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

or

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.

References

[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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Upcoming Conference: Inaugural Pan-American Symposium on the History of Logic – Validity throughout History

At the end of May, UCLA will host the first Pan-American Symposium on the History of Logic[=PASHL]. For four days (24-28 May), experts on different logical and philosophical traditions – from Antiquity to the early 20th century – will meet to discuss about the notion(s) of Validity throughout History.

It is not the first time that I write about this upcoming conference, but this is a pet project of mine and I hope that our readers will forgive me for my self-indulgence. Besides, truth is, I think it is going to be an exciting event, not only for the parties directly involved, but for historians of logic and rationality in general, because we are trying to propose something new in the way we do the history of logic and, hopefully, influence the possible routes that future research should explore.

I should thank profusely the UCLA Department of Philosophy and the Centre for Medieval and Renaissance Studies for sponsoring, financing and hosting this meeting. I also cannot thank enough my co-organisers (Calvin Normore and Milo Crimi) for their time and the hard work that they have devoted to this. But I would also like to use the space at my disposal to say something more about where the PASHL comes from, what it is meant to be, and where we would like for it to go.

The idea stemmed from three different consideration.

(1) As of now, most of the academic events in the history of logic are hosted in European universities – which is understandable, at the very least because on that side of the Pond there is a somewhat stronger emphasis on the history of philosophy and sciences within the standard curricula. However, this means that most grad-students and early career researchers from outside the Old Continent have a hard time attending any of those meetings. The intention of this conference is to offer them a closer alternative.

(2) In recent years, we have noticed a tendency towards a “metaphysical turn” in larger scale conferences in the history of logic, relegating the technicalities of the “old logical stuff” to small workshops. While this is not a problem per se, as much as a mirror of the current research trends and academic interests, it puts a misleading emphasis on the non-logical stuff that is indeed part of traditional logic, however it is clearly not so dominant a part as some nonspecialist might be let believe by looking at those conferences’ programmes or skimming through the proceedings. We have tried to put the emphasis back on the logic in the history of logic. What better starting point than the notion of validity?

(3) Historians of logic tend to be locked in their own subfield bubbles and their interactions are sporadic and limited to closely related traditions, usually with a heavily Western focus. While this a widespread problem throughout the history of philosophy, it is particularly puzzling and urgent in the history of logic since very often contemporary logicians have advanced claims of eternality and universality. We have tried to create a larger space for dialogue and comparison, across time and space. So we will have talks on medieval Latin logic alternating with papers in Ancient, Byzantine, Arabic, Sanskrit, and Early Modern logic – not by focusing on questions of transmission and reception, but on a fundamental conceptual issue.

This spirit of openness and inclusivity has motivated our scientific choices and our invitations, with the intent of having a generational dialogue as well. Our hope is to create a biannual appointment in the Americas and to help make our discipline more comparative, more dialogical and more aware of what is going on in its many subfields.

We have a magnificent line-up (that you can find here) and no registration fee; so if you are in the area, feel free to come by.

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Notre-Dame de Paris and Medieval Philosophy

Monday night people across the world watched in horror as one of the most iconic buildings in France burned. The scenes of the raging inferno and the toppling steeple were horrifying, and the tragedy was compounded by uncertainty — would the rose windows and the bells survive? How many relics would be lost? Were there any casualties? But as the night drew on, I found many people expressing a view of what happened of it being total destruction, irrecoverable, a loss that could never be repaired, a view that I could not subscribe to knowing what I do of medieval history, and I wrote a post on Facebook about an alternative view, a post that ended up going surprisingly viral.

I’m by no means an expert in cathedrals or in ecclesiastical history, but the study of logic and philosophy is intimately connected to both of these thing, and one cannot do research in medieval logic without rubbing elbows with cathedrals all over Europe. As inquiries and interview requests came pouring in (such is the result of 15 minutes of internet fame!), I found myself reading up on the history of the construction of Notre-Dame de Paris, and realised something that I should probably have realised a decade ago: When historians and philosophers speak of the “cathedral school in Paris”, where William of Champeaux taught in the 12th century, and which was one of the incubators for the 13th-century birth of the University of Paris, the “cathedral” in question was Notre-Dame.

