The persistent question begging by materialists

I'm currently reading the Blackwell Companion to Substance Dualism. Chapter 2 is by a certain William G. Lycan. He is a materialist but doesn't think a great deal of the arguments for materialism. Mind you, as it transpires, he certainly regards them more highly than I do.

Anyway, he says:

David Papineau (2002) offers a simple deductive argument for materialism, based on the causal completeness of physics: Conscious events have physical effects; all physical effects have sufficient physical causes; the physical effects of conscious causes are not, or not always, overdetermined by physical causes; therefore conscious events are physical events.

Lycan doesn't define overdetermined, but I think Papineau means the idea that both consciousness per se causes certain physical events, and that quite independently prior physical events also cause the same physical events. A bit like someone being killed by 2 bullets with each solitary bullet being sufficient for his demise.

Anyway, the whole problem with this argument is the implicit assumption that the physical world is closed! That is, all physical events are caused by prior physical events. But common-sense holds that our consciousness per se is causally efficacious. It's the reason why I'm typing the words I am now. Blind directionless physical laws of nature couldn't write this awesome stuff I write! 

Point being that the assumption of physical causal closure is pretty much question begging. I don't think naturalism really involves anything more than this assumption, and materialism is very similar to naturalism. All these arguments for materialism are question begging. Either they assume causal closure, or they redefine consciousness to mean some causal role within the brain.