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liar's paradox problem

Posted on 2003-10-25
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Last Modified: 2012-06-21

I need help explaining whether this sentence is a statement:

 ___________________________
|The sentence in this box is a lie.|
|__________________________|
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Question by:azcalv408
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by:SethHoyt
ID: 9621218
A statement is typically defined as a sentence that is either true or false, but not both. Under that definition, the answer to your question should be clear. Ask yourself this: Is it possible for this sentence to be definitely true or false? That should help you to answer this.

-Seth
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GwynforWeb earned 50 total points
ID: 9621224
In logic a statement must be either true or false the above is neither true or  false. For if it were true it must also be false and visa versa, nothing concernig truth/falsehood can simultaneously both, in essense there are collections of words that do not have the property of truth or falsehood and as such are not logical statements. There are not many but the above is one of them.
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by:GwynforWeb
ID: 9621232
Hi Seth.  I submitted from an unrefreshed page, you must have got there first just as I was starting to type. :-)
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by:zenlion420
ID: 9632523
these are interesting statements though.  i ran across some neat stuff on this sort of thing in "godel escher bach".  hofstadter did a great job, in my opinion, of showing the limitations of formal systems by displaying these "well formed strings" that are simultaneously both well formed, according to syntax, and self destructive, as far as gaining any truth.  i think godel's incompleteness theorem shows the same limitations in math.  or maybe it was TNT, i forget, been years.

aloha,

j
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by:zenlion420
ID: 9632528
wait>>retracting "interesting statements">>turn that into "interesting groups of words".  :)
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by:SethHoyt
ID: 9635622
What I find interesting is how counter-intuitive this can be sometimes. For example,

"This sentence is false."

is not a statement, whereas these:

"This sentence is both true and false."
"This sentence is neither true nor false."

are both statements. They're just false ones. We're not used to thinking about whether a sentence has a decidable truth value, but rather whether it is decidably true. So things like this can be counter to our common sense perception.
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by:zenlion420
ID: 9635741
that's interesting.

thanks,

j
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by:kaller2
ID: 9638318
BUT The expert made a logical statement!  He claimed that logical statements are only those ones where you can decide clearly the truth or the falsehood.

So answer me this - never mind the true side,  how could you ever decide if the expert's answer was FALSE?  YOU CANNOT!  So the logical conclusion is that the expert HIMSELF has made special kind of statement that is NOT logical!

If that is true, then the expert is wrong!!!!!!!!


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by:kaller2
ID: 9638452
I would ask for the points back if I were you.

I would have thought that an experts answers should at least meet his own criteria.  I mean making statements that are impossible to be false, and then presenting them as answers, in the hope of getting points for them. I ask you!  TAUTOLOGY, thats what I call it.  

Thats almost as bad as asking a PARADOX and trying to make it look like a question.

At least I only expect points for a CONTRADICTION.
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