Cambridge Companion to Medieval Logic

It’s been I-don’t-know-how-many-years in the making, but the fruits of Stephen Read and Catarina Dutilh Novaes’s work is now available: The Cambridge Companion to Medieval Logic.

The book is divided into two parts. The first part is temporally organized, focusing on periods and traditions. The chapters in this section cover:

  • The Legacy of Ancient Logic in the Middle Ages (by Julie Brumberg-Chaumont)
  • Arabic Logic Up to Avicenna (by Ahmad Hasnawi and Wilfrid Hodges)
  • Arabic Logic After Avicenna (by Khaled El-Rouayheb)
  • Latin Logic Up to 1200 (by Ian Wilks)
  • Logic in the Latin Thirteenth Century (by Sara L. Uckelman and Henrik Lagerlund)
  • Logic in the Latin West in the Fourteenth Century (by Stephen Read)
  • The Post-Medieval Period (by E. Jennifer Ashworth)

The second part is organized thematically, tracing a single concept or topic across time. The topics covered are:

  • Logica Vetus (by Margaret Cameron)
  • Supposition and Properties of Terms (by Christoph Kann)
  • Propositions: Their Meaning and Truth (by Laurent Cesalli)
  • Sophisms and Insolubles (by Mikko Yrjönsuuri and Elizabeth Coppock
  • The Syllogism and Its Transformations (by Paul Thom)
  • Consequence (by Gyula Klima)
  • The Logic of Modality (by Riccardo Strobino and Paul Thom)
  • Obligationes (by Catarina Dutilh Novaes and Sara L. Uckelman)

Check it out!

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Avicenna in the SEP

Just a quick post today, to note that there is a new article on Avicenna in the Stanford Encyclopedia of Philosophy, by Dimitri Gutas, which has an entire section devoted to his logic and epistemology, as well as a very nice looking bibliography.

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Ex impossibili sequitur quidlibet in the 13th C (part 1)

Two weeks ago, I wrote about Ex impossibili sequitur quidlibet in the 12th C. Today, I come back to one of the promises there, namely, to look at part of Joke Spruyt’s “Thirteenth-Century Positions on the Rule ‘Ex Impossibili Sequitur Quidlibet‘”, in K. Jacobi, Argumentationstheorie (Brill): 161-193.

At the time of Spruyt’s writing, “not much attention [had] been paid to the thirteenth-century conceptions of the validity of consequences” (p. 161). (Since then, this has certainly changed, most notably with Catarina Dutilh Novaes’s Formalizing Medieval Logical Theories.) Looking at the Ex impossibili rule is one way to discern the specifics of various conceptions of validity in the 13th century.

The most basic definition of validity, in which “the antecedent cannot be true without the consequent” (p. 161), has Ex impossibili as an immediate consequence. But this can be accepted either as “the ultimate criterion for evaluating a consequence, or merely as one of the criteria that accompany other, equally important ones” (p. 162), and this is because this most basic definition can be specified in a variety of ways, and in particular depending on how consequences and conditional sentences are defined and distinguished from each other. One point of agreement amongst most 13th-century was that both conditionals and consequences express some sort of relationship between antecedent and consequent (p. 162); the nature of this relationship was a point of disagreement. Two common interpretations were that the relationship was one of causation or one of inclusion. If the relationship between the antecedent and the consequent is one of causation, the opponent of Ex impossibili can argue that “the impossible is nothing and thus cannot cause anything” (p. 162), in which case the rule must be rejected. The proponent of the rule, on the other hand “does not describe consequences in terms of a relationship between beings” (p. 163), but it is not clear to me how this still counts as a causal account of consequences or how it addresses the objection of the opponents. (Maybe if the relationship doesn’t relate beings but something else, then the impossible is something that can fall under that something else?).

13th-century discussions of the syncategorematic term si ‘if’ often included a variant of the question “Whether from the impossible anything follows”. Spruyt notes one exception, Roger Bacon’s treatise on syncategorematic words written between 1230 and 1240 (p. 163), which does not mention the rule at all. She argues, following Braakhuis, that this is a result of Bacon following Priscian’s definition of si as “a continuing conjunction which signifies an ordering of res (p. 163); the relationship which this continuing conjunction indicates is the ordering of prior to posterior. Thus, “the mind grasps two complex res and is affected by the ordering between the two” (p. 163), and as a result of this ordering, a unity is formed (p. 164). Because there are no impossible res, they cannot be related to anything to form a unity. (The relationship that is expressed by si is distinguished from that expressed by ergo. Ergo has the force of assertion, making the antecedent certain, while si lacks this force (p. 164).)

