PhD position in theoretical philosophy at University of Gothenburg

The University of Gothenburg, Sweden, is advertising a PhD position in theoretical philosophy at University of Gothenburg. The theme is open: it can be anything that fits the supervisory capacities of the faculty of theoretical philosophy, including metaphysics, philosophy of mind and language, and epistemology, and the history of philosophy in these areas — people with an interest in medieval philosophy are specifically encourage to apply!

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3 year position in Ancient/Medieval Islamic Philosophy at LMU München

LMU München has a three-year position open for an “assistant” (research and teaching) in late ancient and Islamic philosophy. Deadline is Oct 1, 2020.

Text of advertisement:
Ludwig-Maximilians-Universität München is one of the largest and most esteemed institutions of higher learning in Germany, offering a wide range of academic disciplines.
The Chair for Late Antique and Arabic Philosophy (Prof. Dr. Peter Adamson) at the Faculty for Philosophy, Philosophy of Science and Philosophy of Religion at the LMU seeks to fill a temporary position beginning on April 1, 2021, as:
Academic staff member/Assistant of the chair (initially 3 years)

Your responsibilities:

  • Collaborative research in the areas of concentration of the chair, namely ancient and medieval philosophy – especially late antique philosophy or philosophy in the Islamic world.
  • Teaching: 5 hours per week (roughly corresponds to a 2/3 teaching load in the US).
  • Participation in other activities at the chair (research, teaching, administration)

Your profile:
Prerequisites are an excellent university degree and expertise in the area of research mentioned above. A further requirement is native or near-native facility in German or English. The candidate should have standard computer skills, be creative and capable of teamwork, results-oriented and willing to take on new challenges.

Our offer:
Your workplace is centrally located in Munich and is well-connected by public transport. We can offer an interesting and challenging work environment and good prospects for further career development.

If the candidate is suitably qualified the post-holder can be appointed as an “Akademischer Rat auf Zeit” (i.e. temporary civil servant status; requires doctoral degree). Otherwise salary will be calculated according to group E 13 TVL-employment. The position will end on 31.03.2024, with an option to be extended by another three years.

We particularly welcome applications from female candidates. The University intends to enhance the diversity of its faculty members: disabled candidates with essentially equal qualifications will be given preference. In principle it is possible for the post to be held part-time.

Please send your application with the usual documents (including CV, transcripts, diplomas, list of publications and courses taught), as well as a brief description of your expertise, either by email as a PDF file (max. 5 MB) or by post by 1.10.2020 to the following address.

LMU München
Lehrstuhl für Spätantike und Arabische Philosophie
Prof. Dr. Peter Adamson
Geschwister-Scholl-Platz 1
80539 München

Should you have any questions, feel free to contact us via e-mail ( or by telephone +49 (0)89/2180-72154.

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Sten Ebbesen receives honorary degree from University of Bologna

Anyone who has had more than passing contact with the field of medieval logic, grammar, rhetoric, semantics has come across Sten Ebbesen, whose work is wide-ranging in time, place, and content. In February 2020 he received the “Laurea ad honorem” from the University of Bologna, with a laudatio by Constantino Marmo (another familiar name in medieval philosophy!).

The ceremony was recorded and can be watched on youtube:

Starting around 41:00, he gives a talk (in English, not in Latin!) called “A Scholarly Life”, including much about the study of the history of philosophy. Thanks to BPH who shared this over on Facebook—we figured others would also be interested in this!

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William of Sherwood on Necessity and Contingency

This afternoon I gave a talk on “William of Sherwood on Necessity and Contingency” at Advances in Modal Logic 2020. The slides are available here.

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Dr. Graziana Ciola interviews Dr. Sara L. Uckelman…


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Medieval modal logic: some short readings

I’m deep in the throws of the early research stages of a new paper, which means I need an outlet for collecting information and sorting out thoughts…i.e., I need to write blog posts! This will be the first of perhaps more than one posts where I provide brief excerpts on modal and temporal logic from various texts that are not currently translated and have not been discussed much (if at all) in the secondary literature. I’m not sure what of this will eventually result in a paper, but you won’t know what’s in the texts until you look at them…

I’m starting with texts in volume 2 of de Rijk’s Logica Modernorum (despite it being on “the origin and early development of the theory of supposition”, almost every text in that volume says something about modality, usually in the context of the modal syllogistic).

Ars Burana

This text exists in a single manuscript, and de Rijk says “I think, it may have come into existence in the third quarter of the twelfth century” (II.1:398).

