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Viliam_Bur comments on Open thread, February 15-28, 2013 - Less Wrong Discussion
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In the short story/paper "Sylvan's Box" by Graham Priest the author tries to argue that it's possible to talk meaningfully about a story with internally inconsistent elements. However, I realized afterward that if one truly was in possession of a box that was simultaneously empty and not empty there would be no way to keep the inconsistency from leaking out. Even if the box was tightly closed it would both bend spacetime according to its empty weight and also bend spacetime according to its un-empty weight. Opening the box would cause photons and air molecules (at the least) to being interacting and not interacting with the contents. Eventually a hurricane would form and not form over the Atlantic due to the air currents caused (and not caused) by removing the lid. In my opinion If there is any meaning to be found in a physical interpretation of the story it's that inconsistency everywhere would explode from any interaction with an initial inconsistency, probably fairly rapidly (at least as fast as the speed of sound).
I'd be interested to know what other people think of the physical ramifications.
The paper only showed that it is possible to talk meaningfully about a story with an element which is given inconsistent labels, and the consequences of having the inconsistent labels are avoided.
The hero looks in the box and sees that it "was absolutely empty, but also had something in it" and "the sense of touch confirmed this". How exactly? Did photons both reflect and non-reflect from the contents? Was it translucent? Or did it randomly appear and disappear? How did the fingers both pass through and not-pass-through the contents? But more importantly, what would happen if the hero tried to spill out the contents? Would something come out or not? What if they tried to use the thing / non-thing to detonate a bomb?
The story seems meaningful only because we don't get answer for any of these questions. It is a compartmentalization forced by the author on readers. The problems are not there only because the author refuses to look at them.
So in essence claiming "A and not ~A, therefore B and ~C, the end." That isn't a limitation imposed by the author but an avoidance of some facts that can be inferred by the reader.
Imagine that I offer you a story where some statement X is both completely true and completely false, and yet we can talk about it meaningfully.
And the story goes like this:
"Joe saw a statement X written on paper. It was a completely true statement. And yet, it was also a completely false statement. At first, Joe was surprised a lot. Just to make sure, he tried evaluating it using the old-fashioned boolean logic. After a few minutes he received a result 1, meaning the statement was true. But he also received a result 0, meaning the statement was false."
Quite a let-down, wasn't it? At least it did not take ten pages of text. Now you can be curious how exactly one can evaluate a statement using a boolean logic and receive 1 and 0 simultaneusly... but that's exactly the part I don't explain.
So the "talk about it meaningfully" part simply means that I am able to surround a nonsensical statement with other words, creating an illusion of a context. It's just that the parts of contexts which are relevant, don't make sense; and the parts of contexts which make sense are not relevant. (The latter is absent in my short story, but I could add a previous paragraph about Joe getting the piece of paper from a mysterious stranger in a library.)