A century ago mainstream science was still quite happy to countenance vital and mental powers which had a 'downwards' causal influence on the physical realm in a straightforwardly interactionist way. It was only in the middle of the last century that science finally concluded that there are no such non-physical forces. At which point a whole pile of smart philosophers (Feigl, Smart, Putnam, Davidson, Lewis) quickly pointed out that mental, biological and social phenomena must themselves be physical, in order to produce the physical effects that they do.

Philosophers sometimes also use 'reductionist' more strictly, to mean 'type-identities' between mental and physical categories, and to exclude 'non-reductive physicalisms' like metaphysical functionalism.

The 'phenomenal concept' issue is rather different, I think. Here the question is whether there are concepts of experiences that are made available to subjects solely in virtue of their having had those experiences themselves. Is there a way of thinking about seeing something red, say, that you get from having had those experiences, and so isn't available to a blind person?

I don't think that we can figure out what is going on in conscious colour perception just by phenomenological introspection. We need to know about brain mechanisms as well. We need to figure out what information is present in the mechanisms that constitute conscious colour perception.

I rather incline towards 'conceptualism', in line with my view of colour perception - I don't think that we can represent objects and properties for which we have no concepts, not even in perceptual experience. In this sense I differ from those who defend 'non-conceptual content' like Michael Tye and Chris Peacocke.

I think my view is rather more radical than Pete Mandik's. Both of us want to show that colour perception doesn't transcend what can be conceptualized, but I don't think he goes so far as to deny that it doesn't involve different responses to all the discriminable surfaces.

I think that there are non-physical laws all right: genuine (if not strict) laws written in the language of biology, economics, and so on. But I don't regard that as a contentious issue. Even reductionists about chemistry will think that there are special chemical laws whose formulation makes essential use of chemical terminology.