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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On Bad Academic Writing, Dress Code and the Discreet Charm of the Scholastic quaestio

After an online exchange with Sara Uckemlan, Mark Thakkar, Magali Roques and Edward Buckner about bad academic writing, I scribbled down a few thoughts for The Reasoner about the infamous quaestio and the Scholastic style.


What’s Hot in … Medieval Reasoning


Calvin and Hobbes

Cryptic writing is a cornerstone of a layperson’s perception of academia; however, there’s always a bit of truth in stereotypes. That academic writing is more often than not unnecessarily obscure, muddy, and pointlessly verbose isn’t merely a layman’s misconception, but a real issue about which most academics love to complain. Academic-ese is the stylistic equivalent of showing up to a formal tea party wearing white socks and sandals: it’s only comfortable for the one doing it. While some fields are more affected than others, at some point almost all of us have attended an utterly incomprehensible talk or stumbled upon an article that, while being in our own sub-subfield, was so sibylline that we felt like we had to possess some kind of paranormal divinatory skills just to get the gist of it. And even when a text is comprehensible, chances are that nonetheless it’s dreadfully boring despite a genuine interest in the topic or the soundness of its thesis. There are also funny and witty academic papers, but they are few and far between. Maybe academic-ese is a lot like the common cold that one catches on the bus to work when the flu is going around: if most people around you have it, no matter how careful you are, after a few days you are going to come home with a runny nose. No-one is immune. Whoever is without sin may cast the first stone… yet in academia we love casting stones – it’s our job – even though we are an undeniably sinful lot. But why does academic writing stink so much? That is the question. Among others, Steven Pinker tried to answer it in an excellent (and unusually well written) article, that you can find here. Pinker does an outstanding job of analysing some of the most common and obnoxious features of the academic style, while measuring it against the stylistic ideal for expository prose: that is, the classic style of 17th century French essayists. Academic-ese should aim for clarity and to be informative, however it often complicates things unnecessarily, using the kind of hyper-technical jargon that’s the author’s idiolect, indulging in excessive meta-discourse, and being overly apologetic, self-referential and abstract. The assumption that the reader knows exactly what the author knows is the academic writer’s original sin; incidentally, were things so, writing a paper would be completely pointless – and good riddance if the paper happens to be unreadable. On the other hand the classic style tries to keep it simple, even deceptively so: classic essayists go for a plain and smooth prose, preferring the concrete to the abstract; they present the facts and results of their research, leading their readers along respectfully, under the assumption that the readers are not omniscient but that they are intelligent enough to both know that these are complicated matters and to understand them if explained properly.

Now – you might wonder – what does this have to do with medieval reasoning? Quite a bit, actually: the only writing style with a worse reputation than academic-ese is the medieval Scholastic style. Humanist writers carried out a veritable defamatory campaign against Scholasticism and it was so effective that almost anyone (who doesn’t study the Middle Ages for a living) still associates “Scholastic” with pedantic, prolix and overly subtle hair-splitting. It’s not even a calumny, at least not entirely: Scholastic prose looks just as specialised and occasionally convoluted as any stereotypically bad academic paper. Not only is medieval philosophical Latin padded out with technical terms that are far too reminiscent of academic-ese jargon, but it is also a ways away from the polished and ornate Ciceronian prose (so dear to Scholastics’ Renaissance detractors) as anything can possibly be. Albeit just as artificial as its medieval counterpart, Renaissance Latin is undeniably prettier: the language of Scholastic philosophy is often just as bumbling and coarse as a good chunk of academic English; moreover, medieval Latin is a second language for everybody – so no witty and fancy native speakers there.

Nevertheless, not only is Scholastic style’s ill repute largely undeserved, but it also deserves to be granted a place next to the classic style as a model of neat expository prose. Scholasticism is, first and foremost, a method of enquiry, focused on the analysis of texts and philosophical issues – here “philosophical” is broadly intended to include theological matters, scientific problems and whatnot. Scholastics’ most infamous tool is, without a doubt, the quaestio (question), used extensively both as a teaching device and in writing. Around the second half of the 13th century the quaestio reaches its standard structure, which goes roughly as follows: (1) there is a whether-question (utrum) with two opposite possible answers; (2) the first possible answer is presented along with the arguments supporting it; (3) the second possible answer (sed contra) is presented along with the arguments supporting it; (4) a solution is reached (responsio) either by picking one of the two answers previously presented or by outlining a third conciliatory position; (5) all the previous arguments supporting the discharged answer are refuted one by one.

