There are many fancy logical treatments of this paradox.

The sentence does not express a statement that has a truth value, which means that it does not express a statement at all. There are countless sentences like that. One could devise countless sentences like that. A sentence can be vapid and nonsensical, and "This sentence is false" is one of them.

One need not consider vapid claims, and one need not construct logical proofs of their vapidity.

Metaphysics is the result of specific techniques. Like all philosophy, it is not a thing, but a process, an approach. It results from and requires a misuse of language, mostly in imprecise definitions and ambiguity. It is the rendering of that which cannot be observed (even theoretically) as a higher order of reality than that which can be observed.

It requires that we conceive of the world as having more than one kind of reality, which is a grave error if misunderstood. It can also be seen as mere overgeneralization, but this is not quite correct. Humans are capable of abstraction, and abstraction is and certainly can be performed in ever higher orders. That doesn't mean the world exists in ever higher orders, but only that abstraction does.

It's clearly possible to abstract until all meaning vanishes. Metaphysics occurs when no meaningful context remains for a statement.

Metaphysics is difficult to define if it's treated as a 'thing". It's an activity.

The purpose of education is to describe and instill the values of the elders. Young people need a strong, self-conscious sense of what they are rebelling against to effectively innovate. It's not enough to know how to think. You need to know what to think about.

Moreover, you need to learn the scales to be a good improvisor. You know, unless you're Hendrix, or somebody.

Descartes did not doubt his existence because he was certain that God would not deceive him. He, in effect, said nothing.

We really all believe that there are causes and effects. Only the philosopher can believe that, because some events are caused, that they all are. That's because the philosopher doesn't realize that we decide just what events are, where they begin and end. The philosopher may also not realize that we live on a certain scale, and that causes and effects may obtain on one scale and not another.

We really believe that we make decisions and the only way to deny that is by making certain decisions. Determinism or free will can only obtain in an anthropomorphic universe.

You probably think I'm having a fit because I mistakenly used italics. I meant to emphasize only one word. I can assure you I am not, and was not, having a fit. Bit OI appreciate your concern. I can assure igjugarjuk that I do not believe that metaphysics is too rational. One can misunderstand language, or anything else, and still be rational. Irrational and incoherent are two different things.

You read it wrong. I said that metaphysics is a misunderstanding of language. It requires equivocation of meaning or an error in abstraction, for example. Both of these either destroy or ignore context. There is no meaning without context.

For people like Kripke, x=x has some metaphysical meaning. To people like me, x=x means "for purposes of the present argument, the value of X shall be preserved". Even if we know that x changes. We are simply claiming that those changes are not material to our argument. It's not metaphysics, it's just context. Abstraction removes information, but when abstraction removes all context, it can produce metaphysics.

Science is the isolation of observed variables. Philosophy is a special study of language. Metaphysics is a misunderstanding of language.