The rule is discussed extensively in an anonymous Distinctiones treatise from the first decade of the 13th century, where “it is presented as a rule defended by the nominales and rejected by the reales” (p. 165). The author himself follows the reales. Spruyt highlights one argument he gives against an argument in favor of the principle:

the conditional sentence ‘If Sortes is an ass, Sortes is a goat’ is true because (in virtue of the locus a parte disiunctiva) the conditional ‘If Sortes is an ass, Sortes is an ass or a goat’ is true. Now Sortes is not an ass, therefore he is a goat. So taking it from the beginning: ‘If Sortes is an ass, he is a goat’ (pp. 165-166).

The anonymous author rejects this inference as invalid because “two opposite species cannot be united in one and the same subject” (p. 166). So when it is posited that Sortes is an ass, this immediately denies that he is a goat.

The author must then modify the definition of validity in order to be able to exclude Ex impossibili:

In his opinion, the definition of a true conditional is meant to cover only those conditionals that contain an antecedent that, while not necessarily being true, is at least such that it can be true (p. 167).

Of course, such a modification directly blocks Ex impossibili, but it is also not a very satisfying one!

Spruyt’s article continues by looking at the positions in the Sophistaria wrongly attributed to Walter Burley, Peter of Spain’s Syncategoremata, and Henry of Ghent’s Syncategoremata, all of whom are opponents of the view. Then comes a section on the proponents, including Nicholas of Paris, Matthew of Orléans, and John le Page. We’ll cover these in another post (or two)!

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Modality Three Ways

I’m currently at Advances in Modal Logic, in Budapest, one of my favorite conferences; I’ve been a regular attendee since 2004 (only missed the one in Australia!) and have given historically-oriented papers every time, usually to great interest. In fact, the only drawback of the conference is how few historical papers there are. So here’s an early plug for AiML 2018: We need more medieval modal logic there!

Hanging out with a bunch of people for whom “history of [particular subfield of logic]” generally starts around 1930, or maybe, if you’re lucky, in the 1890s, is always interesting when you’re a medievalist. I particularly enjoy when people react to this “history” and discuss how what they are doing is new/interesting/different. Some of them even recognize that what they are doing is old/interesting/different, i.e., people who explicitly reject Frege and return to Aristotle.

One speaker did so this morning, pointing out what many people do in fact know but rarely incorporate into their formal systems, that English (and in fact many natural languages) has two types of negation — sentential and term. One can say both “It is not that case that AaB” and “Aa non-B”, and these are not equivalent. It’s not hard to move from this observation to a similar one about modality, in that one can have both internal and external modal operators, and the difference between them is usually explained via the de re/de dicto distinction.

But one thing I rarely see people discuss is the fact that given a categorical sentence, there are in fact three places in which one can put the modality (or the negation): At the beginning of the sentence, before the copula, and after the copula. It’s the difference between:

  • \square AaB
  • A\square aB
  • Aa\square B

When I mention this to people, most often the response is that these three aren’t in fact all distinct, or to cast doubt on modal properties like being “possibly B”. This first may be true, the latter may be reasonable. But all three types are syntactically distinguished in medieval discussions of modality, so I am reluctant to dismiss them out of hand. For example, Paul of Venice in his chapter on syllogisms (Tract II, cap. 13) in the Logica Magna distinguishes such constructions:

  • Omnis prima causa de necessitate est deus
  • Contingenter omne creans est deus
  • Omnem primam causam necesse est esse deum

I am not entirely sure which of the formal versions above these map to, but it may be (using \bigcirc for contingency):

\square AaB Omnem primam causam necesse est esse deum
A\bigcirc aB Contingenter omne creans est deus
Aa\square B Omnis prima causa de necessitate est deus

On the other hand, I could be persuaded it is:

Omnem primam causam necesse est esse deum

\square AaB Omnis prima causa de necessitate est deus
A\bigcirc aB Contingenter omne creans est deus
Aa\square B

I’m not sure anyone has investigated this with any systematicity. This would make a great topic for a paper for AiML!

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Ex impossibili sequitur quidlibet in the 12th C

At the AAL conference in Melbourne in July, one of the questions that I was asked was about medieval discussions of ex falso/impossibili/contradictione quidlibet sequiter (and its correlate, ad necessarium quodlibet sequiter).

