WHISC Whimsy #4 concerned the Alanis Morissette album title

Supposed Former Infatuation Junkie

Question 1: How many different bracketings does this string have?

It has 11 bracketings. Here is a method for determining the number of bracketings for strings of any length.

Question 2: How many logically distinct meanings does this string have?

I detect 5. It is tricky to see where they all come from and what they mean.

It is easier to derive some meanings than others, so I'll chunk them up. The first group is the straightforward one:

• [[former]]^now = λf λx λt . f(x)(now) = 0 and there is a time t' < now such that f(x)(t') = 1
• [[supposed]]^now = λf λx λt . at t, there is a y such that y claims f(x)
• [[infatuation]]^now = λx λt . x is an infatuation at t
• [[junkie]]^now = λf λx λt . at t, all of x's desirable times t' are such that, at t', x has a y such that f(y)(t') = 1

I suspect that none of the above fully represents the intended reading of the album cover. Bracketing (1) comes the closest. But that bracketing does not entail that the bearer of the property was ever an infatuation junkie. Alanis's title seems to specify a property that holds of an individual x iff x was an infatuation junkie in the past and is supposed now to have gotten over that. To achieve this, we should begin with (4).

For this reading, we need a special adverbial meaning for supposed, one that will let it modify the meaning of former. (Mere function composition will not do, because it will derive (1).) I offer such a meaning here:

• [[supposedly]]^now = λF λf λx λt. there is a t' such that t' < now and f(x)(t') = 1 and there is a y such that y claims F(f)(x)

I've written this as the meaning of the adverbial supposedly, which I believe has its adverbial suffix clipped off in the album title. This meaning facilitates the interpretation in (4), and it also helps us to achieve (5).

But I must emphasize that my [[supposedly]] is highly suspicious. What it does is make one of the conjunctive conditions for former an entailment, by taking it out of the scope of 'y claims'. This meaning delivers wrong results if we allow it to combine with other intensional modifiers (e.g., fake). Thus, it is tempting to assume that it does not exist, that the reading it represents comes about via (1) and some kind of extra-semantical implicature. But, to me, (5) feels like an independent reading.

The remaining bracketings are nonbinary. I assume that each of them, if interpretable, has the same meaning as one of the above bracketings.

Question 3: Is spurious ambiguity still supposed to be a theoretical problem?

Let's hope not.

Bonus round: Which famous 1972 syntactic generalization is counterexemplified in the first verse of the album's third track, 'Thank U'?

I am withholding the answer for one more week. I am concerned that UMass linguists are not reading enough 1970s-era Haj Ross. I'll provide the relevant line though: How 'bout stopping eating when I'm full up.