¹ Of course, these aren't exhaustive. One could say that all the fundamental properties are at the same time mental and physical like panpsychists or take fundamental properties as being neither mental nor physical, in which case one would be a neutral monist. One could even identify fundamental properties with abstract properties, as some versions of string theory seem to imply. In any case, these other alternatives haven't been as historically prominent as the main ones I present even if nowadays they are more popular than idealism.

² For this use of fundamental see David Chalmers. The Conscious Mind. Oxford (Oxford University Press, 1996), 126–129.

³ I think this definition is inadequate because of its disjunctive nature and some people think that written sentences and certain sorts of pictures have intentionality. One could correct the definition and add that is intrinsic intentionality we are talking about, not derivative intentionality, but some people deny the former kind of intentionality exists without being eliminativists. Still, the definition I present suffices for this study.

⁴ The proposed definition of physical property has two parts: First, I require that physical properties can't be identical to, nor imply, primitive irreducible mental properties, like consciousness or intentionality. Secondly, I require that they are defined by their causal role in explaining the behavior of objects in space-time. Even more so than my definition of mental, this definition of physical has lots of problems. Just two quick examples: Some people believe in categorical properties, whose identity doesn't depend on its causal role; and isn't it weird to rule out physical objects without any causal properties by definition? No one knows how to define ‘physical’ and proposed definitions never find widespread acceptance among physicalists but only seem good for the ones who propose it. I don't think this is as problematic as it seems, because working definitions for specific questions work well enough (for example, even if physicists found out stuff outside space-time, and we had good reason to call those things physical, it's hard to think that has any relevance for the mind-body problem, personal identity or other issues on which substance dualism has any bearing).

⁵ Cartesian dualism would be classified as a kind of Strong Theistic Interactionist Non-spatial Pure Dualism.

⁶ I believe that the most defensible form of substance dualism is a type of Moderate Naturalistic Interactionist Spatial Pure Dualism, even though I think many other forms of dualism resist the following objections well enough.

⁷ If it's the soul that thinks and I am not identical to my soul, then it seems I don't think or only think in a derivative way.

⁸ Believe it or not, this russelian thesis that physics only tells us about dispositional properties is widely accepted by both philosophers of mind and science in recent years and very few objections have been raised against it. For an early proponent of the thesis and its role in the case for dualism, see John, FosterThe Immaterial Self (London and New York: Routledge, 1991)Google Scholar.

⁹ I will hereforth use ‘dualism’ to mean substance dualism.

¹⁰ The criteria of individuation I am speaking here is not supposed to work across possible worlds, but just within a single world. Problems of transworld identity, if they are a problem at all, are a problem for both materialists and dualists.

¹¹ This point is made by Charles, Taliaferro in his Consciousness and the mind of God (Cambridge University Press, 1994): 207–209Google Scholar.

¹² There is only apparent tension between saying that relationships seem to presuppose the numerical difference of their relata and trying to individuate souls by their causal relationships to brains since: 1. The brain's identity is being taken for granted and 2. The soul is distinct from the brain in virtue of possessing phenomenal properties that brain doesn't. The individuative role of the causal relationship isn't to distinguish souls from brains, which can be justified on independent grounds, but souls from each other.

¹³ Kim, Jaegwon (2001). ‘Lonely Souls: Causality and Substance Dualism’, in Corcoran, K. (ed.) Soul, Body and Survival: Essays in the Metaphysics of Human Persons (Ithaca: Cornell University PressGoogle Scholar). For criticism: Bayley, et al. ‘No Pairing Problem’ Philosophical Studies 154 (3):349–360 (2011).CrossRefGoogle Scholar

¹⁴ Tooley, Michael. Time, Tense, and Causation. (Oxford: Clarendon Press, 1997), 200Google Scholar.

¹⁵ In his discussion, Kim assumes that spatial dualists must accept that souls are geometrical points, but since he gives no argument for why there can't be immaterial extended souls, I will consider his arguments independently of this thesis since I believe his charges are independent of the kind of dualism you believe in.

¹⁶ Multiple personalities don't manifest themselves at the same time. Why would souls be so nice as to take turns for the control of the body? There are also cases where both hemispheres are partially separated and some limbs begin to have personalities of their own. However, if there are two souls there, they control different halves of the body, and aren't in competition with one another. Again, why would souls be so nice so as to split their territory? These observations should lead the dualist to believe that genuine co-location of souls doesn't happen in the actual world, if any.

¹⁷ For a statement of such theories see Fair, David's ‘Causation and the flow of energy’ in Erknnetnis. 14:219–215 (1979)Google Scholar. For criticisms check Ehring, Douglas. (1986) ‘The transference theory of causation’ in Synthese, 67: 249–258.CrossRefGoogle Scholar

¹⁸ This example also counts against the energy exchange account of causation. This case is described in Robin, Collins' ‘The energy of the soul’ in Baker, and Goetz, (ed.) The Soul Hypotheses (2011), 123–138Google Scholar.

¹⁹ Averill, E., and Keating, B. (1981) ‘Does Interactionism Violate a Law of Classical Physics?’ Mind 90 (1981), 102–7CrossRefGoogle Scholar.

²⁰ Hart, W. D.The Engines of the Soul (Cambridge:Cambridge University Press, 1988). 127–136Google Scholar.

²¹ Lycan, William ‘Giving Dualism its Due’, Australasian Journal of Philosophy 87 (4):551–56 (2009)CrossRefGoogle Scholar.

²² Baker, Mark. ‘Brains and Souls; grammar and speaking’ in Baker, and Goetz, (ed.) The Soul Hypotheses (2011), 73–99Google Scholar.

²³ There have been many arguments for substance dualism: modal arguments, arguments from the non-vagueness and simplicity of the self, libertarian free-will, from the unity and continuity of consciousness, from the identity conditions of human persons and even inferences to the best explanation as a way of solving the measurement problem in quantum mechanics. The case for dualism is complex and made on multiple grounds. Although I personally don't find any of them convincing, I think that the standard arguments for Physicalism from the past success of science and causal closure are even worse. My suspicion is that they seem good from the perspective of their proponents because they think substance dualism is so obviously false that they don't even bother putting themselves in their opponents shoes to consider possible replies.

²⁴ Just for the record, I am neither a dualist nor an agnostic, but something close to a russelian monist.