The discussion of modality occurs in Part III “On the Conclusion” of the treatise. What follows is my (very rough; with some assistance at the very end from the lovely folks in the Medieval Logic FB group) translation of II.2:207-208:

Of categorical propositions, some are modal, others are of inherence (de inesse). [A proposition] of inherence or of simply inherence (de simplici inherentia) is that in which a predicate is attributed to a subject without determination or is removed [from the subject] simply, as in “Socrates is a man”, “Socrates is not a man”. A modal [proposition] is that in which a predicate is attributed to a subject with a determination, as in “Socrates necessarily is a man”, “Socrates contingently is white”. And those propositions are called “modal” by means of the mode which is put into it, namely “possible”, “impossible”, “contingent”, “necessary”. However, “modes” are so-called because they modify, that is determine, the inherence of the predicate.

Further, it must be known that this label “modal proposition” can be taken not only broadly but also strictly or very strictly. [Taken] broadly as in Boethius in the Commento, whereby all propositions in which some adverbial determinant is put down are said to be “modal”. Whence these are modal [propositions], according to Boethius: “Socrates reads well”, “Socrates disputes prudently”. It is taken strictly in which one of these modes is put down: “true”, “false”, “possible”, “impossible”, “contingent”, “necessary”. It is taken most strictly in which one of these modes is put down: “possible”, “impossible”, “contingent”, “necessary”. And it is according to that usage that Aristotle speaks of the modes in the Periermenias. And according to this, those propositions in which these words “true”, “false”, are put down are called “of inherence”, because they are equivalent to propositions of inherence. For I may say either “It is true that Socrates is a man” or “Socrates is a man”, [and] it is the same, because these propositions are equivalent. Further, these are equivalent: “It is false that Socrates is a man” and “Socrates is not a man”. And because a mode is sometimes preposed, sometimes interposed, and sometimes postposed to the appellation of the dictum, we should inquire what the appellation of the dictum is; but first [we should inquire] what a dictum is.

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Blinkered approaches and narrow-minded European-centrism: an apology

Last week I posted a quick and dirty recommended reading list for “getting started in medieval logic”, as the title of the post said. This post was shared in the Medieval Logic FB group, where it immediately sparked a discussion centering on one very important fact: What I recommended was a list of books for getting started not in “medieval logic” but in “medieval Latin logic”. As if the Middle Ages were only the European/Latin contributions, and completely overlooking the foundational developments by the Arabic logicians!

So this post is a both a public apology — by now, I really should know better than to essentialise and center the Latin practice so! — and also a promise. There are plans in the making to have a guest post, next week or the week after, on “What Should I Read?” which will contain only recommendations on sources from the Arabic tradition. Broaden your horizons! Be a completist! Don’t be like me! 🙂

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What Should I Read? Recommendations for getting started in medieval logic

Two weeks ago I was at a workshop and someone asked me what books they should read if they wanted to get started in medieval logic — not secondary sources, but which primary texts. I told him I’d write up a blogpost for him on that very topic. Jon, this post is for you. 🙂

The 13th Century

I’m going to start off with recommending my favorite 13th-century quartet:

  • William of Sherwood, Introduction to Logic
  • Roger Bacon, The Art and Science of Logic
  • Peter of Spain, Summulae Logicales
  • Lambert of Auxerre, Summa Lamberti

Why these four? First, because they are our first witnesses to the university textbook tradition in logic, and as such provide equal parts Aristotle and novel. Second, because all four are now available in English translation — two of them (Auxerre and Spain) are in bilingual editions, and one of them (Sherwood) has both Latin and English edition easily available. These are a great way for a non-expert to dive into the details of medieval developments in logic in a linguistically-accessible way. Something I recommend doing with these four is picking a single topic, and then seeing what each of the four have to say about the same topic — the answers are often quite divergent!

The Early 14th Century

  • Walter Burley:
    • De Puritate Artis Logicae, Tractatius brevior
    • De Puritate Artis Logicae, Tractatius longior
    • De consequentiis
    • De obligationibus
  • Richard Kilvington:
    • The Sophismata of Richard Kilvington (available in both Latin edition and English translation)
  • Thomas Bradwardine:
    • Insolubilia (available in bilingual edition)
  • William of Ockham:
    • Summa Logicae (portions available in translation)
  • John Buridan:
    • Summulae de dialecticae (available in English translation)

These give you an idea of the breadth of the developments in the early part of the fourteenth century — from the great compendia to the treatises on specialised topics.

