What problem was Ladd trying to solve?

Last weekend I was at an amazing conference on Feminist Philosophy and Formal Logic (which I’ve written about elsewhere), during which there were a number of papers on the history of women and logic. Frederique Janssen-Lauret gave a paper on women in early analytic philosophy, and spoke about Christine Ladd-Franklin’s contribution to logic.

Ladd (as she was at the time) studied at Johns Hopkins under Peirce but was not allowed to formally receive her doctorate. Her dissertation, “On the Algebra of Logic” was published 1883 (and is available from archive.org), and in it, she solved a problem in syllogistic which had purportedly baffled logicians since Aristotle:

The argument of inconsistency
(a\bar{\vee}b)(b\bar{\vee}c)(c\vee a)\bar{\vee}
is therefore the single form to which all the ninety-six valid syllogisms (both universal and particular can be reduced) (p.~40).

I knew a bit about Ladd and her work before Janssen-Lauret’s talk, but this mention of a solution to a long-standing syllogism puzzle piqued my interest immediately — not the least because I wasn’t at all sure what the problem was. As presented, it was a problem about reducing all forms of syllogism to one form, but the idea of “form” here was confusing: Syllogisms are typically spoken of as having mood and figure. Now, “form” here clearly can’t be “figure”, since it is already well-known, and due to Aristotle himself, that every non-first figure syllogism can be reduced to a first-figure syllogism, so the long-standing problem cannot about this sort of reduction, interpreting “form” as “figure”.

If what is meant is, however, “mood”, then the question whether it is possible to reduce all the valid moods to a single valid mood is certainly an interesting one, but I’m not sure that it’s one that has exercised logicians for two centuries — certainly I’d be hard pressed to find a medieval logician who was particularly worried about such a fine-grained reduction, most being content to reduce just to the four perfect syllogisms, Barbara, Celarent, Darii*, and Ferio. So even interpreted in this way, I’m stumped. (And interpreting “form” as something other than figure or mood makes it even more unlikely that the question is one that had bothered logicians for millenia.)

It’s not that I doubt that Ladd provided a solution to some technical problem in the syllogistic — not doubt at all about that — and I’m sure that a precise statement of her problem can be given. What intrigues me here is the social history of the problem: Not what it was but how/when/why did it get recognised as a problem, and how/when/why did people come to think of it as a problem that had plagued logicians since the time of Aristotle?

Looks like I’ve got my next paper topic lined up…

Footnote
* I very nearly wrote “Dario” here, showing that the distinction between names of syllogisms and names of Game of Thrones characters is not as great as you might think. (Come to think of it, “Bocardo” would be a good name for a roughly-and-tumble pirate warrior, donchya think?)

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Not quite medieval, not quite logic: Proclus’s commentary on Euclid

Earlier this week I was following up on some notes I’d scribbled down over a month ago in a meeting with a colleague, one of which was “Proclus: Image in the water”.

A bit of googling later, and I found myself with a translation into English of Proclus’s commentary on the first book of Euclid’s Elements, along with, per the title page, “A History of the Restoration of Platonic Theology” by the later Platonists, and a translation of Proclus’s “Theological Elements”, courtesy of googlebooks. (Thanks, googlebooks!) Cool! On the face of it, it’s neither medieval nor logic, but it’s definitely something related to both and thus of interest to me.

Someone asked me on twitter who the translator was, and the answer turns out to be…I have no idea. The translator does not name himself on the title page, despite the fact that the publication info is given as “London, printed for the author” and I’m sure that the ‘author’ here isn’t Proclus!, and that there is an extensive preface, where the translator discusses the “great difficulty and labour” that attended his work, arising from the problematic state of his sources. (He laments the “great incorrectness” of the Greek edition and notes that he was substantially assisted by the translation into Latin by Francis Barocius the Venetian, done in 1560. There is otherwise no evidence as to the translator in the frontmatter, and there isn’t much out there elsewhere on google about 18th C translators of Proclus, so I thought I’d take a skim through the book to see if I could find any other clues.

Following the preface there is a “Dissertation on the Platonic Doctrine of Ideas” and after that a “Dissertation on the Demonstrative Syllogism” (!) which includes as part of it a substantial epistemological discussion. This is followed by a third discussion, “On the Nature of the Soul”, and a fourth on “The True End of Geometry”.

These four dissertations concluding, we next have a translation of Marinus’s “Life of Proclus, Or, Concerning Felicity”, and at this point I’m half-way through the PDF and am beginning to wonder just exactly when we’re going to get to the actual texts of Proclus. After Marinus’s biography, the translator gives us a bibliography of Proclus’s works, both available (whether fragmentary or not) and lost. (One of the lost books is a commentary on On Interpretation, which would’ve been really interesting!). Finally, nearly 2/3 of the way through the PDF, we get to Proclus’s commentaries, which comprise the rest of the volume. One can only hope that the next volume has the answer — I shall have to see if I can find it. Meanwhile, I might devote a future post to a discussion of the Dissertation on the Demonstrative Syllogism because it appears to be quite interesting.

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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.

Programme:

FRIDAY,MARCH 2ND
DODD HALL -ROOM 399

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

SATURDAY,MARCH 3RD
ROYCE HALL -ROOM 306

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

SUNDAY,MARCH 4TH
ROYCE HALL -ROOM 306

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

DISCUSSANTS WILL INCLUDE MILO CRIMI (UCLA) AND BOAZ SCHUMAN (UNIVERSITY OF TORONTO).

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: http://ufar.ff.cuni.cz/10/about-our-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

Qualifications:

  • 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

Application

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 hana.vamberska@ff.cuni.cz.

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.

Information

For additional information you can contact:
Dr. Jakub Jirsa, Head of department, jakub.jirsa@ff.cuni.cz (job profile and academic matters)

Hana Vamberská, hana.vamberska@ff.cuni.cz (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
(66)

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:

VIO * NON * EST * LAC * VIA * MEL * VAS * ERB * ARC

he quatuor voces designant quatuor modos secunde figure:

REN * ERM * RAC * OBD

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:

VIO NON EST LAC VIA MEL VAS ERB ARC (200).

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.


Notes

[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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