[quote1264425450=salamander]
This sentence is false.

If this sentence is true, it's false. If it's false, it's true. That's paradoxical.

The most common solution brought to this paradox that I've encountered is the semantics one - the one that says the above sentence is meaningless, and therefore can't have a truth value. What I don't understand is why can't a sentence like the above have a meaning but not a truth value? Why does meaning imply truth value?
[/quote1264425450]

"This sentence" has no reference.
This sentence is false, has no truth or falsity.
This sentence is true, has no truth or falsity.
They are not propositions at all.
They do not have meaning.

The extension/meaning of a proposition is its truth value.

This sentence is false, has no extension/meaning.

The liar paradox does not exist.

Whether paradoxical statements have meaning or not depends largely on one's choice of semantics. Typically parts of the proposition might have meaning, but in most senses that clearly is not satisfactory or even relevant in this context. In most practical senses one might say that a meaningful proposition is one that can be given in reply to a meaningful question, not merely in terms of the nature of the proposition, (for example, a meaningless statement could be presented meaningfully as an answer to "What was that statement that you said is a meaningless utterance?",but that does not imply that it is meaningful in terms of its content.)

A useful rule of thumb as a criterion for meaningfulness in a proposition is that if you are in doubt about its meaningfulness, then try negating it. If it is merely false, then its negation will be true. And both the proposition and its negation will be meaningful.
However, although this works well on fully meaningless utterances such as the traditional: "green ideas sleep furiously", as well as are on: "this proposition is not false", what about "Not all Cretans are consistent liars".

But why does that not work here? It seems to me that the reason is that "All Cretans are consistent liars." could be reformulated as: "The set of Cretans that ever tell the truth is empty." then one could non-paradoxically refute the statement by finding a counter example. It would follow that "All Cretans are consistent liars" would be meaningful, no matter who said it, and no matter how truthfully.

So, given that I find myself too sleepy to type coherently, this reduces to a request:
can someone present me with a counter example of an unambiguously meaningless statement that yields and unambiguously meaningful statement, true or false, on negation?

Thanks,

Jon

Whether paradoxical statements have meaning or not depends largely on one's choice of semantics. Typically parts of the proposition might have meaning, but in most senses that clearly is not satisfactory or even relevant in this context. In most practical senses one might say that a meaningful proposition is one that can be given in reply to a meaningful question, not merely in terms of the nature of the proposition, (for example, a meaningless statement could be presented meaningfully as an answer to "What was that statement that you said is a meaningless utterance?",but that does not imply that it is meaningful in terms of its content.)

A useful rule of thumb as a criterion for meaningfulness in a proposition is that if you are in doubt about its meaningfulness, then try negating it. If it is merely false, then its negation will be true. And both the proposition and its negation will be meaningful.
However, although this works well on fully meaningless utterances such as the traditional: "green ideas sleep furiously", as well as are on: "this proposition is not false", what about "Not all Cretans are consistent liars".

But why does that not work here? It seems to me that the reason is that "All Cretans are consistent liars." could be reformulated as: "The set of Cretans that ever tell the truth is empty." then one could non-paradoxically refute the statement by finding a counter example. It would follow that "All Cretans are consistent liars" would be meaningful, no matter who said it, and no matter how truthfully.

So, given that I find myself too sleepy to type coherently, this reduces to a request:
can someone present me with a counter example of an unambiguously meaningless statement that yields and unambiguously meaningful statement, true or false, on negation?

Thanks,

Jon