False statements

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. 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.

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.

Reveal Hidden Content

Originally posted by Shallow Blue
Of necessity (they contradict one another) at most one. And therefore, [hidden]exactly one, since if it were zero, #10 would contradict itself. Hence number 9 is the only true ststement.[/hidden]

Richard

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.

Originally posted by LemonJello
None of the statements are truth-apt.

Nice! ^_^

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

Reminds me of the old dilemma of having a piece of paper with the text "the statement on the other side of this paper is false" printed on both sides. =)

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.

n statements, n-1 'th is true, where n = 2, 3, 4, ... so we'd get

lim n-1 as n-> oo as the ordinal of the statement that is true, and the ordinal approaches infinity as the number of statements increases without limit?

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

Originally posted by LemonJello
It works fine. If they are not truth-apt to begin with, then they are all neither true nor false.

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&rsquo😉; or sentences (‘you will not smoke&rsquo😉 whos ...[text shortened]... expressivism, prescriptivism.

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

Originally posted by mikelom
PERFECTLY asserted.

I guess you are a language teacher, per chance?

-m.

Originally posted by Shallow Blue
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.

Richard