Question Database: Formal Logic
Definite Descriptions
(Ix)(Fx, Gx) will be read as 'the thing that is F is also G.'
'the thing that is F' is called a definite description.
Px = x is PM
Ax = x is Australian
Sxy = x is shorter than y
Tx = x is Treasurer
Hx = x is happy
For example:
| (Ix)(Tx, ~Sx) | The Treasurer is not short |
| (Ix)(Ax & Px, Hx) | The Australian Prime Minister is happy. |
Translate:
(Ix)(Px, (Iy)(Ty, Sxy))
A. The Prime minister and the Treasurer are short.
B. The Prime minister is shorter than the Treasurer.
C. The Treasurer is shorter than the Prime Minister.
Answer: B
Topic:
definite descriptions
Course Level:
First year formal logic
Notes:
Px = x is PM
Ax = x is Australian
Sxy = x is shorter than y
Tx = x is Treasurer
Hx = x is happy
Translate:
(Ix)(Px, ~Hx)
A. The Prime Minister is not happy.
B. It’s not the case that the Prime Minister is happy.
C. Either of them.
Answer: A
Topic:
definite descriptions
Course Level:
First year formal logic
Notes:
Px = x is PM
Ax = x is Australian
Sxy = x is shorter than y
Tx = x is Treasurer
Hx = x is happy
Translate:
~(Ix)(Px, Hx)
A. The Prime Minister is not happy.
B. It’s not the case that the Prime Minister is happy.
C. Either of them.
Answer: B
Topic:
definite descriptions
Course Level:
First year formal logic
Notes:
Russell analysed (Ix)(Fx, Gx) as
(∃x)((Fx & (∀y)(Fy ⊃ y = x)) & Gx)
| (∃x)((Fx | There is an F ... |
| & (∀y)(Fy ⊃ y = x) | ... it’s the only F ... |
| & Gx) | ... and it’s a G. |
Take the two judgements (1) (Ix)(Fx, ~Gx) and (2) ~(Ix)(Fx, Gx).
If Russell is right about definite descriptions
A. They are equivalent – they’re only ever true or false together.
B. (1) entails (2). If (1) is true, (2) is also, but the reverse isn’t true.
C. (2) entails (1). If (2) is true, (1) is also, but the reverse isn’t true.
D. They are independent of each other. Knowing the truth value of one of them doesn’t tell you anything about the truth value of the other one.
Answer: B
Topic:
definite descriptions
Course Level:
First year formal logic