Why medieval logicians aren’t ‘medieval’

‘Medieval’ is so often used as a pejorative, particularly in contemporary culture. One only need to hang around with #twitterstorians and #medievaltwitter to hear the collective teeth grinding whenever ‘medieval’ gets used by, e.g., modern journalists in this way.

Well, it’s time to grind my teeth a bit, but hopefully in a way that is at least a bit productive.

One of the thing that surprised me most when I began working in medieval logic was how interesting all of it was and how little anyone knew about it; why did it take until the 1950s that people started looking seriously at medieval logical texts? Why are their developments still not routinely integrated into modern logical pedagogy and research? The more I read about the history of logic and the history of philosophy, the more I saw that the consequences of the Renaissance and Humanist backlash against “Scholastic philosophy” were still perpetuating on to today. Scholastics weren’t interested in anything other than wrangling about angels on pinheads. Their motives are outdated, their methods are too abstruse. They don’t have anything to tell us today.

And thus we get 500 years of ignorance of medieval logic.

Unfortunately, this negative view of Scholasticism and its methods still abounds. Recently I was reading Steven Nadler’s “Who was the first modern philosopher?”, and in the midst of what is an otherwise very interesting and well-written piece, I came across this:

By contrast, it is more difficult to find such affinity between contemporary thought and medieval Scholastic theories and methods.

Huh, I thought, That’s surprising. I am routinely astounded by the amount of affinity between contemporary logical thought and medieval Scholastic logical theories and methods. I wonder what Nadler is referring to, or what he is classifying as “Scholastic theories and methods”?. A little bit later on, I read:

In terms of its method, the New Philosophy (for this is how contemporaries often referred to it) was generally characterized by a reliance on reason and empirical evidence rather than devotion to religious or ancient authority to determine what is and what is not philosophically and scientifically acceptable.

Huh, I thought, What about the after effects of the 1277 condemnations, wherein the Arts Masters began to investigate Aristotelian mechanics in a wholly secular fashion, without any reference to God and God’s capacities?. And then I read:

The modern philosophers, unlike their Scholastic predecessors and less progressive contemporaries, regarded terrestrial and celestial phenomena as constituted by one and the same kind of matter and governed by a single set of laws.

Huh, I thought again, What about that treatise I translated and analysed in my dissertation, where the anonymous author went to great pains to explain how Aristotelian syllogistics can cover both created and divine matter, to show how the so-called paralogisms of the trinity were in fact simply invalid. That sure sounds like someone regarding terrestrial and celestial phenomena as being governed by the same set of rules and reasons (even if maybe metaphyiscally they are distinct).

Now, Nadler hasn’t set out in his piece to give an account of the character of medieval philosophy; he’s trying to answer a question about “modern” philosophy. Nevertheless, throwaway remarks about how “medieval” medieval philosophy was — which is what the comments above amount to — are problematic. They are problematic because they range from misleading to outright wrong — or, if this is a correct view of medieval philosophy, then the appropriate conclusion to draw is that logic from the late 11th to the end of the 14th centuries was not “medieval”.

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Scholastic learning in late 15th C Italy: One very small snapshot

Today I picked up an ILL book which I’d requested for reasons entirely unrelated to philosophy/logic:

Cesare Cenci, Documentazione di vita assisana 1300-1530, volume II: 1449-1530 (Grottaferrata: Collegii S. Bonaventurae ad Claras Aquas, 1975).

Apparently, no one in Manchester is greatly enthused by Assisi, since virtually all of the pages were still uncut. I spent the better part of an hour this afternoon cutting them, which means I glanced at almost every page.

Capital letters catch my eye, and when I saw a Boetius, my first thought was “Huh, that’s a bit unusual in 15th C Italy, someone’s parents were clearly influenced by antiquity”, until I read the next phrase, de consolatione. Oh! It is the antique Boethius!

And then I saw super sententias elsewhere in the treatise, and sententie Iohannis Damasceni, and then I was reading from the beginning because here was a huge list of books, and I wanted to know the context.

The context is a donation of books from one Çacharias de Tergesto, a member of the Friars Minor and a warden of Istria, along with Almerichus de Mugla, Angelus de Castagnano, Antonius de Mugla, and Pasqualinus de Ubaldinis, to the Basilica of San Francesco d’Assisi in 1467. Because it is so interesting — and I am sure someone who is working in the transmission of Scholasticism in late 15th C Italy will find this relevant — I am reproducing the list of texts below; items in [square brackets] are notes added by the editor, providing further information identifying the texts:

in primis quatuor volumina cum tabulis conventus [s. Mariae] Venetiarum,: primum volumen est secundus et tertius d. Bonaventure super sententias, secundus Alexandri et quartus Ricardi. Item, 13 quinterni in pergameno, in quibus sunt aliqua Augustini et Gregorii. Item, magister sententiarum completus et sententie Iohannis Damasceni; suus. Item, quadragesimale dictum et pelegrino. Item, conpendium theologice veritatis [Hugonis de Argentina], in pergameno, cum tabulis coopertus. Item, tabula martiniana [Martini de Troppau] decreti et decretalium. Item, Tulius de officiis, cum tabulis et corio rubeo, cuius principium: quanuam te, Marce; finis vero: rebus misterii. Item, Persius [satyrae], cum tabulis et corio albo ad ligaturas; finis vero: liber, amen. Item, quadragesimale quodam in papiro, sine tabulis, cuius principium: voca, operarios; finis vero: ego dico sitio. Item, sermones predicabiles, in papiro, sine tabulis, cuius principium: fecit Deus duo; finis vero: tu es sacerdos. Item, Boetius de consolatione, in pergameno, sine tabulis. Item, Tulius de amicitia et paradoxe, in papiro, sine tabulis. (Charter no. 1)

(As it turned out, I was cutting pages while catching up with a friend who is writing her PhD thesis on parchment making practices, so we paused a moment to squee over the fact that some of these were noted as on parchment and others as on paper.

So, not exactly logic, but still, really cool!

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A brief note on logical constants.

Most of my logic this year has been modern rather than medieval, but a few nights ago while reading up on intuitionism for this morning’s seminar, I came across an interesting comment on Dummett’s semantic molecularism:

Dummett’s proposal is that at least some crucial parts of language can be understood independently of any other parts. This applies, first and foremost, to the logical terminology: connectives such as negation, conjunction, disjunction, and ‘if-then’, and quantifiers like ‘there is’ and ‘for all’ [Shapiro, Thinking About Mathematics, pp. 193-194, emphasis added].

What struck me is that these things, these first and foremost examples of what “can be understood independently” of anything else, are exactly those things which the medieval logicians insisted could not be understood independently of anything else.

Do philosophy long enough, and for any person who argues for φ, eventually you’ll find someone who’ll argue just as strenuously for ~φ

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Who thinks that reason is social?

According to Aristotle’s Politics, humans are both rational and social animals. I wonder from what time onwards rationality and sociality were taken to be related. Of course you might think that they are not related in any interesting way. But it is clear that some philosophers took them to be related. One way of putting the problem is to combine these properties in a priority question: What is prior to what? Is rationality prior to sociality or is it the other way round. Is it reason that makes us social or is it sociality that makes us rational?

According to many medieval authors, human rationality is taken to be independent from human sociality. That’s why Aquinas, for instance, famously says that, if humans weren’t also social, they wouldn’t need langage on top of concepts. By contrast, people like Thomasius and Kant claim that rationality might depend on sociality. If we weren’t social, we couldn’t think (properly). So, reason is taken to be, to some extent, social (and therefore linguistic). Now this shift of emphasis seems to become more pronounced in the 18th century, but my hunch is that it might originate at least in Grotius and Pufendorf, who make socialitas the (anthropological) basis of natural law.

But I wonder whether this might not have some roots in earlier authors. Humanist and Renaissance philosophers might come to mind, but not to mine… So if you have any ideas regarding sources about the social nature of reason, please send them my way.

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Public lecture (Durham): “Medieval and Modern Explorations of Human Colour Perception” (Jan. 24)

This isn’t quite logic, but rather metaphysics, epistemology, and perception, but considering the audience of this blog, we figured some here might be interested in the following talk happening next week:
“Medieval and Modern Explorations of Human Colour Perception”

Dr. Hannah Smithson

Abstract: Can science today learn from thirteenth century literature? An interdisciplinary team of physicists, medievalists, Latin scholars and historians of science has embarked on a rich encounter with the great medieval English thinker Robert Grosseteste (1175-1253). The team presents Grosseteste’s treatise the De colore (On colour), to reveal and explore the three-dimensional space within which he characterises colour. His later treatise the De iride (On the rainbow) revisits his theory of colour generation, but with surprising results when seen from modern perspectives. By using medieval studies and modern colour science, the treatises can be interpreted in new, stimulating and more complete ways. Almost 800 years after their inception, Grosseteste’s writings prompt us to explore a new coordinate system for colour.

For more information see here.

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What can you think of?

The St Andrews medieval logic reading group has been working its way through Part II Fascicule 6 of the Logica Magna, which is on the truth and falsity of propositions. In the discussion of the Eighth Way (identified as Peter of Mantua’s by Francesco del Punta), which stems from the following two rules:

  1. A true proposition is an indicative, perfect univocal expression through which the intellect is adequately rendered correct.
  2. A false proposition is an indicative, perfect univocal expression through which the intellect is not adequately rendered correct.