How is this is supposed to be obscure? It looks like a very sensible and linear method to me. Certainly, with its relentless sequences of proofs and refutations, the average quaestio is not as pretty of a read as a fine philosophical dialogue or a wittingly written classic essay, and very few would read it for literary enjoyment; but it is brutally efficient philosophy. The structure of a quaestio is a powerful tool, and for some aspects it complements the classic essay nicely: while classical essayists present their results and support them by avoiding self-reference and meta-discourses, Scholastic writers stage their reasoning process, showing their analysis of the issue at hand, the pros and cons of its possible solutions, and then finally reaching a supported conclusion. This is not to say that Scholastic quaestiones are always easy to follow and that their arguments are always evident and sound: as long as there has been philosophy, there have been bad philosophers as well – and even the bests sometimes require some effort in interpretation and reconstruction. On top of that, the technical terminology of medieval philosophy is indeed not obvious to a modern reader and not everything is always clearly spelled out, despite quaestio’s regimented and systematic structure.

However, many medieval theories and terms – that to us are just irksome and puzzling – would have been familiar and commonplace for the average freshmen in the 13th or 14th century; mutatis mutandis, the same cannot be said of our academic vernacular at its worst.

Overall, the strength of the Scholastic quaestio lies in its structure; it is there that we can pick up a few writing tips from our medieval colleagues: worst case scenario, we would have made a structured and systematic argument – and our reader would at least be aware of what our problem was and how we attempted to solve it. Even lacking the smoothness and polish of Renaissance prose, the quaestio gets the job done efficiently and, in a sense, elegantly: it might not be the prettiest gown at the party, but it’s still a step up from the white socks and sandals of bad academic writing. And besides, wearing an evening dress in the afternoon would be quite out of place and outrageously gauche.

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Bibliography of literature on obligations

For many years now, I’ve maintained a bibliography of literature on obligationes. It has moved around from website to website as I’ve moved around from place to place, and unfortunately my current academic webspace is so limited, I can’t spare any space for it there! Thank goodness for this blog; I’ve uploaded the PDF and it can now be accessed at:

I’ve updated it with a couple of new references (from the Pérez-Ilzarbe/Cerezo collection referenced in last week’s post) — if you know of any papers (recent or otherwise) that I’ve missed, please let me know in the comments!

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Four grades of necessity in Buridan

I’m currently reading through Paloma Pérez-Ilzarbe and María Cerezo’s History of Logic and Semantics: Studies on the Aristotelian and Terminist Traditions, a collection of papers in honor of Angel d’Ors, and learning all sorts of interesting things. In Calvin Normore’s paper, “Ex Impossibili Quodlibet Sequitur (Angel d’Ors)”, he looks at Buridan’s criterion for a good consequence and how it relates to the titular Parvipontanean thesis. Lots of interesting things in there especially in relation to 13th-century discussions of the principle, which I am more familiar with than the 14th-century ones. But what caught my eye was something that reminded me of a paper I’ve got on “possible impossibilities” which has been in draft format around 85% done for the last…um…five years (Some day I will finish it. It’s a good paper!) — namely, four different degrees of necessity that Buridan distinguishes. The discussion occurs in the Treatise on Demonstrations, &sec; 8.6.3 in Klima’s translation, in the context of different types of per se propositions. Because per se propositions have to be necessary, and “there are diverse grades of necessity”, there are therefore also diverse grades of perseity:

The first grade of necessity occurs when it is not possible by any power to falsify the proposition while its signification remains the same, nor [is it possible] for things to be otherwise than it signifies.

Another grade occurs when it is impossible either to falsify it or for things to be otherwise by natural powers, although it is possible supernaturally or miraculously, as in “The heavens are moving”, “The heavens are spherical”, and “[Any] place is filled.”

The third grade occurs with the assumption of the constancy of the subject, as in “A lunar eclipse takes place because of the interposition of the earth between the sun and the moon”, “Socrates is a man”, and “Socrates is risible”. These are said to be necessary in this way because it is necessary for Socrates, whenever he is, to be a risible man, and it is necessary, whenever there is a lunar eclipse, that it take place because of the interposition of the earth between the sun and the moon.

There is yet a fourth mode, which involves restriction. For just as ‘possible’ is sometimes predicated broadly, in relation to the present, past, and future, and sometimes restrictively, in relation to the present or the future, in accordance with what is said at the end of On the Heavens — that no force or power can be brought to bear on the past, i.e., on that which is done, but only on that which is or will be (for we say that everything that has been necessarily has been, and cannot not have been) — the same goes for ‘necessary’ and ‘impossible’, which are also predicated either with restriction or broadly (p. 733).

