Mental Causation Case Study

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In section 6 of Mental Causation by David Robb and John Heil (R&H), functionalism is framed in the context of the causal exclusion problem, and several solutions are provided in attempts to solve it, namely: the autonomy solution, the inheritance solution and the identity solution. I believe the first two solutions to fail in virtue of dependent overdetermination, and that the identity solution cannot maintain unitary properties, as opposed to what R&H suggest.
Functionalism sees mental properties as multiply realizable, which means different causal profiles can lead to the same mental property. This is concluded from the intuition that there is no one physical state that can comprehensively cause every case of a mental property. For example, the physical/neurological processes involved in causing pain can vastly differ between humans and
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Specifically, they commit dependent overdetermination, as they cannot prove if the mental is truly efficacious (since it needs to be realized by the physical). As for the identity solution, besides the problem of mental quausation, I am confused about the distinctions it has made between types and tropes. That is, if the mental is the physical (i.e. a specific mental trope is identical to its physical equivalent), why do they not both fall under the same type? The solution states that “the M-trope and the P-trope are one and the same trope falling under two types, mental and physical”, but how can they not share the same unifying property (i.e. type) if they are the same thing? For the M-trope and P-trope to fall under different types (i.e. have different uniting properties), they must be distinct from each other in some way; or, the types must be the same thing. In other words, the identity solution needs to either give up the idea of unitary properties (types), or it must recognize distinction between the mental and the

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