#1
by 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?