This is by no means an exhaustive list, nor even a very coherent, but nonexhaustive one. It is just a list of the books that I recommend people get started with if they want to become familiar with the standard topics and techniques in late medieval logical developments.

Fellow medieval logicians, which is your favorite primary source (in easily accessible format) that you like to recommend to people? Please share in the comments!

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Book Review: The Aristotelian Tradition: Aristotle’s Works on Logic and Metaphysics and Their Reception in the Middle Ages edited by Börje Bydén and Christina Thomsen Thörnqvist

Last month, I published a review of this book in Revista Española de Filosofía Medieval. The review is freely available to read online here. With a few reservations (specifically regarding its coverage of the Arabic developments), I highly recommend the book, which was interesting, informative, and quite easy to read.

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Infinitary Logic in the Middle Ages?

Earlier this week I attended Computability in Europe, where I enjoyed catching up with many logic and computability friends, and answering random “did they do X in the Middle Ages?” questions. One in particular warranted a blog post; Benjamin Rin (Utrecht) asked me whether there was anything like a historical precursor to infinitary logics in the Middle Ages. I gave him a few references, but then decided it would be worth writing up some of the info in them for wider consumption.

What is infinitary logic?

Classical propositional and predicate logic is finitary: Simple atomic sentences can be formed into more complex sentences via boolean combinations (and the addition of quantifiers, in the case of predicate logic), but these combinations can only be iterated a finite number of times.

Consider a classical predicate language with sufficiently many distinct constants: When interpreted on a finite domain, the universal quantifier is eliminable, as every formula universally quantified formula is equivalent to a conjunction of all of the instantiations of the formula. Similarly, the existential quantifier is eliminable in favor of a disjunction of all the instantiations. However, in the presence of infinite domains, this equivalence breaks down because there is no way to list infinitely many distinct instantiations in a single finite conjunction (or disjunction).

Infinitary logic allows formulas of infinite length — generally in the form of infinite conjunctions and disjunctions, but in some cases also allowing infinitely iterated quantifiers. With infinitary logic, the equivalence between universally quantified sentences and conjunctions, and between existentially quantified sentences and disjunctions, is restored even in infinite domains. (For more information on the motivations for infinitary logics and their syntax, see [1]).

Asking the right questions

I have spent much of my logical career persuading modern logicians of the value of looking to the history of their field. But when asking historical questions about developments in logic, there are better and worse ways to do it. Sometimes a straightforward “Did they do X in the Middle Ages?” or “When did X first develop?” question is perfectly legitimate — for instance, to the question “Did they have propositional logic in the Middle Ages?”, the answer is a straightforward “yes”. Similarly, “When did quantifier/variable symbolic notation first develop?” has a straightforward, determinate answer (and it’s not medieval).

But some modern developments are embedded in a mathematical and symbolic context that was simply not present in the Middle Ages, which can result in those straightforward questions being answered with false negatives. In order for the question “Was there infinitary logic in the Middle Ages?” to be answered positively, there would have to be some notion of recursive definitions of well-formed formulas, the distinction between finite and infinite symbolic formulas, and a well-developed notion of actual infinity (as opposed to Aristotelian potential infinities) — all things which medieval logicians just didn’t have. But rather than accept “no” as the final answer to that question, we can ask a further question, namely: Did medieval logicians have any of the same concerns that motivated the introduction of infinitiary logics, and, if so, how did they address those concerns? That is a much more interesting question to ask, because the answer says something not only about how logic in the Middle Ages worked, but also about how given different technical tools people can come up with different solutions to similar problems. And then we are in a position to ask “are there any aspects of the medieval solutions to these still-occurring modern worries that could be usefully implemented in a modern context?” And that is why studying the history of logic matters — not so that we know the who, the what, and the when, but so that we know the why and the how, because these whys and hows can still be applicable and relevant to today’s concerns.

If the question merely is “Were there infinitary logics in the Middle Ages?” I’d have to answer know. But if the question is “What did medieval logicians have to say about infinitary (or even unbounded) conjunctions and disjunctions?” then we have something to say.

Rules of ascent and descent

And what we have to say starts with the idea of “rules of ascent and descent”. These are rules that tell us what singular statements we can infer from a subject-predicate proposition with a general noun phrase (including quantified noun phrases) as the subject, and when we can infer the generalised form from a collection of singular statements. (A singular statement is one where the subject term applies to exactly one thing, e.g., when it is a proper name (“Socrates”) or a demonstrative pronoun (“that”) or a demonstrate pronoun attached to a noun (“that cat”) or adjective (“that red [thing]”).)

