The Liar's Paradox, Contradiction, and Truth

Nothing at all wrong with that idea, I would say.

 

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Is it conceptually equivalent to the graphic of a snake eating its own tail?

 

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I used to think a snake would disappear if that happened when I was younger.

 

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Wesmorris:

You demonstrated something of interest which is often lost by its obviousness: All contradictions require two halves.

However, one half of the liar's paradox actually is a liar's paradox itself, if phrased slightly differently: This statement is false.

 

But...
False is not opposed to truth. Falcity is the absence of truth. If something is false, it doesn't mean that it's opposite is true. Merely that it conveys no message. Or that it is in conflict with true statements.

Or.. the truth or falcity of a statement is not tied only to the words said, but also on a deeper level of thought. Words have diffrent meanings and contextes depending on, well, lots of stuff.

Truth and False are two diffrent consepts, that vary greatly. True is something that correlates with other things considered true (say, experiences), never changes and always holds true. False fails to keep integrity in all situations. As such, falcity can be "true" temporarily, but will fail in other contexts or points of view.

Or simply, false can be true, but true truth cannot be false. (this sentence is false, as the word "truth" means too many varying concepts. As they shift, the sentence becomes true, or false. I hope you still understand what I'm saying.)

 

Hmm. The paradox itself.

Well, it seems to me that the statement doesn't have a subject that can be true or false, so the statement is neither true nor false but a poorly constructed assertion. There is no content to be evaluated but the claim itself. As such, it seems the incompleteness theorum applies. The sentence itself is self-contained, and as such - cannot be evaluated or whatever that theorum thingy says I can't think of it clearly atm. Just trying what seems like a creative approach that I'm sure has probably been tried a thousand times.

 

hmm... and perhaps another way to view it is to keep close track of time and consider the position presented on perspective I presented above.

by that I mean, the statement read once, and in the moment of it having been read, clearly indicates an attempt at falseness which is only contradicted a moment later by the realization that it must be true for it to be false. So then one might consider "it is true that this is false", which points to a delayed duality of context. In the context of the direct evaluation of the subject "this sentence", "is false" is a correct statement until the context shifts to the whole sentence evaluated at the same time. So again it becomes a matter of context, at least in the half assed, hasty and sloppy analysis. pardon.

 

I like this one:
"Prince_James can not rationally believe that this statement is true."

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nevermind

 

Ogmios:

Yet are not most, if not all, false statements the contradiction of a true one? For instance, suppose that "John walked to the store" is true. You then have:

John walked to the store. - True
John did not walk to the store. - False

Is not the falsehood a contradiction of the truth?

Example of falsehood gaining its fallacy over time?

Wesmorris:

I think this can be resolved by defaulting to my approach: Evaluate a sentence based on whether it affirms as true an impossibility to decide whether it is resolvable or not. If unresolvable, it is necessarily false.

Isn't that like saying "I was going to the store, but then I decided to go home" would have several different meanings depending on how one reads the sentence? I don't really think this is a claim for what the sentence itself is saying though, no?

Pete:

Ha ha ha!

Very true, very true...

Buttt, I think this is again, jokes aside, resolvable by pointing out that it implies an impossibility and affirms it is true.

 

The interesting thing is that only you have to discard it as self-contradiction.

Now consider:
"Pete can not rationally believe that this statement is true."

You should have no trouble determining that statement to be true... but I can not.

 

Pete:

I must say, that is a rather clever take on the Liar's Paradox.

 

There is no paradox. Both sentences are referneces to an assertion of truth; however, one does not exist; hence, this little infinite evaluation of truth is incomplete. To complete the evaluation, an assertion of truth could be inserted between both sentences (as a unique standalone sentence).

 

I stole it from a web site that presented an imagined discussion beween Penrose and an super-intelligent machine in the far future.

Damned if I can find it now.

 

Crunchy Cat:

I fear I am not understanding your idea for its resolution?

 

I think this paradox has a pretty simple solution. For example, take the following statement:

"This statemen is false."

It is neither a true statement, nor a false statement, <I>nor a paradoxical statement</I>. It is, quite simply, an <I>invalid</I> statement. And that is so because it speaks of something that does not exist. For a clearer example, consider these (also given in the OP):

"The following statement is true. The previous statement is false."

In this case, the first statement speaks about the second statement; but the second statement has not come into existence yet. It comes into existence only when it is completed, that is, when it says something. But it speaks about the first statement. If it was already there, then the first statement would not have said that the second one was true.

Even in the first example, the statement starts to speak of itself before it is completed. Therefore it is invalid. Since it is invalid to speak of something that has not been defined yet.

 

Rosnet:

So essentially you agree with me: Because the statement postulates an impossibility we are faced with a paradox and that is all.

 

I'm not sure I undertand what you just said...

I'm saying that there is no paradox. The statement is not a contradiction. It's <I>invalid</I>.

 

Prince_James,

False is, I think, lack of truth. Not its contradiction.

But while a true statement makes others false, a false statement does not make the opposite true. If Jim is brave, Jim is not a coward. But if Jim is not a coward, this does not make him brave. (Especially if someone chooses to say "is not" rather than "is"..)

Or, the opposite of true is false, but the opposite of false is not truth.

Then to move on to LIES, which are communicated information. False, and intentionally so, they can be true unintentionally. Any stated answer can ultimately be true or false depending on how it is interpreted.

Redefine everything, and everything makes sense! If two clearly true statements contradict each other, then clearly some definition or assumption is incorrect.

"The following statement is true. The previous statement is false."

The second sentence is true, as the first is not always correct. The second is always true, so the first holds.
But only as far the second does. The instant the first is correct, the second becomes false. Hence non-linearcy is acheived, and the first becomes false. The second statement is true, and we are clear. The first is false, but the second is true.

a)My pants are white
b)I'm alive
c)etc.

My pants are white as long as they stay white. If I stain them, they are no longer white. Hence the a) becomes false. Of course, one cannot say that BEFOREHAND..

But d)"I will die" will undoubtly hold true. Or e)"if u push some1 theyll push u pack" (or in other words, force and counterforce..)

You could say only old statements can be truely false. I inteded to clarify that any constant (compassion NEVER hurts etc.) statements are not true if they are at some point false. Unless time is specified, this holds true always.
(it might not have anything to do with the actual topic though...)

 

I disagree, for several reasons:

1. The time sequence is a function of the syntax of the language, not the statements themselves which are essentially timeless.
2. You might disagree with what I'm about to say, but it is not invalid to speak of something that is not yet defined.

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3. The paradox can be presented in such a way that there is no defined order of statement:
   Imagine two pieces of paper, labelled A and 1. On A is written "The statement on 1 is false". On 1 is written "the statement on A is true".