

The Liar's Paradox Resolved - StevePatterson
http://steve-patterson.com/resolving-the-liars-paradox/

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schoen
The linked article proposes resolving the liar's paradox by forbidding self-
reference in some circumstances, or questioning the meaningfulness of
sentences that refer to "this sentence".

This is somewhat akin to what mathematicians tried to do in response to
paradoxes like Russell's, but Gödel was still able to construct self-reference
indirectly!

[https://en.wikipedia.org/wiki/Type_theory#History](https://en.wikipedia.org/wiki/Type_theory#History)

One concern with trying to do this is that it seems to rule out of bounds
quite a lot of natural uses of language that talk about the use of language.
The original liar paradox referred to a class of _persons_ (those from Crete)
as liars, rather than a _statement_ as a falsehood.

[https://en.wikipedia.org/wiki/Epimenides_paradox#Origin_of_t...](https://en.wikipedia.org/wiki/Epimenides_paradox#Origin_of_the_phrase)

We could also imagine cases like

"It is impossible to express truth in the English language."

or

"No sentence that contains eight words is true."

or

"No generalization about propositions is correct."

It seems increasingly difficult to maintain that all of these utterances are
meaningless, at least on the specific grounds that the article gives.

Or, to borrow a favorite line from my friend Erik:

"Il ne faut pas croire que la parole serve jamais aux communications
véritables entre les êtres." ("One should not believe that words suffice for
true communication between beings.") -- Maurice Maeterlinck

... which also provides a pretty nice liar paradox if you believe that
Maeterlinck was a being, or that I'm one. :-)

~~~
StevePatterson
There's no problem using language to talk about language. I think you're
referencing performative contradictions rather than self-referential
paradoxes.

The cases where the propositions become inaccurate is where the terms used
have no concrete definition.

The point is, the proposition "This sentence is false" isn't even sensible,
because "This sentence" isn't something that can be true or false. It's just
two words put together in a tricky way.

