Substances are wholes. They exist in one piece and although they may have connections with other wholes these connections do not define its intrinsic nature (i.e. they are extrinsic relations). So a chair always remains a chair. It does not matter if there is someone to sit on the chair, or where one might find a chair. A chair floating in space far from any human bottom is still a chair. However in that the chair is (intrinsically) physical it is intrinsically connected to all other physical objects because they are all connected by physical laws.
The substance dualist therefore holds that each mind is a distinct non-physical thing, an individual whole of non-physical substance whose identity is independent of any physical body to which it may be temporarily “attached”. Substances go together with properties, so substances have properties and properties belong to substances. Properties cannot exist on their own, so for example we do not experience just redness (property) but always something (substance) that is red. For substance dualism the mind is a substance that possesses mental properties (such as believing, sensing, imagining), and body is a substance that possesses physical properties (such as height and mass). While these two substances are ontologically distinct they are nevertheless believed to causally interact with each other.

While the belief that humans are more than their physical body and are perhaps even more essentially an immortal soul has been a common belief throughout history it is less commonly held today amongst philosophers. The most important substance dualist is Rene Descartes (1596-1650) and just as with the theory of knowledge so too philosophy of mind takes much of its initiative from the way his philosophy set up the problem. The main concern of the philosophy of mind is how the reality of meaning, rationality and conscious experience is related to, or arises from, a material world which, in itself, is devoid of such characteristics. While Descartes solution to this problem is almost universally rejected by philosophers today the problem itself remains central and many of Descartes ideas continue to shape our understanding of both body and mind and so consequently the way in which different theories of mind are developed.

Descartes philosophy famously starts, after the destructive application of sceptical arguments, with the claim that at least one thing cannot be doubted “I am thinking, therefore I exist”. This cogito (thinking self) is known through intuitive reason and becomes for Descartes the foundation of his whole philosophy. On the basis of this argument Descartes holds to the epistemic primacy of the mental. That is to say that in the area of knowledge certainty can only truly be found in our consciousness of ourselves as thinking. The physical world and the consciousness of others is removed from this sphere of certainty and can only be guaranteed through finding something that will secure a bridge to these from our conscious thinking. Descartes believed that within his own mind he had the idea of God which could indeed provide the guarantee necessary.

A second claim that is at the heart of Descartes position is the autonomy of the mental. This is based on viewing reality in terms of substances and their attributes. So for Descartes the mind is a separate substance which in no way depends for its existence on the body. Who we ultimately are appears in this move to be reduced to a narrow notion of theoretical reason which though constantly interacting with our material body is in reality quite separate and independent of it. Such a self is a long way from the embodied, social, living breathing human being we might perceive ourselves and others to be.
Related Links
Philosophy of mind, Distinctive features of the mind, Descartes arguments for dualism