Ok, so this is in fact one of the questions on the homework, but there has been a certain amount of confusion surrounding this one. So, let me walk you almost all the way up to it.

Here’s the general plot: We used to treat is boring as being an intransitive verb, but that’s clearly not what it is—it is the verb be plus an adjective. And we just covered adjectives, so now we can go back to re-examine is boring to see if we can come up with a compositional way to look at it as being the combination of be and an adjective.

The thing is, if you think about it, is is not really adding anything to the semantic computation. Bond is boring is true just in case BOND has the property of being boring. The adjective boring is a property, it is something that is either true or false of individuals. The way we write that formally is as a function that takes an individual as input and returns a truth value as output, or type <e,t>. Specifically:

[boring]^M = λx[x is boring in M]

So, what this means in prose is: this is a function that takes something, which we will call “x”, as input, and returns true if “x is boring in M” is true, and false if it is false. That is, the things between the brackets represent the output, which is a metalanguage statement that will evaluate as either true or false.

Now, this is exactly what is boring is supposed to mean.

So, here’s what we have: boring means what I gave above. And combining is and boring results in exactly the same thing. So, it’s as if we never combined anything with boring—the is here is effectively “meaningless.” It doesn’t add anything to the semantic representation of the sentence. As I suggested in class, it might be there solely to satisfy some syntactic requirement of English, but is not serving any semantic function.

The question on the homework boils down to: how do you write a function that combines with something but produces no effect?

The answer is actually quite simple. We write functions, abstractly, like this: λinput[output] (where by “input“, I mean essentially a label that we apply to whatever the input is). So, what we want is a function that takes an input and calls it something (let’s say it calls it “P”, for “property”), and then returns exactly that same thing.

The answer will look like this:

[is]^M = λP[…]

where you fill in the “…” part so that what is returned is, well, the same thing as it got as an input. It got P. It should return P.

I think I can’t go any further here without just writing the answer, but hopefully this got you so close to the answer that you can see what to write.