Potential solution to the Liar Paradox I

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Potential solution to the Liar Paradox I

 
 

Potential solution to the Liar Paradox I

#1  Postby Scott H » Nov 22, 2011 2:25 am

I think I am on the verge of intuitive solution to the Liar's Paradox. My tentative solution is based on some simple language analysis. What I would like to know is: has it been proposed before, and if so, by whom?

The solution is as follows: we distinguish concrete statements from abstract statements. A concrete statement is just a particular instance of an abstract statement. So if I yell, "Trees are falling down!" my utterance considered in its own right is a concrete statement, as is my partner's when he yells it louder. However, both our concrete statements refer to the same abstract statement, (Ex)(Trees(x) ^ FallingDown(x)).

The idea is to designate a concrete instance of the liar statement (S: "This statement is not true") as having the property of untruth. We may then correctly state that S is not true under the defense that our statement, which we may call T, is not identical to the statement S. This allows us to evade the self-referential vicious circle.

Next, we acknowledge the possibility of a false definition. Someone may object, "But that's just what S is saying! The subject of statement S satisfies its predicate, and so by your premise and the definition of truth, S must be true in addition to being false. Contradiction." To guard against this objection, I will argue that one cannot define 'truth' as "satisfaction of the predicate by the subject." This is because all definitions are accompanied by existential claims, and to use a term presupposes that the defined object exists.

An easy example of a false definition is: "What is green?" "It is the color of the scales of the Loch Ness Monster." Here, we have given a definition of 'green' that is literally false, as its existential claim is that there is such a thing as the Loch Ness Monster and that its scales have a unique color.

Similarly, there is no such thing as a predicate that applies to a statement exactly when the subject of the statement satisfies its predicate. Not only is it a circular definition (notice that the word 'predicate' appears twice), but it defines a property that simply cannot exist, as it would then by definition hold two contradictory values for its Liar statement.

What are your thoughts? Does this sound like something that has already been attempted or written about?
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Re: Potential solution to the Liar Paradox I

#2  Postby Lion IRC » Nov 22, 2011 5:12 am

I like it.
Most resolutions of so-called paradoxes involve simple language analysis.
Even Bertrand Russell seemed to realise that his intuition about the reality or otherwise of paradoxes was just a trick of language.
This statement is true? Which statement?
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Re: Potential solution to the Liar Paradox I

#3  Postby Teuton » Nov 22, 2011 7:50 am

Res extensa cogitans sum.
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Re: Potential solution to the Liar Paradox I

 
 

Re: Potential solution to the Liar Paradox I

#4  Postby Cito di Pense » Nov 24, 2011 3:42 pm

Well, as usual, the liar's paradox has a statement that tries to refer to itself implicitly, and so it is a statement without a predicate or a subject.

" ' This statement is false ' is false " means the same thing as " ' This statement is true ' is true "

" ' This statement is false ' is true " means the same thing as " ' This statement is true ' is false "

In no case does it tell you if "this statement is true (false)" is true or false, so you can't use it to detect lying. But we knew that.
The squirming facts exceed the squamous mind
and yet, relation appears

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