Notre Dame de Paris

Notre Dame de Paris, June 1999

Well, the Gothic cathedral was we know it wasn’t begun until after William’s time — construction on that edifice began in the 1160s, whereas William became a canon in 1103 (he resigned in 1108 to move to St. Victor). But one of the points that I stressed in my FB post, which seemed to strike such a chord with so many people, is that a church is more than the building it is housed in. Whether it is the Gothic cathedral completed in the 13th century, whether it’s the earlier Romanesque remodeling, whether it’s the 19th C version with the spire constructed after renewed interest in the cathedral due to Victor Hugo, whether it’s the version to come when it’s prepared, Notre-Dame remains.

The photo above is one that I took in June 1999, on my first trip to Europe, shortly after I’d graduated high school. The three weeks I spent in Italy, Austria, and France were transformative, and I went home knowing that one day, I would be going back to Europe for good. Notre-Dame was one of the last sites that we visited, and I remember staring up at the gargoyles until I got a crick in my neck. Little did I dream then that 20 years later I’d be studying and learning from the same masters that taught there so many centuries earlier.

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On Ladies’ Fashion, Plastic Surgery, and the History of Logic and Philosophy

My last two entries for the column What’s hot in medieval reasoning are really a two-parter on the History of Philosophy and the History of Logic. It’s both a bit personal and more than a bit silly – but I am a rather silly person, so…

It’s not strictly medieval, but it might be of interest.Image result for allegory logic

[Pt. 1 The Reasoner vol. 13, n. 2 (February 2019)]

[P]hilosophers’ convictions about the eternity of problems or conceptions were as baseless as a young girl’s conviction that this year’s hats are the only ones that could ever have been worn by a sane woman.

This passage in Collingwood’s An Autobiography (Oxford 1939, p. 65) has always resonated with me. The thing is, I am not entirely convinced that Collingwood was right, but he might have been onto something – besides women’s fashion. As a historian of medieval philosophy (and a casual historian of fashion), my professional identity is an odd beast, like a unicorn or a chimera. Not in the sense that historians of philosophy are mythical monsters – you can find a few of us wandering around departments of philosophy and it doesn’t look like we are particularly close to extinction, yet. But in the sense that we have multiple natures: we are historians and we are philosophers. On the one hand, the historian within me knows that Lady Philosophy has changed a lot over her long life. My inner historian likes to picture her as an old lady who’s had a few plastic surgeries too many and has lost a few bits here and there – oftentimes to replace them with more or less eccentric prosthetics, only to occasionally switch them over again, to keep pace with the ever-changing fashions of the day. Or perhaps my inner historian entertains the idea that Philosophy is not quite a lady, but rather a barely sketched vaguely written role interpreted by different actors; or even better an artificial person, like an institution: what that institution is and does changes with the people inhabiting it, its practices, its reformations and, overall, the times, and yet the institution itself is still in some sense the same. Some days, my inner historian thinks of Philosophy as a bit of both – the old lady and the institution – , i.e. the same sort of patchwork creature that we, her historiographers, are. Long story short and out of metaphor, a good chunk of philosophical issues and conceptions, that were essential at some point or another in the past, doesn’t count as philosophical at all in our eyes – think, for example, of some of the things historians of ideas, theology, or even science are interested in. The converse would probably be just as true. At the end of the day, my inner historian acknowledges the data and interprets it, trying to tell a coherent story of the hows and whys of this historical development. On the other hand, the philosopher within me is more conflicted, which is not surprising. My inner philosopher wants to believe that philosophical questions and theories, for the most part, are not unsolvable conundrums or unchanging truths – the very same we have been dealing with since the dawn of our discipline – that we have been doomed to address until the end of time, with no real hope of resolution. What a boring and utterly hopeless endeavour would philosophising be then! Yet, my inner philosopher has a recognition that there is some sense in which the stuff she is doing is the same kind of stuff that the philosophers of the past were doing, i.e. philosophy. That recognition might however be misguiding, or even delusional, not merely because my inner philosopher might be that bad at philosophising, but because the recognition itself comes with a preconception – very much shaped by our time and curricula – of what philosophy is supposed to look like. My inner philosopher, then, wonders about whether there is some deep core to philosophy, i.e. a set of essential features making something into “philosophy”, i.e. a common denominator shared by anything that was, is and will be philosophy, across ages and continents. It’s a tempting thought, of which my inner philosopher – fancying herself to be as nominalist as they come and being good friends with my inner historian – is pretty weary. The problem is even more evident as far as logic and its history are concerned.

