Although the big story of this episode is Gabby turning on her ally Christian, I’m not going to write about that. (But just for the record, I think she did it too soon. There were too many Goliaths left and she hadn’t built a relationship with them to avoid their voting her out.) I have an exam tomorrow, which will partially focus on the philosopher Bertrand Russell’s theory of definite descriptions, so for selfish reasons I’m going to write about the breakdown of the Nick-Christian “Mason-Dixon” alliance.

I wrote in Episode 4 about how Nick was smart to name his alliances, because names gave the alliances a dash of mythology rather than simply being pragmatic partnerships. But as the days went on, Nick seemed to build a better rapport with Davie than with Christian, while Christian allied with Gabby (though look where that got him). Nick didn’t seem to do the emotional gardening necessary to maintain the Mason-Dixon alliance with Christian. This eventually resulted in them being on opposite sides of the Carl vote, which led Nick to declare this week that the Mason-Dixon alliance was over.

Does the statement “Mason-Dixon is over” have a different logical meaning than a statement like, for example, “The Gabby-Nick alliance is over”? Neither the Mason-Dixon alliance nor the Gabby-Nick alliance currently exist, so we’re talking about non-existent subjects in both statements. However, the Mason-Dixon alliance did exist at one point, whereas there has never been a Gabby-Nick alliance. Are both statements true or false? Is one true and the other false? Or is there maybe another option?

Most logicians in Bertrand Russell’s time (and now) were trying to create logical systems that could encompass all grammatically well-formed sentences. (An example of a sentence that isn’t well-formed might be: “Fish pig the.”) Even if this turned out to be impossible, they believed that the more they tried, the better our understanding of logic and language would become.

At an early point in Russell’s life, he would have said that “Mason-Dixon is over” is true, but “The Gabby-Nick alliance is over” is meaningless. Even though “The Gabby-Nick alliance is over” seems well-formed, since there has never existed a Gabby-Nick alliance, it would be meaningless to say whether it’s over or not.

The idea that sentences like “The Gabby-Nick alliance is over” are meaningless, however, struck some people as suspicious. If someone doesn’t know that there’s no Gabby-Nick alliance, then “The Gabby-Nick alliance is over” appears to be a meaningful sentence. It seemed odd to some people that a new fact could suddenly make a sentence logically meaningless. Maybe true or false, but not “meaningless”. The meanings appeared quite clear, regardless of new facts.

Russell had the same concern, so he later changed his mind. Instead, he claimed that phrases like “Gabby-Nick alliance” were “definite descriptions”. They posited the existence of the things being described. Therefore, the truth or falsity of a sentence could also be judged on the truth or falsity of its definite descriptions. Using Russell’s new concept, “The Gabby-Nick alliance is over” might be written like this in symbolic logic:

(∃x) {[Gx ^ (∀y) (Gy ⊃ (y=x))] ^ Ox}

Since it’s false that there ever existed a Gabby-Nick alliance, then (∃x)Gx is false, which makes the conjunction (and overall statement) false. In contrast, “Mason-Dixon is over” is true, since the Mason-Dixon alliance does have a historical existence. In his own treatment of this topic, Russell used the example “The present king of France is bald” because there was no present king of France.

One of the main objections to Russell’s definite descriptions is that it has trouble with sentences about fictional subjects. For example, “Santa Claus has a beard.” Santa Claus doesn’t exist (I hope there are no five-year-olds reading this blog), but it still seems true that he has a beard. However, defenders of definite descriptions have said that statements should be considered in particular domains. In the domain of Santa Claus mythology, it’s true that he has a beard. In the domain of the real world, it’s false.

I’ll stop here, but this debate goes on and on. Many dense volumes have been written about Russell’s theory of definite descriptions. Also, this whole blog entry might be a moot point if Nick and Christian can reconcile with each other, since then “Mason-Dixon is back” will also be true.