What is the difference between substance dualism and property dualism? Which position adequately defends dualism and why?
Substance dualism holds that there are two kinds of substances or two states: The physical is all the material, matter. The mental is non-physical; it has no spatial extension; the mental, or mind (not to be confused with brain, which is physical) exists but somewhere immaterial (abstract consciousness, soul, etc.) The mental state exists and can causally affect the physical world, but the mental state is abstract and therefore external to the physical world.
Property dualism holds that there is only one type of substance but two kinds of properties which inhere in that substance: mental and physical. There are different versions of PD but the general idea is that mental properties, emerge, arise or are produced by/from physical properties. Mental properties can be reduced/explained by physical states or they cannot. But, property dualists do hold that there is an ontological difference between mental and physical properties. Examples of properties: redness, spherical. These properties inhere in/on physical properties but, isolated, what/where are they? Thus, they have a quality (property) that is ontologically different from the physical properties and states in which they inhere. Property dualists believe that the consciousness is a property which inheres in a brain as red inheres in an apple.
Analogously speaking, if you think red can exist without inhering in anything then you are a substance dualist; that is, red (consciousness) is not just a property. It is an abstract something that exists somewhere/somehow else and it can manifest through or affect some physical thing. If you think red needs the apple or emerges as a property of it, then you are a property dualist.