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Multiple realizability, in the philosophy of mind, is the thesis that the same mental property, state, or event can be implemented by different physical properties, states, or events. The idea has its roots in the late 1960s and early 1970s when a number of philosophers, most prominently Hilary Putnam (1967, 1988) and Jerry Fodor (1975), put it forth as an argument against reductionist accounts of the relation between mental and physical kinds. In short, a theory of mind that includes multiple realizability allows for the existence of strong AI. The original targets of these arguments were the type-identity theory and eliminative materialism. The same arguments from multiple realizability were also used to defend many versions of functionalism, especially Machine state functionalism.
In recent years, however, multiple realizability has been used to attack the very theory that it was originally designed to defend. As a result, functionalism has fallen out of favor as a dominant theory in the philosophy of mind. The dominant theory ("received view" in the words of Lepore and Pylyshyn) in modern philosophy of mind is a version of generic non-reductive physicalism and one of its central pillars is the hypothesis of multiple realizability.
Complicating our historical understanding, Restrepo noted in 2009 that the thesis of the multiple realizability of the mental was held by Turing at least ten years before the usually attributed authors described the phenomenon. In 1950, Turing expressed the multiple realizability of the mental in the following:
The [Babbage Engine's] storage was to be purely mechanical, using wheels and cards.
The fact that Babbage's Analytical Engine was to be entirely mechanical will help us rid ourselves of a superstition. Importance is often attached to the fact that modern digital computers are electrical, and the nervous system is also electrical. Since Babbage's machine was not electrical, and since all digital computers are in a sense equivalent, we see that this use of electricity cannot be of theoretical importance. ... If we wish to find such similarities we should look rather for mathematical analogies of function.
In several papers published in he late 1960s, Hilary Putnam provides a classic example of the thesis of multiple realizability. In these papers, he argues that, contrary to type-identity theory, it is not the case that "pain is identical to C-fibre firing." Pain corresponds to, or is at least correlated with, completely different physical states of the nervous system in different organisms and yet they all experience the same mental state of "being in pain." Putnam cited numerous examples from all over the animal kingdom to illustrate his thesis. Is it likely that the brain structures of all mammals, reptiles, birds, amphibians and molluscs realize pain, or other mental states, in exactly the same way? Do they even have the same brain structures? Clearly not, if we believe the evidence furnished by comparative neuroanatomy and neurophysiology. How can they possibly share the same mental states and properties? The answer must be that these mental kinds are realized by different physical states in different species. Putnam then takes his argument a step further, and asks about such things as the nervous systems of alien beings, artificially-intelligent robots and silicon-based life forms. Should such hypothetical entities be considered a priori incapable of experiencing pain just because they do not possess the same neurochemistry as humans? Putnam concludes that type-identity and other reductive theorists make an extremely "ambitious" and "highly implausible" conjecture which can be disproved with just one example of multiple realizability. This argument is referred to as the likelihood argument.
Putnam also formulates a complementary argument based on, what he calls, functional isomorphism. He defines the concept in these terms: "Two systems are functionally isomorphic if there is a correspondence between the states of one and the states of the other that preserves functional relations." So, in the case of computers, two machines are functionally isomorphic if and only if the sequential relations among states in the first are exactly mirrored by the sequential relations among states in the second. Therefore, a computer made out of silicon chips and a computer made out of cogs and wheels can be functionally isomorphic but constitutionally diverse. Functional isomorphism implies multiple realizability. This is referred to as the "a priori argument".
Jerry Fodor, Putnam and others also note that, along with being a very effective argument against type-identity theories, multiple realizability implies that any low-level explanation of higher-level mental phenomena would be insufficiently abstract and general. Functionalism, which attempts to identify mental kinds with functional kinds that are characterized exclusively in terms of causes and effects, abstracts from the physico-chemical level of microphysics and hence seems to be a more suitable alternative explanation of the relation between mind and body. In fact, there are many functional kinds such as mousetraps, software and bookshelves that are multiply realized at the physical level.
