More Fun Than Sex Itself! Logic Quiz #3!

[Sunstone]

Here's a logic quiz that's more fun than sex itself!*

Let's say that there exists a person who never believes any false proposition is true, nor believes that any true proposition is false.

Further suppose that person is assigned the task of determining whether any proposition given to her is true or false (i.e. she is assigned the task of announcing whether she believes any proposition given to her is true or false).

Now, there is at least one proposition that she must remain forever undecided about or no longer be someone who never believes a false proposition is true, nor a true proposition is false.

What is that proposition (or its logical equivalent)?



Anyone who submits a correct proposition will be gloriously rated a winner after the quiz closes. To make this quiz as fair as possible to non-logicians, winner status will awarded to any one that I -- at my sole discretion -- deem to be "barking up the right tree". i.e. the wording on your proposition need not be perfect.

*More fun than sex itself -- if you happen to be celibate like me.


EDIT: Yes, we have winners!


Both @Curious George and @Papoon gave winning entries to the quiz.


Basically, what we’re dealing with here is a modified version of “The Liar’s Paradox”.


“I will never believe this proposition is true.” Is an example of a proposition that our heroine must forever remain undecided about.


First, remember that our heroine is someone who never believes a false proposition is true, nor a true proposition is false.


Now, if she believes “I will never believe this proposition is true” to be true, then the proposition is false, and she becomes someone who believes a false proposition is true.


But if she believes “I will never believe this proposition is true” to be false, then that means she believes the proposition to be true*, and then the proposition must be false – in which case she again becomes someone who believes a false proposition is true.


Hence, for her to remain someone who never believes a false proposition is true, nor a true proposition is false, she must forever remain undecided about the proposition, “I will never believe this proposition is true.”


If you wish further clarification, try this simplified version of the quiz:


Is the statement, “This statement is false”, true or false?


If the statement, "This statement is false" is true, then the statement is actually false.

But if the statement, “This statement is false”, is false, then the statement must actually be true.

Questions?

*Assuming bivalence.

 

[Curious George]

Here's a logic quiz that's more fun than sex itself!*

Let's say that there exists a person who never believes any false proposition is true, nor believes that any true proposition is false.

Further suppose that person is assigned the task of determining whether any proposition given to her is true or false (i.e. she is assigned the task of announcing whether she believes any proposition given to her is true or false).

Now, there is at least one proposition that she must remain forever undecided about or no longer be someone who never believes a false proposition is true, nor a true proposition is false.

What is that proposition (or its logical equivalent)?



Anyone who submits a correct proposition will be gloriously rated a winner after the quiz closes. To make this quiz as fair as possible to non-logicians, winner status will awarded to any one that I -- at my sole discretion -- deem to be "barking up the right tree". i.e. the wording on your proposition need not be perfect.

*More fun than sex itself -- if you happen to be celibate like me.

Wouldn't any semantic paradox work? E.g. "this statement is false" or "heterological is heterological"

 

[Papoon]

Everything I say is a lie.

 

[Sunstone]

Keep dem entries comin', folks!

 

[McBell]

There are absolutely no absolutes

 

[beenherebeforeagain]

Moderation in all things, including moderation

 

[Curious George]

Moderation in all things, including moderation

We do not speak of moderation on the forums there is another directory called site feedback for posts like this.

 

[beenherebeforeagain]

We do not speak of moderation on the forums there is another directory called site feedback for posts like this.

Glad I had just finished taking a swallow of my drink before I read that, because it would have been EVERYWHERE!

 

[Sunstone]

Yes, we have winners!


Both @Curious George and @Papoon gave winning entries to the quiz.


Basically, what we’re dealing with here is a modified version of “The Liar’s Paradox”.


“I will never believe this proposition is true.” Is an example of a proposition that our heroine must forever remain undecided about.


First, remember that our heroine is someone who never believes a false proposition is true, nor a true proposition is false.


Now, if she believes “I will never believe this proposition is true” to be true, then the proposition is false, and she becomes someone who believes a false proposition is true.


But if she believes “I will never believe this proposition is true” to be false, then that means she believes the proposition to be true*, and then the proposition must be false – in which case she again becomes someone who believes a false proposition is true.


Hence, for her to remain someone who never believes a false proposition is true, nor a true proposition is false, she must forever remain undecided about the proposition, “I will never believe this proposition is true.”


If you wish further clarification, try this simplified version of the quiz:


Is the statement, “This statement is false”, true or false?


If the statement, "This statement is false" is true, then the statement is actually false.

But if the statement, “This statement is false”, is false, then the statement must actually be true.

Questions?

*Assuming bivalence.

 

[Sunstone]

Wouldn't any semantic paradox work? E.g. "this statement is false" or "heterological is heterological"

Depends on what you mean by a semantic paradox. For instance, is "There are absolutely no absolutes" a semantic paradox. If yes, then there are semantic paradoxes that don't work in terms of our logic quiz. For it is possible for the heroine of our logic quiz to hold that the statement, "There are absolutely no absolutes" is false without contradiction.