Today's task

[tahnan]

Last update on the dissertation: writing a formula that expresses

given a world w, in all worlds w' doxastically accessible for John from w, a given proposition P is true, namely the (unique true) proposition such that: (a) Fred knows the proposition, and (b) there's an individual concept x such that (i) there's some object z such that x maps each world onto the cost of z in that world, and (ii) there's some amount of money y for which the proposition P is the set of worlds such that x maps the world onto the amount of money y.

Which is of course the meaning of John knows the price Fred knows.

Unfortunately, it's only one of two meanings of that sentence. Today's task: deriving the other meaning. I'll be at True Grounds if anyone needs me.

Comments

[cnoocy]

I know the success you will know at this task.

[srl.livejournal.com]

You people frighten me.

[kirbyk.livejournal.com]

The other meaning is something like: Fred has a perception of the price, and John knows what Fred's perception is. John may or may not know if that's the real price.

As opposed to what you gave, which is there's this price, and both John and Fred happen to know it. John and Fred may not know of each other for this to be true.

Yay, language!

[tahnan.livejournal.com]

That's it indeed. One fun fact is that only one of these (the one given above) is present in John knows the price Fred does. If I get really really lucky, I'll understand why that is.

[kirbyk.livejournal.com]

If you said: Sue walks the dog that Larry does, you also get two meanings, though one is quite naughty, because you can walk the dog that Larry does walk, and you can walk the dog that Larry does do.

I briefly thought I understood how it worked, and then I realized I didn't. Which is cool, because I had a brief insight into what Linguists like to think about. :-)

There's a lot more linguistic shorthand at work here than is initially obvious. As a computer scientist, I have a strong inclination to rewrite the sentences into more regular, parsable, but equivalent forms (hello, Noam Chomsky), but the pattern doesn't hold when you change the verb, except when it does. And that's when I realized that I didn't know, and was enlightened.