Jaegwon Kim takes up the challenge of responding to the problems posed by multiple realizability for reductionist theories by suggesting that the physical realization base of a particular mental state is not a particular physical state but the disjunction of the physical states which realize it. Jerry Fodor replies to this objection by formulating a generalization of the multiple realizability thesis. According to Fodor, multiple realizability is not just something that occurs "across physical structure-types" but is a phenomenon that could occur even within the same token system (such as an organism). At different times, the same organism may realize type-identical mental kinds in physically different forms. (This thesis was later given some empirical support with the discovery of the relative plasticity of the human brain).
Fodor uses this generalized multiple realizability thesis to argue against reductionism of the mind and of the special sciences. The key to Fodor's argument is that, in his characterization of reductionism, all mental kind predicates in an ideal and completed psychology must correspond with a physical kind predicate in an ideal and completed physics. He suggests taking Ernest Nagel's theory of reduction, which insists on the derivability of all terms in the theory to be reduced from terms in the reducing theory and the bridging laws, as the canonical theory of reduction. Given generalized multiple realizability, the physical science part of these psychophysical bridge laws will end up being a (possibly infinite) disjunction of all the terms referring to possible physical realizations of a mental kind. This disjunction cannot be a kind-predicate and therefore the entire statement cannot be a law of physics. The special sciences cannot be reduced to physics in this way, according to Fodor.
In 1988, Hilary Putnam applied the argument from Fodor's generalized version of multiple realizability to argue against functionalism itself, including, and above all, his own version of functionalism, machine state functionalism. Noting that functionalism is essentially a watered-down reductionist or identity theory in which mental kinds are ultimately identified with functional kinds, Putnam argues that mental kinds are probably multiply realizable over functional kinds. The same mental state or property can be implemented or realized by different states of a universal Turing machine.
Objections and responses
Early objections to multiple realizability were limited to the narrow, "across structures-type" version. Starting with David Kellogg Lewis, many reductionists argued that it is very common, perhaps the rule, in actual scientific practice to reduce one theory to another by way of "local" and structure-specific reductions. A frequently cited example of this sort of intertheoretic reduction is the case of temperature from classical thermodynamics. Temperature is identical to mean molecular kinetic energy, but this is only true of temperature in a gas. Temperature in a solid is identical to mean maximal molecular kinetic energy, because the molecules of a solid are more restricted in their movements. Temperature in a plasma is something of a mystery, since the molecules of a plasma are torn apart. Therefore, temperature, in classical thermodynamics is multiply realized in a wide diversity of microphysical states.
One common defense of multiple realizability argues that any such response which attempts to address the problem of the possibility of generalized multiple realizability must necessarily be so "local" and "context" specific in nature, referring exclusively to a certain token system of a certain structure-type at a certain time, that its reductions would be incompatible with even a minimally acceptable degree of generality in scientific theorizing. This problem is well illustrated by the controversial question of the plasticity of the human brain. Simply put, neural plasticity consists in the fact that different areas of the brain can, and often do, take over the functions of other parts that have been damaged as the result of traumatic injury, pathology, natural biological development and other processes. Any psychology which is narrowed down sufficiently to handle this level of multiple realizability will almost certainly not be general enough to capture the generalizations needed to explain only human psychology.
Recent reductionists (including Bechtel and Mundale) reply that this is not empirically plausible. In order to conduct research and carry out experiments in the neurosciences, some universal consistencies in brain structures must either exist or be assumed to exist. The similarity (produced by homology or convergent evolution) of brain structures allows us to generalize across species. If multiple realizability (especially the generalized form) were an empirical fact, then results from experiments conducted on one species of animal (or one organism) would not be meaningful or useful when generalized to explain the behavior or characteristics of another species (or organism of the same species; or in the generalized form, even the same organism).
