Formal Semantics 564 Quiz #1 September 30, 1999
The way this quiz breaks down, I estimate that you should allow yourselves 20-30 minutes maximum for questions 1-3, and 30 minutes for question 4, with 15 mins at the end to check things over.
1. Communication: You click on a hyperlink in your favorite web browser, www.nowhere.edu. Your browser gives you an error message: "Unable to locate server: www.nowhere.edu. The server does not have a DNS entry. Check the server name in the Location (URL) and try again." In this situation: a) who's communicating with you? b) who's using English? Justify your answers briefly. (Don't write more than 5-6 sentences at most:)
A good answer to this question should have included the idea that "using" English involves translating a message into English via the syntactic and semantic rules of English (remember the cartoon about "communication" in the first class?). Since the browser isn't doing that, it's not using English. (The programmer who gave the browser the string in the first place was using English, though). And, of course, you're using English when you read the message). As to who's communicating, it depends on whether you think the browser has formed an intention to let you, the user, know something or not. If it has, it's communicating, if not, it ain't. Did the programmer have an intention to let you, the user, know something? Probably, hence s/he's probably communicating.
2. Presupposition and Entailment
Here are two sentences. FYI, Hobbiton is located in the Shire. (They aren't a discourse, but rather unconnected example sentences; treat them as such).
(a) Frodo wanted to leave the Shire.
(b) Merry, Sam, Pippin and Frodo left Hobbiton together.
Indicate below whether each statement is presupposed or entailed by each of (a) and (b):
Presupposed Entailed
(i) Frodo wanted to (a) no no
leave Hobbiton (b) no no
(ii) Frodo was in the Shire (a) yes no
(b) yes yes
(This question was badly laid out... sorry about that).
3. Sense and Reference:
Consider the following:
{x | x „ 6 and x ¾ 10 }
{x | x = 6 or x = 7 or x = 8 or x = 9 or x = 10}
{6,7,8,9,10}
In what way does this illustrate the difference between sense and reference?
(Again, don't write more than 5-6 sentences at most:)
Here, there are three ways of representing the same set, two in predicate notation, one simply by listing. (Well, technically, the first one doesn't represent the same set as the others unless it carries the additional rider of "x is an integer"). The material after the "such that" bar in the predicate notation ones provide criteria for deciding set-membership; the listed set in the third merely points at (directly refers to) the set members. Although they all (are supposed to) refer to the same set, the criteria for determining set membership differ in the first two, and hence can be compared to the different senses of the proper names "Hesperus" and "Phosphorus" in the examples from class, whose reference is identical, but whose sense differs. So, for instance, imagine that you didn't know that 7 was greater than 6. You would know, given the second predicate notation, that the second and third sets were the same set, but you wouldn't know that the first one was the same as the other two (because you couldn't apply the criteria for determining set membership to 7 correctly).
4. Translation and proof
Translate the following argument into a predicate-logical formula, giving a key to your translation, and then prove the conclusion from the premises, using the given equivalences and laws of deduction. Note: Assume the universe of discourse contains only people.
Hint: "Doctor" in this argument has to be a 2-place relation
No one trusts anyone who has blue or green eyes.
(equiv: If someone has blue or green eyes, then nobody trusts him/her.)
If a person doesn't trust their doctor, then he/she doesn't trust anybody.
Josephine is Rianna's doctor.
If Josephine has green eyes, Rianna doesn't trust anybody.
Green(x) x has green eyes
Blue(x) x has blue eyes
Trust (x,y) x trusts y
Doctor (x,y) x is y's doctor
j Josephine
r Rianna
1 ÂxÂy((Green(x) v Blue(x)) --> ~Trust(y,x)) Premise
2 ÂxÂy((Doctor(x,y) Ù ~Trust(y,x)) --> ~¤z(Trust(y,z))) Premise
3 Doctor(j,r) Premise
4 Ây((Green(x) v Blue(x)) --> ~Trust(r, x)) 1, U.I.
5 (Green(j) v Blue(j)) --> ~Trust(r, j)) 4, U.I.
6. Ây((Doctor(j,y) Ù ~Trust(y,j)) --> ~¤z(Trust(y,z))) 2, U.I.
7. (Doctor(j,r) Ù ~Trust(r,j)) --> ~¤z(Trust(r, z)) 6, U.I.
8. | Green(j) Aux. premise
9. | Green(j) v Blue(j) Addition
10. | ~Trust(r,j) 5,9, M.P.
11. | Doctor(j,r) Ù ~Trust(r,j) 10,3, Conj.
12. | ~¤z(Trust(r,z)) 11,7, M.P.
13. Green(j) --> ~¤z(Trust(r,z)) 8-12, Cond. P.