying the truth on purpose that he may deceive. For if a man determines to say a true thing because he perceives he is not believed, that man speaks truth on purpose that he may deceive.

Suppose further that Bob knows that Alice will always believe the opposite of what he says, and that he desires her to be deceived. Then he will simply tell the truth when he speaks to her.

The question then is, who has lied: Have they both lied? Has neither lied? Has only one of them lied? If the defining characteristic of a lie is “an utterance with will of any falsity”, then both have lied, Alice because she willed a false utterance and Bob because he willed a false thing to be believed. Thus if falsity is the characteristic of lying, both of them have lied, regardless of their good (or ill) intentions or the truth of what they actually said.

If the defining characteristic of a lie is “an utterance with will of uttering a false thing,” then only Alice has lied, because she was the only one who actually said something false; what Bob said was true.

If the defining characteristic is “any utterance whatever with will to deceive,” then only Bob has lied, because — regardless of the truth or falsity of what he said — he intended to deceive Alice. Alice did not lie, because she intended Bob to not be deceived.

Finally, if the defining characteristic is “an utterance of a person wishing to utter a false thing that he may deceive,” then of course neither has lied, because Alice lacks the intention to deceive and Bob because he has said something true.

Unfortunately, Augustine never clearly comes down in favor of which one of these cases he thinks is the correct one (rather, he contents himself with defining what is clearly correct behavior which is of course to tell the truth without any intent to deceive).

But to bring the discussion back around to logic, what these edge cases show is that lying is substantially more complex to model than truth-telling. In a truth-telling communicative setting, all we need is more than one agent and some mechanism for making public announcements. In a lying communicative setting, we need more than more than one agent and some mechanism for making public announcements for merely saying something false is not enough: We also need the agents’ knowledge (or belief) about the assertions they’re making, and knowledge about other agents’ dispositions. In order to intend to deceive someone, you must have some belief about what that other person knows or how they will react to certain stimuli. And how exactly should we treat deception? One can intend to deceive someone without succeeding in deceiving them; but how would that get built into a model?

I don’t have any answers to any of these questions right now, but never fear: The reason I’ve been thinking about them is because a friend and I are co-writing a paper on what an artificial system would need to have in order to be able to lie, so hopefully at some point in the future I can report back on what Augustine has to contribute to modern AI research. 🙂

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