Cambridge Philosophy Sample Admissions Test

Question 5 of the sample admissions test for philosophy has intrigued me, mainly because I can't come to a conclusion of what I believe the answer to be! So I though it would be worth discussing it on here to see what everyone thinks. The question is as follows:

Albert says: `Everything Caroline says is true’.
Betty says: `Everything I say is false’.
Caroline says: `Everything David says is true’.
David says: `Everything Caroline says is false’.

Who is the only one who could be telling the truth?

(a) Albert
(b) Betty
(c) Caroline
(d) David

Firstly its worth noting that the question requires a single answer.

Firstly, if Albert were true, it would require for Caroline to be true. As only one person can be true, we can deduce that it cannot be Albert nor Caroline who are telling the truth.

Therefore it must be either David or Betty.

If Betty is always false, then she is false in saying so. We needn't think further, as this backs up he statement and he statement is therefore true. However, would she not be admitting to being true at times in saying that she is false in claiming everything she says is false? This has stumped me.

David is then the only feasible answer; he is also true in claiming Caroline is false (Caroline cannot be true unless Albert is also true, but only one can be telling the truth).

What to you guys think?

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(edited 8 years ago)

Reply 1

btea

It would have to be Albert. David and Caroline contradict each other and Betty contradicts herself!

Reply 2

asdfghjklcupcake

Original post by btea

It would have to be Albert. David and Caroline contradict each other and Betty contradicts herself!

Albert tells the truth -> what Caroline says is true -> What David says is true -> What Caroline says is false => contradiction
David could be telling the truth, which means that Caroline's affirmation is false => not EVERYTHING David says is true, but some things may be.

(edited 7 years ago)

Reply 3

btea

Original post by Mirru

It still stands that the others contradict each other and themselves?

Reply 4

radarmaker

Whippersnapper7 and Mirru are, I think, correct to say David. It's important that it's stipulated that only one of our group can be telling the truth. Here (ignoring Betty for the moment, because she's an interesting side case) are the possibilities:

i) Albert is telling the truth, so Caroline is telling the truth, so David is telling the truth. David says Caroline is lying, which leads to a contradiction.

ii) Caroline is telling the truth, so David is telling the truth. But, again, David says Caroline is lying, and we have a contradiction.

iii) David is telling the truth, so Caroline's statement is false. If Caroline's statement is improperly negated it comes out as "everything David says is false", but in fact should be "not everything David says it is true", so it is possible that he is lying about Caroline. (I have a feeling that it's this negating step that the exercise is targeting - recognising the difference between ∀x ¬Tx and ¬∀x Tx)

Since only one person could be telling the truth, and in (i) or (ii) there could be more than one person, and contradictions arise, the answer is likely (iii). So, David is the most plausible option.

You could perhaps make some case about Betty, but it seems unlikely that you could make that case without at least admitting that her statement is both true and false. I'd plump for David, especially if the question doesn't give you space to try to defend Betty. (Wikipedia and the SEP both have some good stuff on liar paradoxes if you're interested!)

(edited 7 years ago)

Reply 5

ambimineral

I would go for David as well. To me, 'Everything David says is true' being false is not the same as 'Some things David says are true' being false. David's statement about Caroline can be true in this case. I don't see a contradiction there. I could be entirely incorrect though.

(edited 7 years ago)

It's David.

I agree. It is David who is telling the truth.For if Albert is telling the truth, Caroline must be telling the truth. Since David says that Caroline is false, this dispels both what Albert and Caroline say, making them wrong and David's statement true. Since Betty is always false, then she must be false in saying so. David is the best option.