The dualist position hinges on the idea that human beings are made up of two components; the physical and the non-physical. Our body and brain, everything we can touch, move, feel, and manipulate, lies within our physical construct. But we also have a non-physical mind. Our consciousness, emotions, desires, and experiences occupy the mind. They cannot be observed, touched, or perceived, but they still exist in the non-physical realm. While there are many different brands of dualism, the core idea of “dual” entities- a physical and a non-physical- connects them all. Nagel and Kripke fall into the dualist train of thought but promoted their own brand of property dualism.
Property dualism asserts that mental phenomena are merely properties of physical phenomena. You cannot reduce mental phenomena to physical phenomena, nor do mental phenomena exist without physical phenomena . For example, when I put gloves on, I feel warmth. I know that warmth is just kinetic molecular energy, however, my mind detects that molecular energy through a personal feeling of warmth. The feeling of warmth would not be present in my mind without the physical occurrence of kinetic molecular energy, and I would not be able to detect that molecular energy without experiencing warmth. The mental process (or non-physical process), is just our perception of the physical process.
Richard Boyd constructed a counter-argument to Kripke’s brand of property dualism. In the example of pain, Kripke would argue that our perception of pain is the non-physical manifestation of the physical process of C-fibres firing. However, there have been incidents where pain has been felt without the physical process of C-fibres firing. Think of amputee victims who still experience pain in phantom limbs. This non-physical perception of pain, without the physical occurrence of C-fibres firing suggests that mental properties cannot be reduced to components of physical phenomena.
We cannot experience mental phenomena without physical phenomena. We cannot experience physical phenomena without mental phenomena. Therefore, both exist.
Mental phenomena are just our interpretation of a physical action. They are not a different entity altogether, just a different perspective on the same entity.