To what extent is the paradox really solved? Can someone who understands the proof more fully comment on this?
This solution to the paradox say that the context shifts… “this statement is false” can be true if whatever “this statement” is referring to is false; in other words you have nested meanings (type hierarchies) where the whole 4-word sentence is true (meta-meaning) because it is referring to a statement (in this case itself) that is false in a given context.
Seems a bit unsatisfying to me. They’ve redefined the meaning of the sentence so that it now makes sense—but have they really addressed the original paradox or just explained it away?
By the way, Godel’s incompleteness theorem does not rely on the paradoxical aspect of the Liar Paradox to be undecidable. The statement p is undecidable in the given theory it is referring to, even though it is not paradoxical:
p = “This statement cannot be proven in the given formal theory”
To what extent is the paradox really solved? Can someone who understands the proof more fully comment on this?
This solution to the paradox say that the context shifts… “this statement is false” can be true if whatever “this statement” is referring to is false; in other words you have nested meanings (type hierarchies) where the whole 4-word sentence is true (meta-meaning) because it is referring to a statement (in this case itself) that is false in a given context.
Seems a bit unsatisfying to me. They’ve redefined the meaning of the sentence so that it now makes sense—but have they really addressed the original paradox or just explained it away?
By the way, Godel’s incompleteness theorem does not rely on the paradoxical aspect of the Liar Paradox to be undecidable. The statement p is undecidable in the given theory it is referring to, even though it is not paradoxical:
p = “This statement cannot be proven in the given formal theory”