A logical question

1. Aug 14, 2008

some_one

data:

A.each sentence which ends with exclamation mark is lying!
B.sentence A is lying!
C.sentence B is lying.

which claim is wright regarding these sentences?
1.A and C are truthful and B is lying
2.C is truthful while A and B are lying
3. B is truthful while A and C are lying
4.C is lying while A and B are truthful

that exclamation mark thing makes me confused

2. Aug 14, 2008

LowlyPion

A and B can both be truthful if it is really sentences that end in period that are lying.

3. Aug 14, 2008

Werg22

3. B is truthful while A and C are lying

A contradicts itself if assumed to be true. The only way to avoid the contradiction is to assume it is false. Therefore, B is true, and C is false.

4. Aug 14, 2008

some_one

a period meens nothing

how did come to this answer
how did you solve this exclamation mark thing??

5. Aug 14, 2008

Werg22

A proposition is either true or false, bot nut both (law of excluded middle + law of non-contradiction). The question clearly suggests that there is a way to assign truth values to the propositions without creating any inconsistency. Proposition A is either true or false. If we assume it is true, we obtain the following:

a. Sentence A is true.
b. Sentence A is a sentence which ends with an exclamation mark.

c. Therefore sentence A is false.

This is inconsistent; we have obtained both the statements "sentence A is true" and "sentence A is false" from the assumption that A is true. Therefore sentence A is not true. Therefore, it must be false. That said, we are forced to accept that B is true, and then that C is false.

To be noted: some propositions are not classifiable as either true or false, this being perhaps the biggest failure of classic Aristotelian logic. For example, the sentence "This sentence is false." leads to a contradiction whether we assume it is true or false. However, like I said, the question suggests that there is a way to assign truth values without contradictions, and so you may assume the laws of classical logic can be applied.

6. Aug 14, 2008

Redbelly98

Staff Emeritus
There are 3 possibilities:

1. All sentences that end in an exclamation mark are lying.
2. All sentences that end in an exclamation mark are truthful.
3. Some sentences that end in a "!" are lying, and some are truthful.

The trick here is that many people do not think of or consider possibility #3.

7. Aug 14, 2008

LowlyPion

You're right, I meant to say that A was internally consistent with a lie if such was the case, because in saying that exclamation marks are lies - that is a lie. It doesn't mean all exclamation mark sentences are lies however.

B in calling A a lie is merely making a correct observation.

And C of course is a lie because B is True.

8. Aug 14, 2008

some_one

thanks i understand this question now