- 14 Jun '12 06:28 / 1 editHere are 10 numbered statements. How many of them are true?

1. Exactly one of these statements is false.

2. Exactly two of these statements are false.

3. Exactly three of these statements are false.

4. Exactly four of these statements are false.

5. Exactly five of these statements are false.

6. Exactly six of these statements are false.

7. Exactly seven of these statements are false.

8. Exactly eight of these statements are false.

9. Exactly nine of these statements are false.

10. Exactly ten of these statements are false. - 14 Jun '12 12:13

Of necessity (they contradict one another) at most one. And therefore,*Originally posted by Pianoman1***Here are 10 numbered statements. How many of them are true?**

1. Exactly one of these statements is false.

2. Exactly two of these statements are false.

3. Exactly three of these statements are false.

4. Exactly four of these statements are false.

5. Exactly five of these statements are false.

6. Exactly six of these statements are false.

7. Exactl ...[text shortened]...

9. Exactly nine of these statements are false.

10. Exactly ten of these statements are false.exactly one, since if it were zero, #10 would contradict itself. Hence number 9 is the only true ststement.

Richard - 15 Jun '12 00:12

None of the statements are truth-apt.*Originally posted by Pianoman1***Here are 10 numbered statements. How many of them are true?**

1. Exactly one of these statements is false.

2. Exactly two of these statements are false.

3. Exactly three of these statements are false.

4. Exactly four of these statements are false.

5. Exactly five of these statements are false.

6. Exactly six of these statements are false.

7. Exactl ...[text shortened]...

9. Exactly nine of these statements are false.

10. Exactly ten of these statements are false. - 16 Jun '12 02:49

A sentence is truth-apt if there is some context in which it could be uttered (with its present meaning) and express a true or false proposition. Sentences that are not apt for truth include questions and commands, and, more controversially, paradoxical sentences of the form of the Liar (‘this sentence is false’ or sentences (‘you will not smoke&rsquo whose apparent function is to make an assertion, but which may instead be regarded as expressing prescriptions or attitudes, rather than being in the business of aiming at truth or falsehood. See expressivism, prescriptivism.*Originally posted by Shallow Blue***That doesn't work. If none of them are true, all of them are false, which makes #10 true, which contradicts your assumption.**

Richard

Read more: http://www.answers.com/topic/truth-apt#ixzz1xv9NWjfw - 16 Jun '12 12:57

What would be the case as i -> infinity, that is, as the number of statements approaches infinity, each statement saying "Exactly i of these statements is/are true"?*Originally posted by Pianoman1***Here are 10 numbered statements. How many of them are true?**

1. Exactly one of these statements is false.

2. Exactly two of these statements are false.

3. Exactly three of these statements are false.

4. Exactly four of these statements are false.

5. Exactly five of these statements are false.

6. Exactly six of these statements are false.

7. Exactl ...[text shortened]...

9. Exactly nine of these statements are false.

10. Exactly ten of these statements are false. - 17 Jun '12 07:19 / 1 edit

It works fine. If they are not truth-apt to begin with, then they are all neither true nor false.*Originally posted by Shallow Blue***That doesn't work. If none of them are true, all of them are false, which makes #10 true, which contradicts your assumption.**

Richard

At any rate, the OP presumes that such statements are truth-apt (not explicitly, but in the spirit of the exercise as it was given). I rather doubt that. (But this is debatable.)

If I am wrong and indeed such statements are truth-apt, then I would agree with the solution you gave. - 17 Jun '12 11:04

That is only true (and the term "truth-apt" only meaningful) in one specific branch of logic. Real life is not that branch, and neither are logical puzzles unless explicitly stated.*Originally posted by LemonJello***It works fine. If they are not truth-apt to begin with, then they are all neither true nor false.**

Richard - 17 Jun '12 14:52

PERFECTLY asserted.*Originally posted by SwissGambit***A sentence is truth-apt if there is some context in which it could be uttered (with its present meaning) and express a true or false proposition. Sentences that are not apt for truth include questions and commands, and, more controversially, paradoxical sentences of the form of the Liar (‘this sentence is false’ or sentences (‘you will not smoke&rsquo whos ...[text shortened]... expressivism, prescriptivism.**

Read more: http://www.answers.com/topic/truth-apt#ixzz1xv9NWjfw

I guess you are a language teacher, per chance?

-m.