The legitimacy of these inferences was significantly discussed during the 12th century, with the followers of Adam de Petit-Pont (called the Adamites or the Parvipontanians) accepting these principles, but others, in particular Abaelard and the so-called Nominales rejecting it. My point of contact with these discussions is via the Tractatus Emmeranus de Positio Impossibilis (1st half of the 13th C, edited by de Rijk in 1974), a treatise on the genre of obligationes which takes not a false statement but an impossible one as the positum. The author points out that the only way this genre can be sustained as a useful one is if the types of inferences used are restricted; in particular, the author singles out the “Adamite” thesis by name in order to identify it as unacceptable in the context of impossible positio:

And we should note that in this question everything does not follow from an impossible obligation. Thus, in this question one must not concede the consequence of the Adamites—namely that from the impossible anything follows [p. 218]

The principle is also attributed to Adam by John of Salisbury in the Metalogicon.

A couple of good modern discussions of this thesis can be found in Iwakuma 1993 (covering the 12th century), Spruyt 1993 (on the 13th century), and d’Ors 1993 (for the 14th century). In this post, I focus on Iwakuma’s paper and the 12th century.

The best-known 12th-century sources for the ex impossibili thesis are the Ars Meliduna and Alexander Neckam’s De Naturis Rerum (p. 125). The Ars Meliduna is written by a Melidunensis rather than a Parvipontanus, but the Parvipontani thesis is discussed in book IV, chapters 37-39. Neckam, on the other hand, accepts the thesis in a discussion in chapter 173, according to Iwakuma’s reinterpretation. In this section, Neckam starts off saying “Miror etiam quosdam damnare opinionem dicentium ex impossibili per se quodcumque sequi enuntiabile“, and gives six arguments. The first is a direct proof of ex impossibili, but Iwakuma says the remaining five “appear at first sight to have nothing to do with the thesis” (p. 126). The second argument is “one of the earliest presentations of the Liar’s paradox” (p. 126), and the other arguments “are very similar to the second in their structure” (p. 126). Iwakuma explains the relevance of the Liar paradox to questions of ex impossibili as follows:

Alexander’s second argument amounts to show that such an impossible antecedent is followed by a contradiction, namely Socrates says something both true and false. And once the contradiction holds, then it is easy to construct an argument to show that it is followed by any consequent, following the steps of the first argument…In just the same manner, one can interprete the other four arguments as proofs of the thesis. For in every argument of the four the antecedent of the first premise can be understood as impossible, and the conclusion is a contradiction (pp. 127-128).

But Iwakuma’s main aim in the paper is not discussion of Neckham and Ars Meliduna, but rather “to introduce two hitherto unknown texts and to comment on them, as well as on those already known, relevant to the thesis ex impossibili quidlibet sequiter” (p. 123). The two texts are MS Avranches 224, f. 3, from the late 12th century, and MS Munich clm 29520(2, also from the late 12th century.

The Avranches text discusses two counterarguments to the thesis, then gives two proofs of it (and a proof of the corollary ad necessarium) as well as responses to the purported counterarguments. Unfortunately, I neglected to scan the appendix in which this text is edited, and since Iwakuma doesn’t say anything further in the body of his article I can’t add anything more. (Guess I need to get that book via ILL again…or someday just purchase myself a copy!)

The Munich MS is incomplete, lacking the beginning so that it “leaves us uncertain as to what it discusses” (p. 130), though Iwakuma conjectures that it was probably written by a Parvipontanus on the ex impossibili thesis. As evidence, he points to a discussion of solutions to a problem set by Abelard wherein the solutions of the Nominales and the Melidunenses are rejected, but not the Parvipontani solution. In the same section, two more theses (ex inmodali sequitur modalis, et e converso and ex explicita sequitur inplicita, et e converso) are admitted; both of these are denied by the Porretani and Montani schools, but are consequences of ex impossibili, for:

a modal/immodal antecedent, if being impossible, is followed by any consequent, including immodal/modal ones. Similar considerations apply to inplicita/explicita propositions (p. 132).

If Iwakuma is right in his analysis and identification, then “this is one of the few valuable pieces of evidence on the Parvipontani‘s thesis from their own pens” (p. 133).


