Dualism or Cartesian Dualism is the philosophical position that there are two kinds of "stuff": usual ordinary matter, and spirit. Rocks, light, clouds, etc. are composed of ordinary matter, whereas minds and souls are composed of a fundamentally different type of matter. Dualism stands in contrast to monism and philosophical materialism. Dualism is an ontological position, ontology being a branch of metaphysics.
Perhaps the major counterargument to dualism is the fact that the existence of a soul, or of soul matter, has never been demonstrated. Much experimental work has been done in psychology, but none of it has shown that there needs to be a separate type of matter to explain how minds work. As far as science can tell at present, the mind is simply the result of the operation of a brain made of ordinary matter.
If mind matter exists, it must interface with the body somehow: signals from the eyes (which are made of ordinary matter) must pass to the mind, which must then decide what to do next and somehow signal the muscles to move appropriately. It should be possible to discover where and how this mind-body interface works, for instance by studying people who have sustained mental problems as a result of physical injury or stroke.
Evolution also argues against the existence of a mind outside the body: the brain is an expensive organ, requiring a lot of resources, such as oxygen, to function properly. If the seat of thought is not in the brain, but in an external mind in a separate plane, then there is no need for the human brain to be as large as it is. Natural selection should have favored those individuals with smaller brains as being better able to keep their brains functioning in times of scarcity.
The philosopher Daniel Dennett presents a case against Cartesian dualism in his book, Consciousness Explained.
Current models of cosmology include the notions of "dark matter" and "dark energy", which are different from ordinary matter and energy. These are different from "soul matter", since they were postulated to explain certain large-scale features of the universe, rather than to explain how minds work.
Dualism in Science
One of the major problems with dualism is that if there are two fundamentaly different kinds of substance, then how can they act upon each other?
Science has had precisely this problem, and one of the grand projects of the scientific endeavor has been to find a way of reconciling certain dualities. Thus, the duality of energy and matter has been resolved in quantum mechanics and the standard model, and the duality of space and time has been resolved in Einstein's theory of general relativity. It remains to be seen how these two remaining realities - spacetime and particles - might be resolved.