Problem Set 8
PHIL 11
Question Set 1
Let’s consider a language we’ll call QL2. Here are its proper names and predicates, along with their interpretation.
Domain: all people
d: Denise
o: Oscar
r: Riley
M: ① is mad
G: ① is glad
H: ① hired ②
F: ① fired ②
Below are some wffs of QL2. Translate each into English.
1. Hdr
2. (Frd ∧ ¬Fro)
3. (Mr → For)
4. ¬∀xMx
5. ∀x¬Mx
6. ∃x(Mx ∧ Fdx)
7. ∀y(Hdy → Gy)
8. ¬∃xHxx
9. ∃y∀xHyx
10. ¬∀z(Frz → Mz)
Now translate each of the following into QL2.
11. Riley hired both Denise and Oscar.
12. Denise fired Riley, but Riley isn’t mad.
13. If Denise is glad, then either she hired Riley or she fired Oscar.
14. No one fired Denise.
15. Everyone whom Riley hired is mad.
16. There is someone who fired Riley but didn’t fire Oscar.
17. Everyone fired at least one person.
18. No one is both mad and glad.
19. Anyone who hired someone is glad.
20. There is someone that was not fired by anyone.
Question Set 2
Let’s consider a language we’ll call QL3. Here are its proper names and predicates, along with their interpretation.
Domain: all streets
s: Shattuck
t: Telegraph
O: ① runs through Oakland
B: ① runs through Berkeley
I: ① intersects with ②
W: ①is wider than ②
Below are some wffs of QL3. Translate each into English.
1. (Os ∧ Bs)
2. (Bt → ¬Ot)
3. ∀xOx
4. ∃y¬By
5. ∀x(Ixs → ¬Ixt)
6. ¬∃xWxt
7. ∀x((Ixs ∧ Ixt) → (Ox ∧ Bx))
8. (¬∃xIxx ∧ ¬∃xWxx)
9. ∀x∃yIxy
10. ∃y∀xIxy
Now translate each of the following into QL3.
11. Telegraph runs through Oakland but not Berkeley.
12. Shattuck intersects with Telegraph if and only if Telegraph intersects with Shat-tuck.
13. Shattuck doesn’t run through Berkeley if it intersects with Telegraph.
14. There is a street that either intersects with Shattuck or intersects with Telegraph.
15. Any street that is wider than Telegraph intersects with it.
16. There is a street that is wider than Shattuck only if there is a street that is wider than Telegraph.
17. No street intersects with both Telegraph and Shattuck.
18. Every street that runs through Berkeley is such that it does not run through Oakland.
19. There isn’t a street that both intersects with Shattuck and is wider than it.
20. There is a street that intersects with every street that runs through Berkeley.
Question Set 3
Below are some sentences that are arguably ambiguous between two different read-ings. Translate each of the two readings into QL2 or QL3 as appropriate.
1. Riley didn’t fire everyone.
2. Someone wasn’t hired by Denise.
3. Every street is wider than a certain street.
4. Every street that runs through Oakland isn’t wider than Telegraph.