We talked a bit about tall and the fact that it really seems to mean something like “tall as compared to other things of the same sort.” And it came up that even something like red is probably relative too (cf. red hair vs. red paint).

But for the purposes of the homework, you can treat boring as being absolute. If you treat it as relative, then it has to be relative to something that isn’t in the sentence (for a sentence like Bond is boring), which is a complication I didn’t intend for you to have to deal with.

That is, if boring is really “boring relative to the comparison set”, then we would have to assume that Bond is boring really means something like “Bond is (a person and) boring (for a person)”—we’d have to assume that there’s some kind of hidden abstract noun there, rather like the one in the poor (which we would take to mean “the poor (people)”). It can be done, but it was not what I was intending for you to have to do when I wrote up the homework.

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.

So, I have gotten a few questions about homework #4 throughout the day, but I haven’t had a chance to post anything about them due to a very crowded schedule. I will post a few comments now at least.

First, though: if you have questions about something, don’t think you’re alone just because the blog is empty. It’s of course better to try to come up with the questions sooner rather than later so I have a chance to answer and post comments, but it’s also true that at least part of the homework depended on Tuesday’s lecture. So, well. Anyway, on to the posts.

On the sentence structures that you were supposed to draw for parts of homeworks 2 and 3, I had you number the nodes. But, just to clarify: there’s no secret, magic, or rules behind my choice of what number to assign to which node. I generally started from 1, and I started at the bottom, but you can number your nodes however you want, the only thing the number is there for is as a way to identify which node you’re talking about when you compute the meanings.

Just as a note of reassurance, there are still things to cover tomorrow that are relevant to the homework. Don’t despair if you look at it and feel that you don’t quite know how it should work. You probably don’t, and that’s probably to be expected, given that it has not yet all been presented to you. The introduction you’ve had so far to the components of F1 were a little bit less than fully systematic, but over the next class or two, this should be remedied.