A common argument against reductive physicalism is multiple realizability, the possibility that a psychological process ( say ) could be instantiated by many different neurological processes ( even non-neurological processes, in the case of machine or alien intelligence ).
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Realizability can be seen as a formalization of the BHK interpretation of intuitionistic logic; in realizability the notion of " proof " ( which is left undefined in the BHK interpretation ) is replaced with a formal notion of " realizer ".
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Realizability can be seen as a formalization of the BHK interpretation of intuitionistic logic; in realizability the notion of " proof " ( which is left undefined in the BHK interpretation ) is replaced with a formal notion of " realizer ".
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Putnam's invocation of multiple realizability does not, of course, directly answer the problem raised by Smart with respect to useful generalizations over types and the flexible nature of the type-token distinction in relation to causal taxonomies in science.
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Thus, unlike standard versions of functionalism ( often called " Functional State Identity Theories " ), FSTs do not allow for the multiple realizability of mental states, because the fact that mental states are realized by brain states is essential.
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The second view, which might be termed the computational or Brouwer-Heyting-Kolmogorov interpretation of propositions, takes the view that we fix a computational system up front, and then give a realizability interpretation of propositions to give them constructive content.
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Indeed, one of Hilary Putnam's arguments for his version of functionalism relied on the intuition that such alien creatures would have the same mental states as humans do, and that the multiple realizability of standard functionalism makes it a better theory of mind.
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Jerry Fodor, Putnam and others immediately noted that, along with being a very effective argument against type-identity theories, multiple realizability implied that " any " low-level explanation of higher-level mental phenomena would be insufficiently abstract and general.
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Putnam uses multiple realizability against functionalism itself, suggesting that mental events ( or kinds, in Putnam's terminology ) may be diversely implemented by diverse functional / computational kinds; there may be only a token identification between particular mental kinds and particular functional kinds.
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Modified realizability does not justify Markov's principle, even if classical logic is used in the meta-theory : there is no realizer in the language of simply typed lambda calculus as this language is not Turing-complete and arbitrary loops cannot be defined in it.
