Reader query regarding Logic, Eloise and Abelard

I’m a logician/philosopher of logic and recently I’ve been working in game theoretic semantics. In this area, it is quite common to talk about two game players: Abelard and Eloise. The normal way of things is that Eloise tries to show that there is a model for a collection of sentences and Abelard tries to show that there isn’t. Or Eloise tries to show that a sentence is true in a particular model and Abelard tries to show that the sentence isn’t true in the model. Eloise tends to show things are true or things exist (the E is connected to the existential quantifier) and Abelard plays the dual role (associated with the universal quantifier). Along with this choice of names comes the practice of using feminine pronouns for Eloise and masculine pronouns for Abelard.

Wilfrid Hodges says this in the Stanford entry Logic and Games:

“There are two players. In general we can call them ∀ and ∃. The pronunciations ‘Abelard’ and ‘Eloise’ go back to the mid 1980s and usefully fix the players as male and female (though feminist logicians have asked about the propriety of this type-casting).”

The only hint of the feminist logicians’ question that I can find is page 12 of the file from Hodges’ website. Here, he describes how he introduced the use of the names and mentions that someone wanted to present a conference paper “on the dangers of personalising the mathematical content”. The conference was cancelled.

Regardless of the particular issue that Hodges is thinking about, I have been wondering whether this is a good practice or not. I’ve done a bit of twitter surveying with very limited success. One female logician said they were worried it may affect someone. One female logician said they had no problem with it. Two male logicians said they didn’t see a problem. And one female philosopher (non-logician) said she didn’t find it problematic. As you can see, I got very few responses!

Given that logic is in such a bad state of affairs in terms of gender imbalance, I want to try and get this right. I’m particularly concerned with not affecting students new to logic. I don’t want to use the convention if it is problematic; on the other hand, having any convention that encourages the use of feminine pronouns and examples of women involved in logic may be a good thing.

I’d appreciate any thoughts, comments, or references that you may have.

7 thoughts on “Reader query regarding Logic, Eloise and Abelard

  1. The obvious reference is to Abelard (the medieval logician/philosopher) and Heloise, his student. Their correspondence is somewhat renowned, though I confess to not having read it myself. It is usually characterized as a romantic correspondence, but this brief summary indicates that there is much more contained therein: The text is available online here: Wikipedia has an entry on her:

    Perhaps part of the issue is that an ignorance of the history of philosophy leaves people deaf to the allusion.

  2. the story of heloise and abelard is very fraught, as everyone may know. I believe they became lovers; he was her teacher. She became pregnant, her family had him castrated (I’ve heard various stories about why they did). She was consigned to a convent, where she did not want to be. Pretty awful stuff, handed down to us with very old conceptualizations of what was going on.

    I think pedagogically it is a bad idea to use such figures in game theoretical semantics. That’s not because I know it will have bad effects, but because I don’t know what effects it will have, what use the students will make of it out of class, and so on. I really don’t think the important question is “How do you feel about using these names.”

    It is also, in what I think of as an unpleasant way, using people made notorious in part because of their sexual activity. Ugh.

  3. I have a different view on this than Anne. Non-experts, and even some experts, simply assume a romantic relationship between Descartes and Princess Elisabeth. Teaching their correspondence affords an opportunity to highlight Elisabeth’s philosophical acumen, irrespective of any personal relationship between the two (though there doesn’t appear to have been any). I don’t see why Abelard and Eloise can’t be used in the same way — there is a sordid romantic story attached to it, much more than with D and E, but Eloise’s side of the correspondence is robust philosophy, and that fact can be highlighted and emphasized. The sordid side of the story is off-putting, but there is a way of leveraging that to promote gender equity in philosophy. Abelard gets read all the time by medievalists, in all sorts of contexts. Eloise does not. That is unfortunate.

  4. Lisa, I’d completely agree if they were using the content of her thought, but they aren’t, as far as I understand it.

  5. My thoughts about using Eloise’s and Abelard’s names were on the positive side. I never thought about their actual stories too much, except for the fact that there are not _that_ many women in the Middle Ages who are widely known for their intellectual abilities, so mentioning her seemed a good thing in terms of visibility (but having read what annejjacobson says, I may have to rethink that).

    Another reason I liked using female and male names is that in a discipline with heavy underrepresentation of women, it does not hurt at all to have more feminine pronouns, etc.

    Regarding their roles in logical games, I don’t think there is actual gendering (which also contributed to the fact that I kind of liked this convention). If anything, Eloise is the more active and creative member of the pair: she makes her moves, and then Abelard struggles to catch up with her.

    Thinking about my own usage, I’m not sure I actually used the names. But when mentioning the two players, I think I usually use pronouns of different genders referring to them. Without the names attached, my guess would be I choose who to call who more or less at random.

  6. IY: “Regarding their roles in logical games, I don’t think there is actual gendering (which also contributed to the fact that I kind of liked this convention). If anything, Eloise is the more active and creative member of the pair: she makes her moves, and then Abelard struggles to catch up with her.”

    There is a chapter in Andrea Nye’s book on feminism and logic _Words of Power_ on Abelard. Concerning the correspondence with Heloise, she writes: “Fortunately, Abelard’s logic was not powerful enough to convince Heloise… Heloise refused Abelard’s logic, refused to duel on Abelard’s terms with his weapons” (100). So there seems something fitting about their respective identifications with the universal and existential quantifier in game theoretic semantics!

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