[Pt. 2 The Reasoner vol. 13, n. 3 (March 2019)]

Just as with Lady Philosophy – or possibly even more so – several of Logic’s more or less committed lovers entertain the notion that their beloved remains eternally beautiful and true, i.e. that there is some unchangeable set of core features that make up Logic. Maybe this common attitude in thinking about Logic is due, at least in part, to the normative persuasion that Logic has always seemed to have. Or perhaps it’s because of the mathematical attire that Logic has put on in her modern incarnation. And certainly the fact that those devoted suitors of Logic often seem to believe her to be a young lady, born around 1879 or a handful of years earlier, reassures them in their belief of her unchanging nature and eternality – no matter how said belief is at odds both with Logic’s supposed young age and with the numerous deep changes that she has undeniably gone through during her presumedly short life. Philosophy is undeniably a silver fox, or a snake who has shed her skin and reinvented herself a few times too many; but as of now there aren’t many radical ongoing disagreements about what Philosophy is or is supposed to be – not so much about Logic, though. Even without committing to a form of logical pluralism – or especially then – many may even agree about Logic being in some sense normative. However, they disagree a lot about what the actual norms are, and overall about what Logic really is. At the end of the day, paraphrasing Anandi Hattiangadi, we are not even able to provide an adequate account of what we disagree about when we disagree about logic. (If you are curious about logical disagreement and want to go through a recent overview, go check out her chapter in C. McHugh – J. Way – D. Whiting (eds.), Metaepistemology, Oxford 2018). To complicate matters even further, if we look back at those long centuries between roughly Aristotle’s time and the publication of Frege’s Begriffsschrift, we find a bunch of folks claiming to be doing logic and debating about what that is as well as what it’s supposed to be. At this point, Logic’s fashion sense is on a different wavelength: she appears draped in a regimented version of ordinary language and sometimes she goes a little heavy on the ontology. Yet, she is still mainly about figuring out what follows validly from what, she is conflicted about what counts as formal, as well as what she should be doing with herself. Overall, traditional Logic is both recognisable enough for a modern reader to perceive her as something very much like a three-for-one deal combining Logic, metalogic and philosophy logic, or as what we would call reasoning at the very least. But traditional Logic is also other and different enough that sometimes we don’t really grasp what’s going on and have no idea about what to make of it. Many historians of medieval logic in particular are quite convinced that the object of their studies is not logic at all, but something else entirely that happens to be “logic” in a merely equivocal sense – see, for example, Laurent Cessali’s “What is Medieval Logic After All? Towards a Scientific Use of Natural Language” and ”Postscript: Medieval Logic as Sprachphilosophie” in Bulletin de Philosophie Médiévale 52 (2010), respectively p. 49-53 and 117-132. Personally, I think that there are several historical and philosophical reasons to be weary of this kind of approach – but this is a topic for another issue. Overall, I much prefer Paul Vincent Spade’s way of framing the problem (paraphrasing): “They called it logic, and they were there first”. Taking the self-proclaimed logicians of the past seriously – at least insofar as they claim to be logicians! – we might actually try to asses whether Logic is neither as young as she is often made out to be nor a series of identity thieves stealing one name to carry on very different lives. Over the course of her long existence, Philosophy has had a few drastic makeovers but has remained – for the most part – recognisable in her evolution, without any harsh breaks in continuity. While it would be unwarranted to claim that Logic has simply put on a fancy new dress embroidered with mathematical symbolism, she might have gone through a more radical and extreme version of the process Philosophy went through, with some breaks in continuity, to the point that she doesn’t look like herself anymore, but rather like a distant cousin. Who knows, maybe reconstructing the details of what Logic was and her changes over time could help us deal with our own disagreements and figure out what else Logic could be. It would probably still be better than holding onto the conviction that Logic is eternal: “if logic is eternal, then it can wait” (attributed to Oliver Heaviside), but a lady should never be left waiting!

