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Oscar_Cunningham comments on Open Thread for February 18-24 2014 - Less Wrong
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Is anyone else bothered by the word "opposite"?
It has many different usages, but there are two in particular that bother me: "The opposite of hot is cold" "The opposite of red is green" Opposite of A is [something that appears to be on the other side of a spectrum from A]
"The opposite of hot is not-hot" "The opposite of red is not-red"
Opposite of A is ~A
These two usages really ought not to be assigned to the same word. Does anyone know if there are simple ways to unambiguously use one meaning and not the other that already exist in English?
(Basically, are there two words/phrases foo and bar so that one could say "The foo of hot is cold, but the bar of hot is not-hot")
"Complement" is sort of a word for the second one.
I think complement can mean both too. E.g. red and green are complementary colors, whereas the sets "red" and "not-red" are complements.
My sense of the word complement is that if two things are complements, they sum to 1, or some equivalent.
A is the complement of ~A because P(A or ~A) = 1
Red and green are considered to be complementary colors because together they contain all primary colors of pigments. [although, that is based on the societal understanding that the primary colors are Red, Yellow and Blue. This is actually incorrect. For pigments, the primary colors are really Magenta, Yellow, and Cyan. For light, they are Red, Green, and Blue.]