I was chatting with Chris Hill and Michael Pace yesterday about unless, and I wasn’t really having much luck convincing them that it didn’t mean if not. So I thought I’d see if my loyal readership were any easier to convince.

For the following case, imagine that I have two boxes in front of me, a red box and a black box. The red box contains 19 red marbles and 1 black marble. The black box contains 19 black marble and 1 red marble. I am going to choose a box at random and then choose a marble from it at random. Do you think the following sentences are definitely true, probably true, probably false or definitely false? (Or something else?)

(1) I will draw a red marble unless I choose the black box.

(2) I will draw a red marble if I choose the red box.

(Make sure you’ve decided what you think before reading on.)

I think that (2) is probably true, but (1) is definitely false. So unless I choose the black box does not mean the same thing as if I choose the red box. I assume that in context choose the red box is the negation of choose the black box. Anyway, that didn’t convince either Chris or Michael, which is sad because it’s clearly a sound argument.

Let’s try a different argument then. In front of me there is a wall of beer bottles. Some of them are Guinness bottles, which are black. Some of them are Dos Equis bottles, which are clear. (Actually, they are brown-ish, but let’s call them clear for convenience.) Beer bottles as far as the eye can see. Well, except for a fake Guinness bottle somewhere hidden in the wall. If I were looking at the fake bottle, I would think it were a real bottle. The fake bottle is a fair way from where I am looking at in the wall. I am actually looking at a Guinness bottle, but there are lots of clear Dos Equis bottles around it.

Anyway, what do we think of (3) through (6)?

(3) If I were not looking at a beer bottle, I would not believe I were looking at a beer bottle.
(4) If I were not looking at a black beer bottle, I would not believe I were looking at a black beer bottle.
(5) I would not believe I were looking at a beer bottle unless I were looking at a beer bottle.
(6) I would not believe I were looking at a black beer bottle unless I were looking at a black beer bottle.

On Lewis’s theory of conditionals, (3) is true and (4) is false. But it is very implausible, I think, that (5) is true and (6) is false. So perhaps that’s another argument that unless is not if not.