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Buridan is dead, long live Buridan!

Semblablement, où est la reine 

Qui commanda que Buridan 

Fut jeté en un sac en Seine? 

Well into the 15th century the “buzz” about Buridan’s life and death was still circulating [1], since François Villon could record it in his Ballade des dames du temps jadis alongside some mythical and historical anecdotes that may sound more familiar, at least to a modern reader, presumably without any worry of being too cryptic.

Although it is probable that Buridan’s death was neither that unusual nor so gruesome, we still don’t know much about it, beginning with even when it was.

There is evidence leading to suppose that Buridan died on the eleventh of October, but the year is unclear. [2] We know that he was still alive and well in the summer of 1358, since he was dealing with an administrative incident between his Nation (Natio Picardiae) and the Natio Anglicana.

In 1356, a dispute erupted between these two nations concerning a student, John Mast, who, having determined with the natio Anglicana to which he belonged, petitioned to incept with the natio Picardie. Themon Judeus, Anglican magister artium, refused his approval. The controversy was not settled until the end of 1358. A general assembly had already convened in the beginning of June 1357 and decided to exclude the two proctors (i.e. the heads of the nations) from being part of the committee that would arbitrate the dispute. In July, John Buridan was sent to submit a rotulus with the arguments of the natio Picardie and to argue their case before the committee. The two nations resumed the negotiations in July 1258 and the representatives reached an agreement on 12 July [3].

It is generally presumed that Buridan was dead by 1361, since a benefice from the Collegiate Church of St Paul-sur-Ternoise (Arras) – of which Buridan had been the beneficiary for some time, possibly for life – was devolved to someone else. [4] On the one hand this would make for a reasonably persuasive argument that at this point Buridan was not among us anymore – because who would pass on some easy money that had been coming on the side already for a while? On the other hand, one might argue that benefices of this kind were destined mostly to advanced students and young masters in need of financial support, and certainly not to popstar philosophers at the end of their prestigious careers. Besides, there may be hints here and there that could lead us to forward the date, or at least to do more research on the issue. For example, as Bert Bos noticed several years ago, one of the manuscripts of Buridan’s Quaestiones super octo libros Physicorum (Liège, 144 C, f. 2ra) reads: “Tabula questionum libri primi Physicorum magistri Iohannis Buridani in vico straminum Parisio anno domini MºIIIº66º pronuntiatarum”[5]. That “1366” could well be due to a scribal error. If it turns out to be confirmed by other sources, we would not have a much better approximation of Buridan’s date of death, but we might have to reconsider the physiognomy of Parisian philosophy in the third quarter of the 14th century.  And that is definitely worth checking out!

 

 

[1]  Edmond Faral, Jean Buridan: Maître des Arts de l’Université de Paris, Extrait de l’Histoire littéraire de la France, Tome 28, 2e partie, Paris 1950, Imprimerie Nationale.

[2] Stephen Read, “Introduction” to John Buridan, Treatise on Consequences, New York 2015, p. 1; for some more references, check Read’s notes (n. 1, p. 163).

