Swinburne of "siphoning off"--is dualism the foundation of natural science?

This is an extremely important argument, and explains to a large extent how I reply to people who say that the progress of science is evidently going to push in favor of materialism with respect to the philosophy of mind. It's my claim that modern science is grounded, in a important sense, in dualism. That is, science at the time of Galileo was able to treat the physical world as a machine because it could dump all the qualitative stuff into the mind. But if the mind is supposed to be physical, how did that work back then?

No one replied when I put this up before, so I am putting it up again.

I was motivated to do so by noticing what looked to me to be an argument from scientific progress for materialist reductionism in Doctor Logic's comments. He wrote:

Well, every scientific regularity we discover is like a 'heads'. Every reductionist flip is like another 'heads'. After hundreds of these, it is not rational to conclude that mind is likely to be non-physical. In order to conclude that, the supernatural model would need to accurately predict some experience that's as improbable as heads-up fair coin tosses in a row. Of course, supernatural claims make no predictions that can make this kind of come-back.

It seems to me, however, that the success of scientific discoveries do not show that materialist reduction of the mind is inevitable, and that whatever difficulties we might encounter along the way (say, in dealing with consciousness), are "bumps in the road" to be smoothed out in the inevitable advance of science onward and upward on its road to a complete reductionist account of everything. If I am right, that advance of science was grounded, at its outset, by a cleavage between mind and matter. Science was free to analyze what was quantitatively analyzable through mechanistic analysis and treat everything else as mental. These successes are reasons to suppose that we won't be able to provide a mechanistic analysis of the mental, not that we will.

From Richard Swinburne’s The Evolution of the Soul (Oxford: Clarendon Press, 1986) p. 191.

There is a crucial difference between these two cases. All other integrations into a super-science, or sciences dealing with entities and properties apparently qualitatively distinct, was achieved by saying that really some of the entities and properties were not as they appeared to be; by making a distinction between the underlying (not immediately observable) entities and properties and the phenomenal properties to which they give rise. Thermodynamics was conceived with the laws of temperature exchange; and temperature was supposed to be a property inherent in an object. The felt hotness of a hot body is indeed qualitatively distinct from particle velocities and collisions. The reduction was achieved by distinguishing between the underlying cause of the hotness (the motion of the molecules) and the sensations which the motion of molecules cause in observers. The former falls naturally within the scope of statistical mechanic—for molecules are particles’ the entities and properties are not of distinct kinds. But this reduction has been achieved at the price of separating off the phenomenal from its causes, and only explaining the latter. All reduction from one science to another dealing with apparently very disparate properties has been achieved by this device of denying that the apparent properties (i. e. the ‘secondary qualities” of colour, heat, sound, taste, etc.) with which one science dealt belonged to the physical world at all. It siphoned them off to the world of the mental. But then, but when you come to face the problem of the sensations themselves, you cannot do this. If you are to explain the sensations themselves, you cannot distinguish between them and their underlying causes and only explain the latter. In fact the enormous success of science in producing an integrated physico-chemistry has been achieved at the expense of separating off from the physical world colours, smells, and tastes, and regarding them as purely private sensory phenomena. The very success of science in achieving its vast integrations in physics and chemistry is the very thing which has made apparently impossible any final success in integrating the world of the mind with the world of physics.