Davidsonian supervenience is insufficient for physicalism, since it fails to rule out doubled qualia. Physicalism thus requires fine-grained supervenience to augment Davidsonian supervenience.
(1) No two entities can differ at a time with respect to their mental properties without differing at that time with respect to their physical properties.
(2) No single entity can change with respect to its mental properties without changing with respect to its physical properties.
(FGS) If, at a given time, a single entity instantiates two distinct mental properties, it must do so in virtue of instantiating two distinct physical properties.
Doubled qualia occur when two minds, one whose qualia are inverted with respect to the otherâ€”a â€œgreen mindâ€ and a â€œred mind,â€ respectivelyâ€”share a supervenience base. What it means to share a supervenience base is that there are no physical differences in virtue of which the red mind and the green mind differ. Davidsonian supervenience, the conjunction of (1) and (2), does not rule out doubled qualia. To imagine doubled qualia, begin by imagining someone other than you, Person X, who is not your physical doppelganger. Let us stipulate that there is some physical difference between you and Person X. Unlike you, let us suppose, there are two minds inside of Person Xâ€”a red mind and a green mindâ€”where you only have the standard-issue red mind. Suppose further that all and only the physical properties that give rise to Xâ€™s red mind are the same physical properties that give rise to Xâ€™s green mind. If you are having a hard time imagining this, that is likely due to your tacit or explicit acceptance of FGS. Your acceptance of (1) and (2) canâ€™t explain this. In particular, the difference between you and Xâ€”the fact that you have only a red mind where X has a green one as well as a red oneâ€”is fully consistent with (1), since we have stipulated that there is a physical difference between you and X. Do you think that doubled qualia are weird? If so, then you will find the following intolerably bizarre.
Intermittently Doubled Qualia.
To get warmed up for intermittently doubled qualia, stop to appreciate the following stipulation about Person X: the red mind and the green mind need not have any awareness of each other whatsoever. What this means, then, is that for all you know, your qualia are doubled right now. For all you know, thereâ€™s someone else â€œin thereâ€ with you right now and what itâ€™s like to be them is just like what itâ€™s like to be you except for the inversion of the color qualia bit. Now, imagine further, that you undergo the following recurring physical change. The set of physical properties P1, that suffice to instantiate just the red mind are replaced by a set of distinct physical properties P2, that suffice for both a red mind and a green mind. So, according to the intermittent doubled qualia thought experiment, you change from P1 to P2 and back again which changes you from un-doubled qualia to doubled qualia and back again.
Perhaps you think that intermittently doubled qualia are impossible. You may be right. But hereâ€™s one thing that wonâ€™t rule them out: clause (2) of supervenience. Clause (2) prohibits you from changing mentally without changing physically, but the intermittent doubled qualia thought experiment stipulated that there were physical changes accompanying the change to a doubled state. Davidsonian supervenience rules out only some of the obvious impossibilities concerning qualia. (1) rules out (a) inverted and (b) absent qualia. (2) rules out (c) fading qualia and (d) dancing qualia. Neither (1) nor (2) rules doubled qualia. And Iâ€™m betting physicalists would very much like to rule out doubled qualia. Then physicalists should explicitly embrace FGS.