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