Paul gives us the following very strange argument, that this Way “asserts that no one can think of non-being, nor can anyone think of what is not thought of”.

For he [presumably Peter of Mantua] argues as follows: Precisely being can be thought of. Therefore, non-being cannot be thought of. The premiss is clear, since being can be thought of and nothing that is not a being can be thought of. The opposite implies a contradiction. Similarly, he proves that only what is thought of can be thought of, from which he concludes that what is not thought of cannot be thought of [p. 59, emphasis added].

I can guarantee that this is the strangest philosophical position you’ll see this week.

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Ex impossibili sequitur quidlibet in the 13th C (part 2)

Oh, look, it’s Thursday again! Time to write another medieval logic post. We’re still doing Aristotle in my intro class, so I haven’t any new interesting medieval tidbits from class prep to share. So I guess I’ll just return to the question of ex impossibili sequitur quidlibet in the 13th century; you can find part 1 of the discussion there. In this part we return to Spruyt 1993 and continue our discussion of views opposing ex impossibili, taking up the positions in the Sophistaria wrongly attributed to Walter Burley, Peter of Spain’s Syncategoremata, and Henry of Ghent’s Syncategoremata.

First, Spruyt notes that it isn’t actually clear whether the author of the Sophistaria was an opponent or proponent of the thesis, but she takes him to be an opponent since “he starts off his treatise with arguments in favor of the rule, and quite a number of Medieval authors who wish to defend a certain position often begin by presenting arguments to the contrary” (p. 168). These arguments include:

(1) The necessary follows from the impossible. But nothing is more contrary to the impossible than the necessary. So if even the necessary follows from the impossible, anything which is less contrary to the impossible will also follow (and everything is less contrary to the impossible than the necessary).

(2) An argument from the definition of valid argument (which Spruyt doesn’t further discuss).

(3) If you are a man and not a man, then you are not a man. If you are a man, then either you are a man or anything is true. Thus, if you are a man and not a man by disjunctive syllogism, anything is true.

The arguments against the position are especially interesting to me because they involve impossible positio. First, assume that nothing that follows from something is contrary to it (contra (1)). If anything followed from an impossibility, then in impossible positio, then “one can never give inadequate answers to an impossible positio” (p. 168). It follows then that nothing would be contrary to the impossible, “there would be no such thing as positing the impossible, or an impossible position, and this is false” (p. 168). That is, if there is nothing contrary to the impossible, then the impossible isn’t really impossible after all.

The next argument against “has even more to say about the notion of ‘impossible'” (p. 168). First, a distinction is made between things which are impossible per se and things which are impossible “in virtue of a natural situation”. Then, a conditional sentence is paired up with a corresponding syllogism in such a way that if the syllogism is not valid, then the conditional isn’t true. In a syllogism, one cannot get from one and the same assumption to the same conclusion both affirmed and denied, so in the corresponding conditional, this can’t happen either:

from a man being an ass follows a man being an animal and not the denial of a man being an animal at the same time. Thus, from the impossible man being an ass does not follow just anything (p. 169).

One consequence of this argument is that syllogisms with impossible premises must be unsound.

The third argument against is that if the rule were sound, it would have to be based on some topic, but it is not clear which topic would apply.

The distinction between things which are impossible per se and which are only naturally impossible comes up again when the author discusses his own position (which Spruyt says is not clear); it appears that he accepts the rule when the impossibilities involved are “impossible containing contradictory opposite statements”, i.e., ones that are impossible in themselves (p. 169). (This notion of gradations of impossibilities is not uncommon in 13th-century texts; William of Sherwood also makes similar distinctions.)

Next up: Peter of Spain’s views as in the Syncategoremata (dating c1230). His position is based on the fact that in his view, “if we wish to infer consequent from antecedent, there must also be some topical relationship involved” (p. 170): There needs to be more than just the relationship of consequence between the antecedent and the consequent. As Spruyt puts it, with this view in hand, “small wonder that he does not adhere to it”, that is, ex impossibili, for there will, in general, be no topical relation underpinning the consequence from an impossibility to an arbitrary sentence.

Henry of Ghent’s view in his Syncategoremata (written about 30 years after Peter’s) is similar to Peter’s. He takes the consequence relation between antecedent and consequent as being one of cause and effect, which limits the types of things that can follow from an impossibility, because, in general, an impossibility will not be the cause of an arbitrary other thing. In order to block the validity of ex impossibili following immediately from the standard definition of a true conditional, he modifies the definition so that the “conditional is true when the conditionalized truth of the antecedent posits the truth of the consequent” (p. 173) — something that cannot be done with an impossibility.

In part three, we’ll look at Spruyt’s discussion of 13th-century arguments in favor of the rule.

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