## 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.

## Integrating medieval logicians into Introduction to Logic

Term starts next week, and I am so pleased to be teaching again what is probably my favorite course ever, Introduction to Logic. Most of it is going to be a pretty standard Intro Logic course: syntax and semantics of propositional and predicate logic, derivations, and meta-results (soundness/completeness). But I’m planning to liberally sprinkle in historical material, because I can — and because I want to normalize the idea that the tradition of logic developed continuously from Aristotle (and even outside of Aristotle) and that one should expect to learn something of the history of one’s subject in an introductory class. This means that the first formal system that we look at will be the syllogistic (Informal poll: Should I assign them portions from the Prior Analytics for the first week’s reading? Or is that too mean to freshmen?). They’ll get the syllogism mnemonics and the associated proof-theory, and the system provides an excellent introduction to meta-theory.

I also want to get them to think about the question of “what is logic?” In our first lecture, on Monday, I’m planning to share with them this definition from Roger Bacon’s Art and Science of Logic:

Logic, as a science, is the habit of distinguishing what is true from what is false by means of rules or maxims or dignities by which we can comprehend the truth of a locution through our own efforts or with the help of others. And logic is so-called from logos, which means discourse, and lexis, which means reason or understanding — as it were, the science either of reason joined to discourse or of discourse joined to reason.

I love this definition, because of the way it highlights four important features about the discipline of logic:

• It is aimed at distinguishing truth from falsehood.
• It is rule-governed.
• It can be a joint venture.
• It involves discourse.

I’m going to point out to them that modern logicians generally would stop after the first two bullets, but that, in my opinion, the second two bullets should not be discounted. Among other things, I want to encourage them to work on their exercise sets in groups, to realize that the best way to understand the material is via helping other people to understand it, and I will be arguing that there are certain aspects of the development of logic which can be understood only through a dialogical/discursive lens. Throughout the rest of the year, I hope to have them read Avicenna, Sherwood, Buridan, Ockham, Burley, and others, as well as some of the medieval Indian Buddhist debate treatises.

The first lecture is on Monday, but I won’t be covering quite enough material to assign any technical homework for the next week’s tutorials. However, last night I had the traditional “first lecture of the year” dream (in which Dream Sara was nowhere near as efficient at getting through the material as Real Sara, who is planning to cover twice as much…), in which Dream Sara came up with an awesome assignment for them, to get them (a) into the library (or at least onto the internet), (b) writing, and (c) used to the idea that there was logic throughout history. I will be asking them to name (1) three logicians who lived before 1000, (2) three logicians who lived and died between 1000 and 2000, and (3) three logicians lived after 2000. Then, they need to pick one from each category and write 150 words (with references) on what is distinctive about this person’s works/views.

I can’t wait to see who they all choose to write about!

## Introduction: Graziana Ciola

Hi, everyone!

I am Graziana – and I am so late it was fashionable a few seasons ago.

I am completing my PhD in Philosophy (History and Philosophy of Logic) at the Scuola Normale Superiore in Pisa. My work focuses on Medieval Logic – in particular on XIV century theories of consequences – and on the notions of consequence, inference, entailment, validity. My thesis, under the supervision of Massimo Mugnai (SNS) and Calvin Normore (UCLA), is on Marsilius of Inghen’s Consequentiae – text of which I am preparing also a critical edition.

My main research interests are in the history of late medieval philosophy, medieval scientific thought, history and philosophy of logic.

I like to think that “…. philosophers’ 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.” (R. G. Collingwood, An Autobiography, Oxford 1939, p. 65)

## 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.

## 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!