Discussions of the rules of ascent and descent can be found mainly in three different genres of logical texts, in the 13th and 14th centuries: treatises on supposition, syncategoremata, and sophisms.

Treatises on supposition

The 13th century saw the development of a semantic genre called “the properties of terms”, of which the two most important properties were signification and supposition. [2] The signification of a term, very roughly speaking, the meaning of the term independent of any considerations of its use in a sentence: For instance, the word ‘cat’ signifies all cats, both present, past, and to come. All meaningful/significative words can be divided into two types, those that signify on their own (such as ‘cat’, ‘dog’, ‘man’, and other nouns, verbs, and adjectives), and those that only signify in conjunction with another term (such as ‘and’, ‘not’, ‘every’, ‘only’); these latter words are said to ‘consignify’. But while a term’s signification is fixed, its supposition — the objects signified by the word that are actually under consideration — varies according to syntactic context. For instance, if I speak of ‘every cat’, then, absent any other modifiers in the sentence, ‘cat’ supposits for every presently existing cat. If, however, I speak of ‘that cat’, then ‘cat’ supposits only for the single cat that I am indicating with the demonstrative pronoun. What, then, is the relationship between statements predicating the same predicate of ‘every cat’ and ‘that cat’? Certainly, if something is true of every cat, then it will be true of that cat as well — if every cat is an animal, then that cat is an animal. And that is an application of a rule of descent! But the rule is stronger: Not only is that cat an animal, but this one is too, and this one, and this other one as well, and so on for all the cats. Alternatively, if that cat is an animal, and this one is as well, and this one, and this other one, and so on for all the cats, why, then all cats are animals. (And this would be a rule of ascent.)

“and so on”? Hold that thought…

Treatises on syncategoremata

Just as words can be identified as either significative or consignificative, they can also be identified as categorematic or syncategorematic. [3] Specific treatises were devoted to the analyses of syncategorematic words, including universal, partial, and indefinite quantifiers, modifications of quantifiers (e.g., exceptives and exclusives), and demonstrative pronouns, all of which are intimately related to rules of ascent and descent.

Treatises on sophisms

Once you define how words work and the rules that govern them, then you can come up with puzzles — and the inferential relationships between the different types of supposition that a word can have, and how that supposition can be modified by modifying where in the sentence the word (or phrase) occurs were a prime source for such puzzles. These puzzles, called sophisms, were sometimes discussed in separate treatises specifically devoted to the topic; and questions of when and how one can descend from a universal or ascend from a partial were discussed in the context of puzzles that question the standard statements of the rules.

What is the problem, and what do people say about it?

The problem is the “and so on”: How does one know when one has exhausted all of the possibilities, whether ascending or descending? Though the problem is most acute in infinite domains, it even arises in finite domains, because there is still an asymmetry between the quantified sentences and the conjunctions, in that every conjunction entails each conjunct, but no single conjunct entails the entire conjunction (except in degenerate cases where one of the conjuncts is an impossibility, or where the conjunction only has one conjunct). This means that descent is simpler than ascent, as we now show:

Suppose that we have four cats, Widget, Slinky, Goldwine, and Nefertari. If we know that ‘Every cat is an animal’, we can descend to ‘This cat is an animal’, pointing to Widget; ‘This cat is an animal’, pointing to Slinky; and so on. If we stop at Goldwine, then we are still expressing truths, just not all of the truths we could possibly express. Suppose, on the other hand, that we know that ‘this cat is an animal’, pointing to Widget; ‘this cat is an animal’, pointing to Slinky; and ‘this cat is an animal’, pointing to Goldwine; this alone does not warrant an ascent up to ‘Every cat is an animal’, because there is a cat that we haven’t yet included in our enumeration, namely, Nefertari. The problem is that adding Nefertari to the list is not enough: Even after we’ve said ‘this cat is an animal’, point to her, we are not yet in a position to say ‘Every cat is an animal’, because we need a further constraint: “And these are all the cats”. When the domain is finite, it is possible to add this further statement; in an infinite or unbounded domain, it is not always straightforward to do so.

How, then, do medieval authors handle the “and so on”? In this post we will look at four authors; and in a future post I’ll hopefully look at others (particularly some 14th-century ones), as well as some of the sophisms that arise from the ascent/descent rules.

William of Sherwood

William of Sherwood first mentions descent when defining the two types of personal supposition (which is when a word stands for a thing bearing the form signified by the word), in his Introduction to Logic [4]:

[Distributive confused personal supposition is] mobile when a descent can be made, as in the term ‘man’ in the example above [‘Every man is running’]. It is immobile when a descent cannot be made, as here: ‘Only every man is running’ (for one cannot infer ‘therefore only Socrates is running’) [pp. 108-109].

