Slot machines

And possible worlds!

C S

T T

T F

F T

F F

Proposition: Something that can be true or false

Alternative definition for proposition: A set of worlds

C: This set of worlds

S: This set of worlds

C ∧ S: The intersection of C and S

T

F

T

F

Yet another definition for proposition: A function that maps worlds to truth values

Stalnaker (1978): You presuppose propositions(qua functions from worlds to truth-values)

Something is presupposed if it is in the common ground, i.e. the context set.

But the context set is not a set of propositions;It is a set of possible worlds.

According to Stalnaker, a proposition is presupposed if it is true in every world in the context set (maps every world to T).

A dialogue

What did you get?

Total ignorance: every world is in the context set

Dialogue, cont’d

What did you get?

I got all the same color!

Context set = C

Dialogue, cont’d

What did you get?

I got all the same color!

I got all the same shape, too!

Context set = intersection between C and S

Along comes Mr. Pig…

What did you get?

Total ignorance: every world is in the context set

Why is this dialogue infelicitous?

What did you get?

I got all the same shape, too!