Type-Identity Theory Strikes Back

when presented under PSI, token-reduces to x, when presented under PS2 iff 

We could introduce the additional condition that the property structures involved here should be property structures that mimic the structure of multiple realization, reflecting, for example, the intuition that every mental token (that is one object presented as an instance of mental kind M) reduces to a physical token (that is the same object presented as instantiating a physical kind, where this kind is one of the realizers of M). This nicely fits the idea that the realization relation is an explanatory relation to give an example, on this view, a pain token is a pain token in virtue of being a token of C-fiber stimulation. 

The notions of type- and token-reduction introduced here bear upon an appropriate understanding of anti-reductionist aspirations in the context of ontological non-reductive physicalism If we assume that there are different, irreducible kinds of properties, but still assume that token- or substance monism is true, then we could use the notion of token-reduction and type-reduction to capture this idea. Non-reductive physicalism, in its ontological version, consists in the affirmation of token-reduction and the denial of type-reduction for the relevant class of tokens and types. The explication proposed above enables us to give an idea of what reductive type- and token-identity theories consist in, and, combing the two, it yields a characterization of non-reductive physicalism. The next sections discuss the application of the explication of reduction to more recent versions of type-identity theory. 

Does multiple realizability really attack type-identity theory It seems obvious that many innocent properties are multiply realizable. For example, a specific mean kinetic energy of an entity can be realized by infinitely many spatial states of the entity s constituents (Kisfler 1999). This does not affect its being a basic kind. Thus, multiple realizability does not seem to threaten identity-theories per se. The trick is to introduce a distinction between heterogeneous multiple realization and homogeneous multiple realization. The former is bad for the identity-theorist, 

As already mentioned, the argument comes in different forms - some tell the story in counterfactual terms (Lewis 1980), some claim that actually, mental kinds are multiply realized (Kim 1992 Fodor 1974 Block and Fodor 1972 Putnam 1967 Endicott 1993) - and it should be noted that type-identity theory is lost even if there were just one high-level type which is multiply realized, if the argument is sound. 

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