Anonymous. 2001. “The Emmeran Treatise on Impossible Positio“, in M. Yrjönsuuri, Medieval Formal Logic (Kluwer Academic Publishers): 217-223.

de Rijk, L. M. 1974. “Some Thirteenth Century Tracts on the Game of Obligation”, Vivarium 12: 94-123.

d’Ors, Angel. 1993. “Ex Impossibili Quodlibet Sequitur (John Buridan)”, in K. Jacobi, Argumentationstheorie (Brill): 195-212.

Iwakuma, Y. 1993. “Parvipontani‘s Thesis Ex Impossibili Quidlibet Sequitur: Comments on the Sources of the Thesis from the Twelfth Century”, in K. Jacobi, Argumentationstheorie (Brill): 123-133.

Spruyt, Joke. 1993. “Thirteenth-Century Positions on the Rule ‘Ex Impossibili Sequitur Quidlibet‘”, in K. Jacobi, Argumentationstheorie (Brill): 161-193.

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Avicenna in a Castle

Every August, I, a hundred of my friends, and all the medieval re-enactment gear you could want spend 10 days at Raglan Castle, in Wales. It is an amazing castle, and a very special place with lots of memories as I’ve been doing this since 2008. The length of the event lends itself to leisure, and one of the things I love to do is bring along medieval texts to read aloud and discuss. This year, I brought along Asad Q. Ahmed’s translation of the section on logic of Avicenna’s Deliverance — a book which has been sitting on my shelf for almost four years but which I have not yet read. The Deliverance was written in 1027, a turning point in Avicenna’s logical career. Ahmed says in the introduction: “Somewhere around 1027, Avicenna starts to show less patience with Aristotle himself, frequently pointing out the failure to implement one set of principles consistently throughout the Organon.” The Deliverance, however, was a compilation of work written prior to 1027, and so reflects a more orthodox approach.

Slightly over half a dozen of us spent more than an hour on the text. Not having read any of it, I didn’t do any preparation in advance of the discussion, so some of our discussion centered around “Well, I’m not entirely sure what he’s referring to here, possibly X”. We read all of sections 1-8, and then I glossed over and summarized sections 9-40. Here are some of the interesting points that came out of the discussion.

In section 1, “On Conceptualization and Assenting and the Method of Each”, Avicenna claims that “all primary cognition and scientific knowledge is either conceptualization or assenting”. Conceptualization is acquired by definition, while assenting comes via syllogism. Both definition and syllogism are divided into (1) the real, (2) the unreal but “beneficial to some extent in its own way”, and (3) the “false that resembles the real”. He makes the interesting point that humans are not naturally disposed to being able to distinguish these three; but since logic involves being able to make these distinctions, that is why it’s important to study logic. As evidence for the claim that people, by their nature, are not able to distinguish these three types is that if this weren’t the case, then “there would occur neither any disagreement among the wise nor any contradiction in the judgement of any single one of them”.

Both definitions and syllogisms are hylomorphic, being composed of matter and form. What is interesting here is that in order for a definition or a syllogism to be a good one, both the matter and the form must be good in combination with each other. For “just as corruption in the building of a house may occur on account of the matter even if the form is correct or on account of the form even if the matter is sound (or on both their accounts together)”, so may a definition or syllogism have be defective either because the form is good but the matter is not; the matter is good but the form is not; or because neither is. This is a distinctive view to me (if anyone knows of anyone else who holds such a view, please share in the comments!), because usually the importance of the form of a valid argument is stressed because if the form is good, then the argument will be good regardless of the matter that is inserted. Unfortunately, Avicenna doesn’t give an example of a syllogism or definition where the form is good but the matter is not.

Having introduced the subject matter of logic, in section 2, Avicenna explains what the benefits of logic are. (Chapters like this are always my favorite, because they justify how I spend my life.) He first explains the different types of good definition and syllogism. There are two types of good definitions, true definitions and descriptions (which are merely convincing rather than true), while there are three types of good syllogism. The first is the correct type, and is called demonstration. The second is a convincing syllogism which “generates a kind of assent that resembles certainty”, and these are the dialectical ones. Then there is a weak type which “generates overwhelming belief”, and these are the rhetorical ones. Finally, there is the false definition, which is called misleading, and the false syllogism, which is called sophistical. A sophistical syllogism “presents itself as a demonstrative or dialectical syllogism, while not being so”. Finally, there is a fifth type of syllogism which does not generate any type of assent but rather effects the imagination, and this is called the poetic syllogism. (Side note: I’ve never heard of the poetic syllogism before. Is this in Aristotle? Who else discusses these?)

