PHIL12A
Section answers, 6 April 2011
Julian Jonker
1
How much do you know?
1.
Here are two questions from last time. Assess whether the following arguments are (a) tautologically
valid, (b) logically valid but not tautologically valid, or (c) invalid. In both arguments,
c
is a new constant
which names any large cube that exists in the world. If there are no large cubes, then
c
names any object.
(a)
(Ex 10.6)
1
∃
x(Cube(x)
∧
Large(x))
→
(Cube(c)
∧
Large(c))
2
Tet(c)
→ ¬
Cube(c)
3
Cube(c)
4
∀
x
¬
(Cube(x)
∧
Large(x))
The argument has the truthfunctional form:
1
A
→
(
B
∧
C
)
2
D
→ ¬
B
3
B
4
E
It is not tautologically valid. Nor is it logically valid: suppose that there is a large cube, and call it
c
. Then
the premises of the argument are true, and the conclusion false.
1
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(Ex 10.7)
1
∃
x(Cube(x)
∧
Large(x))
→
(Cube(c)
→
Large(c))
2
∀
x
¬
(Cube(x)
∧
Large(x))
↔ ¬∃
x(Cube(x)
∧
Large(x))
3
Tet(c)
→ ¬
Cube(c)
4
Tet(c)
5
∀
x
¬
(Cube(x)
∧
Large(x))
The argument has the truthfunctional form:
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 Spring '08
 FITELSON
 Logic, Ex 10.14, Ex 10.16, Ex 10.18, Ex 10.19

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