I find this discussion fascinating. First, the distinction between natural and supernatural necessities is quite relevant in connection with positio impossibili and the way this genre of obligatio is used in connection with theological reasoning. Second, the third grade sounds an awful lot like contemporary “analytic truths”. Third, it’s not entirely clear to me what the difference between the first and the third grade is; can anyone suggest an example of something that is necessary according to the third grade but not the first? Fourth, with the discussion of the fourth grade, Buridan has almost everything he needs to run Diodorus’s Master Argument — the different ways to define ‘necessary’, the necessity of the past — all he needs now is to ask whether there is something possible which neither is nor will be true!

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Spotlight on Thomas Bricot

I’m moving office right now, which involves packing up all of my books (my dept. admin expressed doubt when I said seven crates wouldn’t be enough; I’ve now filled up that many twice, and still have about 1-2 more crates’ worth left), and packing up all my books involves looking at all of them, and being reminded of the fact of just how many texts on medieval logic there are that have hardly been touched at all when it comes to modern commentary and analysis.

One of these is Thomas Bricot’s Tractatus Insolubilium, edited by E. J. Ashworth and published by Ingenium in 1986. The book has always interested me in part because it is so short — always a bonus when your Latin skills are never quite what you wish them to be — and I thought today I’d spend a bit of time poking around to see just what there is (or is not) that has been written about this book so far.

First, a bit about Bricot himself, because his name is certainly not one of the better known. He was born in Amiens, France in the middle of the 15th century, and he obtained his BA, MA, and doctorate from the university of Paris in 1478, 1479, and 1490, respectively. After 1490 he held various ecclesiastical and academic posts, in Amiens and Paris, and he died in Paris on April 10, 1516, so we’ve just missed one of his centenaries! More details about his life can be found in his entry in Thomas Sullivan’s Parisian Licentiates in Theology, A.D. 1373-1500. A Biographical Register; Sullivan calls Bricot “a leading figure in Parisian philosophical studies” (p. 115), and Ashworth notes that

Bricot’s work enjoyed considerable success in Paris in the last two decades of the fifteenth century as one can see from the number of editions printed there, as well as in other French centres (p. xiii)

and indeed, much of the references that I found to Bricot modernly are in the context of incunabula (cf., e.g., the Glasgow Incunabula Project). Ashworth’s edition of the Tractatus is based on printed editions only, as no manuscripts of the text are known (or were known in the 1980s). The earliest of these printed editions is from 1491, but the treatise was almost certainly composed earlier, in the 1480s, when Bricot’s focus was on philosophical rather than theological matters. (See more about his works here; a digitized version of the 1498 edition of the treatise on insolubles is available online here).

Given that Ashworth edited the text, it is no surprised that she is also the primary producer of modern commentary on his work:

  • Ashworth, E.J. 1972. “The Treatment of Semantic Paradoxes from 1400 to 1700”, Notre Dame Journal of Formal Logic 13, no. 1: 34-52.
  • Ashworth, E.J. 1974. Language and Logic in the Post-Medieval Period (D. Reidel), especially chapter 2.
  • Ashworth, E.J. 1977. “Thomas Bricot (d. 1516) and the Liar Paradox”, Journal of the History of Philosophy 15, no. 3: 267-280.
  • Ashworth, E.J. 1978. “Theories of the Proposition: Some Early Sixteenth Century Discussions”, Franciscan Studies 38: 81-121.
  • Ashworth, E.J. 1994. “Obligationes Treatises: A Catalogue of Manuscripts, Editions and Studies”, Bulletin de Philosophie Médiévale 36: 116-147.
  • Ashworth, E.J. 2016. “The Post-Medieval Period”, in the Cambridge Companion to Medieval Logic, ed. C. Dutilh Novaes & S. Read (Cambridge University Press): 166-193.

However, recently Hanke has been studying Bricot’s semantics, especially with respect to the views of one of Bricot’s students, John Mair, in his 2014 article, “The Bricot-Mair Dispute: Scholastic Prolegomena to Non-Compositional Semantics”, History and Philosophy of Logic 35, no. 2. (Interestingly, both Bricot and Mair were satirized by Rabelais (cf. Cambridge History of Renaissance Philosophy, p. 794; the CHRP discusses Bricot’s Aristotelian natural philosophy but not his logic). Finally, Bricot is discussed by Lagerlund in his chapter on “Trends in Logic and Logical Theory” in the Routledge Companion to Sixteenth Century Philosophy (2017).

So, there’s a short spotlight on the life of Thomas Bricot and modern discussions of his logic, for anyone who would like to investigate this rather underinvestigated author!

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