[3] See Denifle – Chatelain (eds.), Auctarium Chartularii Universitatis Parisiensis, vol. I, p. 206-212 and 233-236.  On a side note, among the witnesses deemed trustworthy who signed the settlement (specially chosen and summoned for the occasion), we find both John Buridan and Albert of Saxony. The day after, the masters from both nations met to celebrate the happy resolution of the controversy at a local tavern. William Buser was there (he helped with the part of the bill that the nation’s funding did not cover), Albert of Saxony was there too (and he apparently had to borrow money from John Mast, the student!), and presumably so was Buridan, being one of the witnesses – although we don’t know for certain, but that might just be because Buridan knew how to manage his own money wisely.

[4] Read, p. 1-2

[5] E.P. Bos, review of Hubien’s edition of the Tractatus de consequentiis, in Vivarium XV (1977), p. 159-160.

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Who is Luisius Turrianus?

All right, this isn’t quite medieval, nor quite logical, but in the context of researching “Pepper is sold here and in Rome”, I came across a post-medieval text that mentions this example, in the context of a theological discussion. And I had no idea who the author is.

The text is Tractatus de Augistissimo Trinitatis Mysterio, printed in 1630. The text is attributed, in Latin, to “Luisii Turriani”. This name does not appear in any wikipedia — not totally surprising since often the Latin forms of names of Renaissance people don’t appear in the relevant articles. The issue is that it’s not immediately clear what the right vernacular is — I searched for “Luisio”, “Luigi”, “Luigio”, “Ludovico”, “Lodovico”, etc., working under the (ungrounded) assumption that the author was Italian.

However, I then took a closer look at the dedication of the book, which is:

Ad illustrissimum, et excellentissimum Dominum D. Bernardinum Fernandez de Velasco Castellae, Legionisque Comitem Stabilem, Ducem de Frias, Marchionem de Berlanga, Comitem de Haro, & Castilnouo, antiquissimorumque Larium de Velasco, & Lara Dominum, Regium cubicularium, &c.

(The duke in question is probably the 6th duke of Frías (c1610-1652), rather than the 1st duke of Frís (c1450-1512), who bore the same name.) Perhaps Turriani was Spanish, not Italian.

If one googles for “Luisii Turriani” one gets a number of library catalog records; the Tractatus de Mysterio is not the only thing he wrote. There’s a Diuersorum opusculorum theologiae, a Disputationum in secundam secundae D. Thomae De iustitia, a Tractatus de Angelis, a Disputationes de poenitentia, and a Tractatus de censuris [et] irregularitate, among others (this list may be complete) — and these are the only hits google has. But! The library catalogues also list these works under the authorial name “Luis de Torres”, and one even gives his dates as 1562-1655! We’re getting closer…

But none of the Luis (de) Torres in wikipedia is the right one. (Nor indeed are either of the Ludovico de Torres). Digging through google hits for “Luis de Torres 1655”, we find precious little information. He was a Jesuit (this is clear from the title page of the De Mysterio: “Luisii Turriani Complutensis e Societate Iesu in Eiusdem Complutensi Collegio”, and he was previously a professor of theology. This page gives his birthplace as Alcalá.

James Tunstead Burtchaell, Catholic Theories of Biblical Inspiration Since 1810: A Review and Critique, gives de Torres’s birthdate as 1582, not 1562, and simply calls him “a Spaniard”, and lists him in a group of Jesuits who held the “more rigid view that the entire text of the Scriptures had been supplied word-for-word by the Spirit to the human writers” (p. 88).

And that’s about it. I have been unable to turn up anything more on this elusive — yet prolific! — figure, other than that he is likely not the Don Luis de Torres Mazuela(s) (or Ma&ccedila;uela(s)) who is mentioned here, here, and here.

Anyone got any more info on this guy? I’d be very interested to know more about him!

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