Is this logical statement true or false?

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tomandlu
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Is this logical statement true or false?

Postby tomandlu » Sat Dec 23, 2017 6:03 pm UTC

"All absolute statements are wrong, including this one."

This was prompted by listening to radio presenter, after a panel had made their forecasts for next year, who something like "the only thing I can guarantee is that all those predictions will be wrong." I thought he should have added "including this one."
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Re: Is this logical statement true or false?

Postby gmalivuk » Sat Dec 23, 2017 6:20 pm UTC

"All absolute statements are false" is false, because if it's true it's false, but if it's false then at least one absolute statement is true, but it need not be this one, so you avoid the "This sentence is false" paradox.

I'm not sure "including this one" affects the meaning or truth value in one way or another, because "All statements are false" is already an absolute statement, and "all" already means it includes this one.

However, "All those predictions will be wrong" is not self-referential in the same way, because it's talking about some specific set of predictions that doesn't include this one (else it would be "these" and not "those"). It's either true or false depending on the truth or falsity of all those predictions being referenced.
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Re: Is this logical statement true or false?

Postby tomandlu » Sat Dec 23, 2017 9:27 pm UTC

gmalivuk wrote:"All absolute statements are false" is false, because if it's true it's false, but if it's false then at least one absolute statement is true, but it need not be this one, so you avoid the "This sentence is false" paradox.

I'm not sure "including this one" affects the meaning or truth value in one way or another, because "All statements are false" is already an absolute statement, and "all" already means it includes this one.

However, "All those predictions will be wrong" is not self-referential in the same way, because it's talking about some specific set of predictions that doesn't include this one (else it would be "these" and not "those"). It's either true or false depending on the truth or falsity of all those predictions being referenced.


Sounds reasonable. I'm endlessly trying to work out the difference between the apparently reasonable but essentially nonsensical ("everything I say is a lie; I am lying") and the merely false ("I am both X and Y even though X <> Y"). Where I struggle (I think) is when it's not clear whether a statement is being contradicted or clarified. "All statements about the future are false, including this one" does not seem 'false' to me - provided you read it as "most statements about the future are false" (which is fairly useless about statements and the future, but therefore probably accurate, although that's not the point). However, "All statements about the future are false, with the exception of this one" seems more consistent without any equivocation, but less 'true'.

I guess what I'm quibbling about is reasonable readings - why is "all absolute statements are wrong, including this one" distinguishable from "almost all absolute statements are wrong," since the former self-acknowledges its own fallibility.

I guess I'm still puzzling over the different types of truth and falsehood and just plain nonsense (and, yes, I'm repeating myself. It's Christmas). [edit to add] Or, alternatively, I'm puzzling over 'truth' when the statement explicitly refers to the speaker's untrustworthiness.

(btw, pudding cat won't get off my mouse, so apologies for any weird typos - I think I caught most of them, but she did manage open an encrypted drive)
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Re: Is this logical statement true or false?

Postby gmalivuk » Sun Dec 24, 2017 5:33 am UTC

tomandlu wrote:why is "all absolute statements are wrong, including this one" distinguishable from "almost all absolute statements are wrong," since the former self-acknowledges its own fallibility.
It's distinguishable because the first one says something about 100% of a set, and the second only says it about almost 100% of that set.

I feel like you're expecting something deeper than is actually there. The important difference between your pair and "all swans are white / almost all swans are white" is that the first of your pair explicitly includes itself and thus cannot be true, whereas other "all / almost all" pairs may be true or false depending on other things about the world.
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Re: Is this logical statement true or false?

Postby measure » Mon Jan 01, 2018 6:45 am UTC

gmalivuk wrote:[O]ther "all / almost all" pairs may be true or false depending on other things about the world.

In the case of "statements about the future" (and indeed most classes of statements) half are true and half are false since for every statement A that is false ~A is true and vice versa. It really bugs me when song lyrics or motivational sayings or whatever say something like "There are <n> truths for every <m> lies" with n != m.

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Re: Is this logical statement true or false?

Postby gmalivuk » Mon Jan 01, 2018 4:31 pm UTC

"This sentence is true" is true but "This sentence is not true" has no consistent truth value.

Also arguably most statements as well as their negations have no truth value because they're things like "Colorless green ideas sleep furiously."
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Re: Is this logical statement true or false?

Postby Eebster the Great » Tue Jan 02, 2018 12:21 am UTC

gmalivuk wrote:"This sentence is true" is true but "This sentence is not true" has no consistent truth value.

Also arguably most statements as well as their negations have no truth value because they're things like "Colorless green ideas sleep furiously."

I would argue that this is either meaningless, and therefore not a logical statement (even though it is a syntactically valid English sentence), or that it does have meaning, and it is simply false, since there are no colorless green ideas, and therefore there can't be any sleeping, furiously or otherwise.

Also, while "this statement is false" cannot be assigned a truth value, "this statement is true" can be assigned either truth value, with that value justified self-referentially, so it is both true and false. Obviously these cannot be expressed in a consistent logical system, but they probably can be in some paraconsistent ones.

It's possible that in some mathematical sense, "most" statements have no truth value or multiple truth values, but I don't know how you would go about computing that.

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Re: Is this logical statement true or false?

Postby jaap » Tue Jan 02, 2018 7:32 am UTC

Eebster the Great wrote:[...] or that it does have meaning, and it is simply false, since there are no colorless green ideas, and therefore there can't be any sleeping, furiously or otherwise.

In mathematical logic such a statement would be considered true. Non-existent objects have any property you can name because to prove it false you would have to provide a counterexample, i.e. one of those non-existent objects but without that property.

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Re: Is this logical statement true or false?

Postby Eebster the Great » Tue Jan 02, 2018 8:10 am UTC

I guess it depends on what you take "sleep" to mean. If I said "fairies sleep in my basement," I think you could reasonably say that is false. If I said "all fairies sleep in my basement" or "every fairy sleeps in my basement," I feel like it would be different.

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Re: Is this logical statement true or false?

Postby Pfhorrest » Sun Feb 18, 2018 7:53 am UTC

tomandlu wrote:Is this logical statement true or false?

No.
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