This week's Strange Horizons has a story by fellow Codexian Cat Rambo, who I saw quite a bit over the summer when she was volunteering at Clarion West.

#

In other news, Colorado Congressman Tom Tancredo just described my sunny adoptive home as a a "third world country".

''Look at what has happened to Miami,'' the WorldNetDaily quotes Tancredo as saying in an interview. ``It has become a Third World country. You just pick it up and take it and move it someplace. You would never know you're in the United States of America. You would certainly say you're in a Third World country.''

Which is just what I was thinking as I was walking from my roomy rented house to the Starbucks on campus, and...

Wait.

Hmm...

#

Oh, and since it actually brought out a suprising amount of interest when I mentioned something about the topic earlier, I thought I should follow up by saying what I ultimately said about the Liar paradox in my paper.

I like the Keith/Caroline solution as well, though I'm not sure there's any way of using it for the Liar that wouldn't run up against the counter-examples of perfectly meaningful, non-paradoxically true or false sentences that refer to some further sentence that doesn't exist yet when the first sentence is written. (Or, say, "This sentence has seven words in it.") I'm going to have to think about that.

Meanwhile, my own extremely unimaginative solution--basically a re-working of something Saul Kripke said--is as follows.

Truth is correspondence between what we say and extra-linguistic reality.

Take the following three sentences.

(A) Snow is white.
(B) For God's sake, don't open the door.
(C) Pumpkin pie penetrates jazz.

(A) is a proposition, which for present purposes (the exact nature of propositions is actually very controversial in analytic philosophy circles) just means that it's the sort of thing that can be true or false. (B) is clearly a non-proposition. It would obviously be a category mistake to ascribe truth or falsehood to it. (C) shares the subject-verb-object structure with (A) and is composed of perfectly understandable English words, but they don't seem to add up to a claim about anything in external reality, even a false one, since we don't know what it could possibly mean.

I want to say that the Liar sentence and all similar sentences, including the constituent parts of mutli-sentence paradoxes, is a pseudo-proposition just like (C), although less unambiguously so. Sentences can meaningfully ascribe truth or falsehood to other sentences, and do so all the time, but for them to be meaningful, the series of sentences ultimately has to ground out in a sentence that asserts or denies something to be the case about the world.

E.g. in the pair...

(1) (2) is false.
(2) Walter the cat is fat.

...(1) is meaningful, because (2) is. Since (2) is true, (1) is false.

By contrast...

(3) (4) is false.
(4) (3) is true.

...doesn't ultimately ground out in a meaningful statement.

The superficially tricky part is what to say about...

(5) (5) is not true.

If it's meaningless, so it's not true or false, then it's not true, right? But if it's not true, then it is true. Contradiction.

I want to say that the part where all that goes wrong is the "if it's meaningless, then it's not true or false" derivation.

Why? Well, a statement that attributes truth or falsehood to a non-proposition is itself a non-proposition (e.g. "it if false that, 'For God's sake, don't open the door'" is a meaningless psuedo-proposition if anything is.) Also, a statement that denies a pseudo-proposition is itself a pseudo-proposition. After all, if I can deny X, and I know what I mean when I deny it, then X might be false, but it's clearly not meaningless.

Put those two premises together and you have the counter-intuitive result that "the Liar Sentence isn't true or false" is *itself* a meaningless statement, which is strange, but does get around the paradox.