The Treachery Of Images
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Many would say that this is a pipe. Others would say it is a painting of a pipe. However, they're both wrong. It is in fact a photograph of a painting of a pipe, which is stored on a server and therefore is a digital representation of a photograph of a painting of a pipe - probably far from what Magritte intended when he painted the original. Even there, when he had the conception of it, it was just an idea of a painting of a pipe. He obviously did not paint what he intended to paint, because when Magritte put his idea of a painting of a pipe to canvas, it became a painting of a pipe, which is very different from a notion of a painting of a pipe.
The statement "Ceci n'est pas une pipe" is recursive because that statement is actually a painting of a statement. The sentiment itself, as mentioned before, is very true, but what is not a statement cannot be called true or false, so the painting of a statement that says the painting of a pipe is not a pipe is in fact invalidating itself.
There are some inherent problems with trying to apply the Transitive Property of Equality to this conundrum. Such property says that if a = b and b = c, a = c. One could say that the digital representation of the photograph of the painting of a pipe = photograph of painting of pipe because their information is about the same. So, the photograph of the painting of a pipe = painting of pipe. And the painting of a pipe = the digital representation of the photograph of the painting of a pipe. If you tried to hang that digital representation of a painting of a pipe on your wall as is, you'd have some problems; even more so if you tried to smoke it.
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