You can't win the lottery unless you buy a ticket.
I won't go unless you come too.
In the first, you could translate "unless" as "if-not," so not buying the ticket guarantees not winning, but the converse is false: you aren't guaranteed to win if you buy the ticket. In the second statement, many of my workmates read "unless" as "if-and-only-if-not," so if you don't come too, I certainly won't go, but if you come, I will certainly come. If we take our case to the web, we'll find lots of support for the "if-not" translation, but also some for a combination of both. For the purposes of mathematics, I'll stick with the "if-not" version, but I can see that it's slippery.
Another good confrontation with real-world interpretation came when I asked students to explain the double-meaning in the headline:
Iraqi head seeks arms
They noted that the two meanings of head (the body part perched on your neck, and the leader of some entity) paired up neatly with two meanings of arms (the body parts hanging from your shoulders, and weapons), and they concluded that the headline certainly meant to pair the leader meaning of head with weapons. I realize that Condie probably wasn't thinking of this headline when he made La Sala, but it does leave open the question of whether the other interpretation of the headline doesn't have some support in the real world (wherever that is).
2 comments:
Maybe some english phrases are left better UNtranslated into symbolic form? Or we could transform a given phrase into something closely related, and THEN translate it into symbolic form.
"You have won the lottery, therefore you must have bought a ticket", says almost the same thing as the first statement, but it's much easier to state it symbolically: won => bought ticket, or W => B.
On second thought...
"you aren't guaranteed to win if you buy the ticket", but we're talking about the possibility of winning, not about actually winning:
"If you buy a ticket then it's not the case that you can't win the lottery."
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