| 1. | It is also related to topos theory via the realizability topos.
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| 2. | Kleene's realizability theory identifies the functions with the computable functions.
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| 3. | In 1950 Turing expressed the multiple realizability of the mental in this way:
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| 4. | Program extraction using realizability is implemented in some proof assistants such as Coq.
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| 5. | The fact that brain structures are homologous is no evidence either for or against multiple realizability.
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| 6. | Fodor used this generalized multiple realizability thesis to argue against reductionism of the mind and of the special sciences.
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| 7. | If instead the realizability interpretation is used in a constructive meta-theory, then it is not justified.
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| 8. | However, there have been some functionalist theories that combine with the identity theory of mind, which deny multiple realizability.
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| 9. | Realizability is one of the methods used in proof mining to extract concrete " programs " from seemingly nonconstructive mathematical proof.
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| 10. | Most variants of realizability begin with a theorem that any statement that is provable in the formal system being studied is realizable.
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