I have a question about colors. I always wonder if other people see the same color as I see. For example, we can agree that apple's color is red, but is it possible that we are refering to different colors as RED?

First, take a look at Question 2384 and its answers, which are closely related to your question. Your question is related to what is called the "inverted spectrum", a philosophical puzzle posed by John Locke, one version of which is this: Is it possible that objects that have the color you describe as "red" are seen by me as if they had the color you describe as "green", even though I also describe them as red, and vice versa? Posing the problem is difficult; e.g., objects arguably don't "have" colors, but reflect light of certain wavelengths, which are perceived by us as certain colors. "Is the color that I perceive as, and call, red the same as the color that you perceive as what I call blue?" is another way of posing the puzzle. Part of the problem is that there doesn't seem to be any way to decide what the answer is (if, indeed, it has an answer). What experiment would decide between these? Perhaps such color-perceptions (more generally, what are called "qualia") are such that a functionally complete theory of the mind (or brain) would not enable us to distinguish between them. For more on this, see the Stanford Encyclopedia of Philosophy article on "Inverted Qualia".

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