The liar paradox

Philosophical, mathematical and computational logic, linguistics, formal argument, game theory, fallacies, paradoxes, puzzles and other related issues.

Re: The liar paradox

Postby 0oqpo0 on September 4th, 2011, 8:27 pm 

I make a distinction between the liar statement and the liar claim, the liar claim being, "I am lying"
For this, I pieced together this:

I am lying:
-----------------------
In referring to my own truth condition, my claim is other than the actual answer I consider it to be.
-----------------------

So you need to use some type of truth condition system, true, false, neither, both, undefined and then the statement does what it does best, turns it into something else.
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Re: The liar paradox

Postby Don Juan on September 7th, 2011, 3:26 pm 

Owen wrote:Without adding referential context, 'This statement is false' has no sense or meaning.
The subject 'This statement' cannot have the predicate 'is false'.


What if we specify and add the referential context as referring to the very statement 'This statement is false.'?
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Re: The liar paradox

Postby zoot on April 7th, 2013, 9:58 pm 

Owen wrote:'This statement' is an incomplete description which has no reference.
'This statement' is not a statement at all. Therefore it cannot have the property of 'truth' or 'falsity'.

No reference? It refers to itself. In general, I'm very skeptical that the solution to the Liar will be found by pointing to its self-reference, because (1) there are plenty of self-referential statements that are perfectly reasonable, and (2) in any case, there are non-self-referential Liars. Just consider:

(a) The next statement is false. (b) The previous statement is true.

It would be fairly absurd to suggest that either (a) or (b) have no reference. Indeed, (a) and (b) only become paradoxical when placed together in that order; in most other contexts, there's nothing wrong with them:

(a) The next sentence is false. (c) The moon is made of cheese.

I don't think that your approach touches extended Liars such as the (a)/(b) pair above.
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Re: The liar paradox

Postby What? on December 18th, 2013, 1:56 am 

Owen wrote:The simplest version of the paradox is the sentence:
This statement is false.


That's not the simplest possible version. Consider:

Let the red dot/period below stand not only for the idea of falsehood, but for reference to itself as an instance of falsehood.

.


We specifically let certain sequences of vocal sounds, or their written representations, stand for ideas and such. In any case...

...there is no possible world in which exists no one, and no actual falsehood, but in which exists solely and merely the idea of falsehood.



Curly, one of the Three Stooges, is reading a fiction-fantasy story. The story is about a kid who discovers that he can use his smart phone's math app to change himself into a real-life, fire-breathing dragon: all the kid has to do is enter 2+2=4, and, Poof!, he is turned into a real fire-breathing dragon.

But, real dragons don’t know how to work smart phones, so the story ends when the kid becomes a real dragon. It was a very short read.

But, it was just the right length for Curly. Putting the book down, Curly says, "Hey, Mo!, Look at this! Here's a story about some fictional arithmetic!"

"No, you bonehead!" says Mo, "That's real arithmetic!"

"It can't be!" says Curly, "The story’s fantasy!"

“No, you moron!” pipes up Larry. “The story is true. Otherwise, it couldn’t have real arithmetic in it!”

Curly thinks a bit, then asks Moe, "What do you think Moe? Is the story fantasy, or is the story real?"

"It's impossible to decide", says Moe. "It's one of those paradoxes."

"Pair o' boxes?" asks Larry.

"No", says Moe. "Paradox."

"Two ox?", says Curly?

"Para-dox", enunciates Moe.

"There ain't no Docs in this story" says, Curly. "I should know, I read it."

"He means docks", says Larry.

"Oh, never mind", says Moe in frustration. "It's way over your heads."
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Re: The liar paradox

Postby What? on December 18th, 2013, 2:03 am 

zoot wrote:I'm very skeptical that the solution to the Liar will be found by pointing to its self-reference, because (1) there are plenty of self-referential statements that are perfectly reasonable, and (2) in any case, there are non-self-referential Liars. Just consider:

(a) The next statement is false. (b) The previous statement is true.



Try these three pairs on for size:


The next statement is false. The previous statement is false.

The next statement is true. The previous statement is false.

The next statement knows what you are thinking. The next statement knows what you are thinking.
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