Sungsu Kim has recently responded to this objection by pointing to the important distinction between homology of brain structures and homoplasy. Homologies are any characteristics of physiology, morphology, behavior or psychology that are shared by two or more species and that are inherited from a common ancestor. Homoplasies are similar or identical characteristics that are shared by two or more species but that are not inherited from a common ancestor, having evolved independently. The feet of ducks and platypuses are a good example of homoplasy, while the hands of humans and chimps are a good example of homology. The fact that brain structures are homologous provides no evidence either for or against multiple realizability. The only way to empirically test the thesis of multiple realizability would be to examine brain structures and determine whether some homoplasious "psychological processes or functions might be 'constructed' from different material" and supported by different brain structures just as the flight capacities of bats and birds emerge from different morphophysiologies. The emergence of similar behavioral outputs or psychological functions brought about by similar or identical brain structures in convergent evolutionary lineages would provide some evidence against multiple realizability, since it is highly improbable that this would happen, if not for constraints on the type of physical system that can realize mental phenomena. This, however, would not completely refute the possibility of realizibility of mental states in radically different physical systems such as non-carbon based life forms or machines.
Jaegwon Kim has recently argued against non-reductive physicalism on the grounds that it violates the causal closure of the physical. The rough idea is that physics provides a full explanation of physical events. If mental properties are causally efficacious, they must either be identical to physical properties, or there must be widespread overdetermination. The latter is often held to be either unlikely or even impossible on conceptual grounds. If Kim is right, then the options seem to be either reduction or elimination.
In his mechanistic account of computation, Gualtiero Piccinini appeals to the notion of medium independence. To understand this, we must first differentiate three related qualities: variable realizability, multiple realizability, and medium independence. A property is said to be variably realizable if it can be instantiated by different realizers. For a property to be multiply realizable, the property must be able to be instantiated by different realizers and different mechanisms. For example, consider a winged corkscrew and a waiter's corkscrew. Both have the property of removing corks and do so through the same mechanism - a screw and pull mechanism. Because the mechanism is fundamentally unchanged, the property is variably realizable. Next, consider the property of trapping mice as instantiated by mousetraps. Consider the classic spring mousetrap and the glue mousetrap. Both instantiate the same property, the ability to trap mice, but they do so through different mechanisms. As such, the property is multiply realizable. Medium independence has an criteria over and above those of multiple realizablity. A property is medium independent if it can be instantiated by differnt realizers and different mechanisms and if the inputs and outputs of the mechanisms are also multiply realizable. As you can see, a mousetrap is not medium independent; it must take a mouse as an input. A computer, though, is medium independent. A computer can be constructed from different parts assembled into different mechanisms and, importantly, can take different types of inputs and outputs. In typical digital computers, the inputs and outputs are voltages, but in quantum computers, the inputs and outputs would be different. 
- "Multiple Realizability" entry at Stanford Encyclopedia of Philosophy by John Bickle
- Restrepo, R. (2009). Russell's Structuralism and the Supposed Death of Computational Cognitive Science. Minds and Machines 19(2): 181-197.
- Turing, A. (1950). Computing machinery and intelligence. Mind 59. In J. Copeland (Ed.), The essential Turing (pp. 433–460). Oxford: Claredon Press, p. 446.
- Piccinini, Gualtiero (2015). Physical Computation: A Mechanistic Account. Oxford: Oxford University Press. p. 10. ISBN 9780199658855.
- Putnam, Hilary, 1967. "Psychological Predicates," in W. H. Capitan and D. D. Merrill (eds.), Art, Mind, and Religion, Pittsburgh: University of Pittsburgh Press, pp. 37–48.
- Putnam, Hilary. Representation and Reality. 1988. Cambridge, MA: MIT Press.
- Fodor, Jerry. The Language of Thought. 1975. New York. Thomas Cromwell.
- Bechtel, William and Mundale, Jennifer. Multiple Realizability Revisited in Philosophy of Science 66: 175-207.
- Kim, Sungsu. Testing Multiple Realizability: A Discussion of Bechtel and Mundale in Philosophy of Science. 69: 606-610.
- Kim, Jaegwon. Multiple Realizability and the Metaphysics of Reduction on Philosophy and Phenomenological Research. 52: 1-26.
- Shapiro, Lawrence A. Multiple Realizations.