PHIL 102 FALL 2004 – QUIZ ONE PRACTICE: BASIC IDEAS
Don't Panic! The quiz won't be so long – I've
given extra problems for practice.
• Name:
• TA:
• Section Time:
- Attempt as much as you possibly can: there is partial credit,
and no negative credit.
- Read questions carefully: answer all parts.
- Write answers clearly and neatly: if it can't be read it
can't receive any credit.
- Assign time carefully: you have the whole period. Leave quietly
if you finish early.
- Write in the spaces provided. Use the back of the sheet or
note paper if needed.
- If you have questions raise your hand and wait for us to
come to you.
1. For each of the following (atomic) sentences what are the names,
the predicate and its arity? (Make sure that you list all the names
in each case)
E.g., 'Mark and Matt share an office'
Predicate: ___ and ___ share an office Arity: 2
Names: Mark, Matt
(a) 'The Moon is a satellite of the Earth'
Predicate:
Arity: Names:
(b) 'Jackie, Jermaine, Marlon, Michael and Tito were in a pop group'
Predicate:
Arity:
Names:
(c) 'John, Paul, George and Ringo were in a pop group'
Predicate:
Arity:
Names:
2. Give the truth value – or say 'not evaluatable' if appropriate
– of the following in Gödel's World.
(a) Between(c,a,f)
(b) ¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬Large(c)
(c) SameSize(a,b) v SameShape(a,b)
(d) FrontOf(a,b) ^ FrontOf(c,a)
(e) SameRow(a,b) v (SameColumn(a,b)
^ SameColumn(b,f))
(f) (Small(a) ^ Tet(a))
^ ¬(Small(b)
^ Tet(b))
(g) ¬(¬Larger(a,b) ^ ¬Larger(a,c)) ^ ¬Larger(a,f)
(h) ¬{¬[¬Cube(a) v Tet(a)] v Dodec(a)}
3. Put the following arguments into Fitch format, and indicate
whether they are valid or not. (Use English not FOL to write the various
statements.)
(a) 'All dogs prefer Bone–O. All
Corgis are dogs. So all Corgis prefer Bone–O'
(b) 'a is in front of b and a is in front of c, hence b is in the same row as c.' (Take these predicates as defined
for Tarski's World.)
4. For each of the following arguments, say whether they are valid
or invalid (given the meanings of the predicates in Tarski's World).
For any valid arguments, say in which of Worlds A–C they are sound.
For any invalid arguments, say which of Worlds A–C is a counter–example.
(a)
(b)
5.
(a) If P ^ ¬(Q v R) is true, what
can you infer about the truth value of Q?
Circle one of the following: It's true
It's false Can't tell
(b) If (P ^ Q) v ¬R is false, what can you infer
about the truth value of Q?
Circle one of the following: It's true
It's false Can't tell
(c) If (P ^ Q) v ¬R is false and R is true, what can you infer
about the truth value of Q?
Circle one of the following: It's true
It's false Can't tell
(d) If you are told that an argument is valid, what can you infer
about its conclusion in a given world?
Circle one of the following: It's true
It's false Can't tell
(e) If you are told that an argument has true premises and true conclusion
in some world, what can you infer about it?
Circle all that apply: It's valid
It's sound It's invalid Can't tell
(f) If you are told that an argument is sound in some world, what
do you know about its conclusion in that world?
Circle one of the following: It's true
It's false Can't tell
6.
(a) For each of the following, indicate whether the predicate is
SYM(metric), TRAN(sitive), REF(lexive) or an EQ(uivalence) relation –
circle all that apply:
'___ scores no more than ___ on the test': SYM
TRAN REF EQ
'___ scores less than ___ on the test': SYM TRAN
REF EQ
'___ and ___ are taking the same course': SYM TRAN
REF EQ
SameShape(_, _):
SYM TRAN REF EQ
(b) Give a pair of relations – not used in Tarski's World – that
are inverses
7. Give informal proofs of the following, justifying each step with
transitivity etc, or that predicates are inverses, or the indiscernibility
of identicals (i.e., the informal version of = Elim).
(a) Since Superman is faster than Batman, and since Bruce Wayne is
Batman, it follows that Bruce Wayne is slower than Superman.
(b)
| FrontOf(a,b)
| FrontOf(b,c)
| FrontOf(c,d)
|-------------
| BackOf(d,a)
8. Complete the following formal proof: add steps or justifications,
or complete justifications by citing the supporting steps.
| 1. SameShape(c, f)
| 2. SameShape(e, d)
| 3. Tet(c)
| 4. f = e
|–
| 5.
= Elim 1, 4
| 6. SameShape(c, d)
_____ 2, 5
| 7. Tet(d)
Ana Con _,
_
9. In each blank give a sentence equivalent to the one above it –
use any general facts about Tarski's World. In (a)-(c) don't use the same
predicates as those given, while in (d)-(e) don't just swap the predicates!
(a) Larger(c, f)
(b) SameShape(b, d)
(c) Sam is Billy's sister.
(d) ¬(Large(a) ^ Dodec(a))
(e) I am neither French nor Scottish.
Solutions
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