The inverted spectrum is the hypothetical concept, pertaining to the philosophy of color, of two people sharing their color vocabulary and discriminations, although the colors one sees—one's qualia—are systematically different from the colors the other person sees.
The concept dates back to John Locke. It invites us to imagine that we wake up one morning, and find that for some unknown reason all the colors in the world have been inverted, i.e. swapped to the hue on the opposite side of a color wheel, the complementary color. Furthermore, we discover that no physical changes have occurred in our brains or bodies that would explain this phenomenon. Supporters of the hypothesis of qualia as non-physical entities argue that, since we can imagine this happening without contradiction, it follows that we are imagining a change in a property that determines the way things look to us, but that has no physical basis. In more detail:
Metaphysical identity holds of necessity
If something is possibly false, it is not necessary
It is conceivable that qualia could have a different relationship to physical brain-states
If it is conceivable, then it is possible
Since it is possible for qualia to have a different relationship with physical brain-states, they cannot be identical to brain states (by 1).
Therefore, qualia are non-physical.
The argument thus states that if we find the inverted spectrum plausible, we must admit that qualia exist (and are non-physical). Some philosophers find it absurd that an "armchair argument" can prove something to exist, and the detailed argument does involve many assumptions about conceivability and possibility, which are open to criticism. Perhaps it is not possible for a given brain state to produce anything other than a given quale in our universe, and that is all that matters. The question, however, can arise how these critical philosophers, using the same armchair technique that they are criticizing, refute the robust argumentation of the Inverted spectrum experiment?
C. L.