Metalanguage

Posted by on

Last’s weeks puzzler on Car Talk seemed almost relevant to this class. Perhaps a bit of a stretch.

We needed a new sign above our garage and Tommy decided to hire a sign painter for the job, instead of turning Crusty loose with a can of spray paint, like the last time.

He instructed the sign painter to paint a sign which simply said, ‘Click and Clack’s Garage.’ Those four words.

When it was finally finished and hung in place, Tommy stood there and carefully studied the new sign. After several minutes he spoke: ‘I don’t like it. Something’s not right.’

‘What’s wrong?’ asked the sign painter. ‘Did I misspell something or use improper punctuation?’

‘No, it’s nothing like that.’

Tommy then uttered a sentence in which he used one of the words on that sign five times in a row. There were other words in that sentence, but one of the words in that sign was used five times in a row. And here’s the interesting part: the sentence made sense and, furthermore, it explained what was wrong with that sign.

And the question very simply is, what’s the sentence?

The thing about the answer is that it requires mixing the language with the metalanguage, so I’m not sure I really buy the answer, but it is…
Continue reading ‘Metalanguage’ »

BUCLD notes

Posted by on

A couple of weeks ago I handed out a short list of talks that seemed to have something to do with semantics. However, in the meantime there have been a couple of changes. So: Don’t trust the locations (particularly) on the handout, trust the online schedule instead.

Systematically, things labeled “B” on my handout will meet in the East Balcony as part of session C, things labeled “C” will meet in the Conference Auditorium as part of session B, and things labeled “A” will meet in Metcalf Small as part of session A.

HW5, question 2

Posted by on

Homework 5 was prepared in a bit of a rush, and there are a couple of oddities about question #2.

If you read the directions carefully, you’ll see that it is anticipated that the sentences in the problem might have more than one interpretation, based on the de re/de dicto distinction. However, when the context is taken into account, most of them are not really ambiguous, but must be either one or the other. Not all, but most.

Writing a paraphrase for a de dicto reading is a challenge, because it’s almost always possible to still come away with a de re interpretation. One way to do this relatively effectively is to use some…or other, as in Some student or other.

Also, at the end of the context for (3), it was supposed to read “She thinks he will win”, but I left out “thinks”.

More comments on modal bases

Posted by on

This isn’t really new information, but I thought just for clarification I’d sort of say again some things about what modal bases are.

A sentence like Pat might have eaten the sandwich can be true or it can be false, first of all.

The modal base is basically a set of worlds the comparison is being made with — so Pat might have eaten the sandwich would be false if it turns out that in none of the worlds in the comparison set are ones in which Pat has eaten the sandwich is true. A modal takes the comparison set and asserts something about how many of those worlds have the property that the rest of the sentence is true. So, Pat must have eaten the sandwich asserts that Pat has eaten the sandwich is true in all of the comparison worlds, Pat might have eaten the sandwich asserts that Pat has eaten the sandwich is true in at least one of the comparison worlds, Pat probably ate the sandwich asserts that Pat ate the sandwich is true in more of the worlds in the comparison set than it is false in, and so forth.

The comparison set itself can differ as well—that’s where the concept of modal base comes in. If you’re just comparing basically all of them, that’s the root modal base, and it would have the meaning of “capable” essentially (Pat can lift a piano). You can also limit it to just those worlds that you believe are candidates for the actual world—that is, those worlds that are consistent with your beliefs. That’s the epistemic modal base, and has a meaning something like “as far as I can tell” (Pat must have lost his keys). Then, there’s one that limits the comparison to just those worlds in which some kind of rules are being obeyed—this one is the deontic modal base, and it will generally carry a “permission” or a “judgment of propriety” kind of meaning (Pat may leave class early, Homework must be turned in on time).

So, Pat might have eaten the sandwich can be true, even if Pat has eaten the sandwich is false in the actual world. What it requires to be true is (assuming the epistemic modal base) that at least one of the worlds that you believe are still candidates for being the actual world, based on what you know, is a world in which Pat has eaten the sandwich. That it is not inconsistent with your beliefs that Pat ate the sandwich.

There are a number of things I believe, and so that divides all of the possible worlds into those that are consistent with my beliefs and those that are not. The epistemic modal base is the set of worlds that are consistent with my beliefs. However, there is also the possibility that I believe something that isn’t in fact true. So: if I believe p and q, but p is actually true and q is actually false, then the epistemic modal base would be all of those worlds in which p and q are true, but the actual world won’t be among them.

So, from the handout, what I believe is true is basically defining the epistemic modal base—all of those worlds in which my beliefs are true. Within those worlds, some are worlds in which Pat has eaten the sandwich and some are worlds in which Pat has not, assuming that I don’t have a belief about Pat eating the sandwich. (If you believe Pat ate the sandwich, then it would be only those worlds in which Pat ate the sandwich that are in the epistemic modal base, and the sentence should be Pat must have eaten the sandwich instead).

I don’t know if that makes it any clearer, but perhaps.

Extra patience required

Posted by on

Rather than the usual 426,600 seconds between Thursday and Tuesday classes, this week the Tuesday class isn’t until an entire 430,200 seconds have elapsed since Thursday.

On the upside, if you don’t like how your 1-2am Sunday morning goes, you can have a second go at it, immediately afterwards.

Midterm: Numbers and letters

Posted by on

Ok, so I’ve had a chance to do the numbers, and this is how I view numbers you may have gotten on the midterm in “letter grade” terms:

A 37 and above
A− 33−36
B+ 29−32
B 25−27
B− 21−24
C+ 17−20
C 13−16

I will try to have the key for you soon. The scores are scaled to fit the difficulty of the material and the test (so, it’s not based on the standard percentage scheme, but I think it’s a fair scale).

For the homework scores, I am viewing them like this: If you find the average of your homework score, dropping the lowest one, where √++ is 5 and √−− is 1, it would look like this:

A 4.25 and above
A− 3.75−4.24
B+ 3.25−3.74
B 2.75−3.24
B− 2.25−2.74
C+ 1.5−2.24
C 1−1.49

I may slide the homework scale a little bit one way or the other when we reach the end of the semester, but if you want to compute the grade I’d likely assign if the semester ended right now, I think this will provide a good approximation.

Wednesday 10/25 office hours moved to Monday 10/30.

Posted by on

Sorry for the very late announcement, but departmental engagements have arisen that will keep me from being able to hold my normal Wednesday office hours today (10/25).

Given that there is no homework due on Thursday, I hope this will not be a great inconvenience.

I will have extra office hours on Monday, partly to handle questions about homework if there are any, and also to handle advising questions, and if you are looking for Linguistics advising, you can always contact me just to make a specific appointment sometime outside of office hours.

Extra office hours will be Monday 12-1:30.

Practice midterm key: Typo on question 5 part e

Posted by on

Another typo. I was trying at one point to create a plausible contradiction, but gave up, yet it seems I left a completely unrelated answer there for part e.

The real answer is either of these:
(p→q)∧p
p→(q∧p)

Incidentally, the words that would have gone with the answer I left in the key would have been The gate is open and the gate is not open or the llama didn’t escape..