Opposites are often thought of in pairs, like black & white, up & down, good & bad. We can make this a bit more general by introducing shades of grey. However, I often find it useful to include something opposite to both of the opposites, e.g., black, white and clear. In the case of up and down, the grey value would be "level", and the third value would be "nowhere". In the case of good and bad, the grey value would be "neutral", and the third value is something I don't know the word for.

This has come up in my thoughts in a few places.

When thinking about the Liar paradox -- "this sentence is false" -- we want to assign it a truth value that is neither True nor False. I suppose it could make sense to think of it as being half-true and half-false. However, the Liar paradox is analogous to a function in a program which calls itself recursively, and returns the opposite of that recursive call. In this case, we wouldn't say that the liar function half-returns-true and half-returns-false, but rather that it never returns at all.

Another place this has come up is in religion. People often ask, are you religious, or atheist? If you say you're neither, then they respond: ahh, you're agnostic! But agnosticism is like grey. It is somewhere between black and white, not sure which way it wants to go. I'm not agnostic. I'm a non-theist. To me, the question is not "is there a God?", but rather, "what is the nature of reality?" I don't know enough about the nature of reality to know whether the question of whether there is a God even makes sense.

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