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 http://wilfridhodges.co.uk/history16.pdf 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.