I’ve gotten a couple of questions on question #7 of the practice final. What it asks you to do is translate the following into English:
λp [ ∃x [ p = λw [ person(x) ∧ poisoned-the-vodka(x, w) ]]]
There is a sense in which this question isn’t really “fair” in that we’ve never really talked about these things in these terms.
But, here’s where that was going: p here is supposed to a proposition. A proposition is something that is true in some worlds, false in others. Although we haven’t been doing this, we can make the world dependence explicit by saying that a proposition is a function from possible worlds to truth values. So, e.g., John weeps is a function that, given a world w is either true (if John weeps in w) or false (otherwise).
That is: λw [ John weeps in w ]
So, now, suppose that you have the proposition λw [ person(w) ∧ poisoned-the-vodka(x, w) ] for some x. That will be one of the possible answers to the question Who poisoned the vodka?.
The idea in the formula in question 7 is that a proposition is in the set of propositions the formula is describing if there is an x such that the proposition is x poisoned the vodka.
I’ll try to stick to things we actually covered, on tomorrow’s test…