According to Kretzmann, “Sherwood’s notion of logical descent is quite stringent…Sherwood’s descent is unquestionably irreversible” [fn. 29].

Immobility arises purely on the part of descent; a few pages later, in Rule V, Sherwood argues that it may still be possible to ascend in the case of immobile supposition:

Sometimes, however, distribution remains immobile, as in ‘not every man is running’, ‘only every man is running’, and other cases of that sort. It is called immobile, however, not because we cannot ascend in the subject but because we cannot descend [p. 119].

That is, Sherwood indicates, obliquely, that from ‘Not Socrates is running’ we can ascend to ‘Not every man is running’: But this is because of the way in which negation interacts with quantification, namely, the fact that to negate a universal a single counterexample is all that is required.

Sherwood does not discuss the case of general ascent from a conjunction to a universal.

Roger Bacon

Roger Bacon, in his Art and Science of Logic [5], also invokes the notions of descent and ascent when defining his typology of supposition. However, he is more explicit as to what descent is:

Confused and distributive supposition occurs, therefore, when a common term supposits for all its inferiors and there can be a descent to any one of them, as in ‘Every man runs; therefore this man runs, and that one, etc.’ [∥ 219]

Merely confused supposition occurs when such a descent cannot be made.

Despite the fact that “ascent” appears in the index, Bacon does not explicitly mention ascent at all.

Lambert of Auxerre/Laigny

Like the preceding two authors, Lambert‘s first mention of ascent or descent in the Summa Lamberti [6] is in his definition of strong mobile supposition:

Strong mobile supposition is what a common term has when it is interpreted necessarily for all its supposita and a descent can be made under it. This happens when a universal affirmative sign is added directly to a common term, as when one says ‘Every man runs’, and likewise when a universal negative sign is added indirectly or directly to a common term, as when one says ‘No man is a stone’…It is called mobile with respect to a term having such supposition because in a term having such supposition a descent can be made on behalf of the supposita contained under it [∥ 1263].

He does not discuss ascent at all.

Peter of Spain

Finally, we look at what Peter of Spain has to say in his Summule logicales [7]. His primary mention of descent is in the context of defining mobile supposition:

[That term ‘human’ supposits] movably because descent is permitted to anything whatever that it supposits for, as in:

Every human;
therefore, Sortes


Every human;
therefore, Plato [p. 249]

However, he also, unlike the others, considers sophisms arising from the rules and definitions of supposition, one of which invokes the notion of descent. Due to the great length this post has already gotten to, we will save it for future work.

Brief conclusions

The four preceding views that we looked at have a number of things in common: First, they are all 13th-century, and second, all of them (with the exception of Peter’s second example that we haven’t discussed here) come from treatises or chapters on the properties of terms. These two features together provide a likely explanation for the third commonality, namely, that most of them discuss the “and so on” problem. This is something that we can expect to find more explicit discussions of in treatises on sophisms (logical puzzles) arising from supposition theory — as we see in Peter’s second discussion of it –, as well as in later authors (we’ll try to visit the 14th century in a future post!) for whom the fact that there is a potential problem had been raised via the sophisms literature.


[1] Bell, John L., “Infinitary Logic”, Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.).

[2] For more on both of these, see both Uckelman, Sara L., “William of Sherwood”, Stanford Encyclopedia of Philosophy (Summer 2016 Edition), Edward N. Zalta (ed.) and Read, Stephen, “Medieval Theories: Properties of Terms”, Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.).

[3] Well, strictly speaking, words are neither categorematic nor syncategorematic, but they are used categorematically or syncategorematically. Cf. Uckelman, Sara L., “The Logic of Categorematic and Syncategorematic Infinity”, Synthese 192, no. 8 (2015): 2361-2377.

[4] Kretzmann, Norman (ed.), 1966, William of Sherwood’s Introduction to Logic, Minneapolis: University of Minnesota Press.

[5] Bacon, Roger, 2009, The Art and Science of Logic, Pontifical Institute of Medieval Studies. Trans. by Thomas S. Maloney.

[6] Lambert of Auxerre, 2015. Logica or Summa Lamberti. University of Notre Dame. Trans. by Thomas S. Maloney.

[7] Brian P. Copenhaver (ed.), 2014, Peter of Spain: Summaries of Logic, Text, Translation, Introduction, and Notes. Oxford University Press. With Calvin Normore and Terence Parsons.

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