On confusing reduction with elimination
This summary I wrote from an old post helps explain the relation between reduction and elimination, since that came up in a discussion here.
The Churchlands wrote an essay entitled “Intertheoretic Reduction: A Neuroscientist’s Field Guide,” in On the Contrary: Critical Essays 1987-1997 (Cambridge, MIT Press, 1998) in which they distinguish three types of intertheoretic reductions: conservative, reforming, and eliminiative. The reduction of temperature in a gas to the mean kinetic energy of the gas’s molecules was a conservative reduction, in that it doesn’t require us to reconceive temperature in any radical way in order to view it as the MKE of the molecules. The secondary qualities of temperature, how it feels, are not denied, they are simply pronounced to be the way we react to temperature rather than something in temperature itself. If the concept of temperature was essential to the meaning of our lives, this type of reduction would not threaten us in any way.
The second type is a reforming reduction, which shows that an earlier theory had significantly misconceived the phenomena it covered. Newtonian mass is replaced in relativity theory with mass relative to a frame of reference, but we were not just dead wrong when we used the concept of mass.
The most radical is an eliminative reduction. In this, the old idea is so wide of the mark that it is simply deleted by the new theory. No single has does the work of phlogiston, but phlogiston is replaced by a theory that distinguishes between oxygen, carbon monoxide, and carbon dioxide.