Avicenna then notes that the relation of logic to deliberation is the same as grammar to speech and prosody to poetry, but while “a sound nature and innate faculty of discernment can perhaps dispense with the study of grammar and prosody”, there is no substitute for the study of logic.

Sections 3 and 4 cover Simple Utterances and Complex Utterances. The former are those utterances which are significative on their own, no part of which is significative, while the latter are those utterances which are significative but which have significative parts.

Sections 5 and 6 cover Universal and Particular Simple Utterances, which are distinguished on the basis of whether they signify “the many by way of one coinciding meaning” or not. Here, “the many” can either be many in existence, such as “man” which signifies many men, or in the imagination, such as “sun” which signifies one existing sun but nothing prevents it from signifying in the imagination many other suns. Particular simple utterances are those “whose unique meaning cannot possibly be anything more than a unique thing”. Examples of particular simple utterances include proper names and deictic descriptions such as “this sun” or “this man”.

This is pretty much all Avicenna has to say about simple utterances at this point, and the next section, 7, is a long one dedicated to what counts as essential, because every universal utterance is either essential or accidental. An essential utterance “sets down the quiddity of that of which it is said”, which, you have to admit, is not an entirely helpful definition. A further gloss is provided that

the essential is such that, if the meaning [of the subject] is understood and occurs in the mind and if the meaning of what is essential to it is understood and occurs in the mind at the same time, it would be impossible for the essence of the subject to be understood unless first the meaning [of that which is essential to it] is already understood to belong to it.

From this it is clear that the essential is not that which is merely inseparable from its substance. For it is inseparable of a triangle that the sum of its angles equal two right angles, but this is not an essential property of a triangle, because one can understand “triangle” without necessarily first understanding “sum of its angles equally two right angles”. This can be contrasted with the example of “man” and “animal”; “animal” is essential to “man” because you cannot understand “man” without understanding “animal”.

Given all this, section 8 is a short discussion of the Accidental, which is that is not essential. After this point, we stopped reading aloud entire sections and rather I skimmed and summarized.

Sections 9 and 10 are on answers to the questions “What is it?” and “Which thing is it?” We skipped these sections and went on ahead to the classification of the five types of universal utterance (section 11), genus, specific difference, species, property, and accident, each of which is given their own section (12, 14, 13, 15, 16, respectively). Sections 18-20 cover nouns, verbs, and particles, and then we have definitions of statements (21), which are merely complex utterances; propositions (22), which are statements in which “there is a relationship between two things such that the judgment ‘true’ or ‘false’ follows from it”; and attributive propositions (23), where the two things being related can both be picked out by simple utterances.

Statements themselves can also be related to each other, and the result is a conditional proposition (24). There are two types of conditional propositions, conjunctive and disjunctive. A conjunctive conditional proposition is one like “if the sun rises, the morning exists” (25), while a disjunctive conditional proposition is one like “Either this number is even or this number is odd” (26).

After this we are introduced to concepts of affirmation and negation, subject and predicate, singular and indefinite propositions, and then into everything that goes into the Square of Oppositions. At this point we stopped reading from Avicenna and I grabbed a stick and began drawing in the sand. It was not very easy to photograph, but here you go:

square of oppositions drawn in sand

Avicenna in a castle

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Call for proposals/interest/suggestions/ideas: British Society for the History of Philosophy

The British Society for the History of Philosophy is having a three-day conference at the University of Sheffield, April 6-8 2017, and has just sent out a call for proposals.

Would any of our readers be interested in clubbing together with me to put together a proposal or two on logic?

Call for Papers

The British Society for the History of Philosophy invites scholars to submit symposium and individual paper proposals for its general conference. Symposia and individual papers are invited on any topic and any period of the history of philosophy.

Proposals for either symposia (3-4 thematically related presentations) or individual presentations (approximately 25-30 minutes) are welcome. Symposium submissions are especially encouraged.

Proposal Submission Deadline: 1 October 2016

Decision by: 1 December 2016

Submissions should be sent as an email attachment (in Word) to:

Proposals for symposia should include:

– Title of symposium
– Symposium summary statement (maximum 500 words)
– Titles and abstracts of papers (maximum 500 words for each paper)
– Address of each participant, including e-mail, phone, and institution
– Name and email of symposium organizer, who will serve as contact person

If you are interested, comment below; depending on who is, we can decide on number of sessions/specific topics, and then think about specific abstracts, etc.

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