Because the two frequencies are incommensurable, the attractor of such a system wraps densely around the torus, but is not periodic. Systems with one of these three kinds of attractor are easily understood using traditional mathematical models and analytic techniques. CNDSs exhibit behavior different from each of the three classes of systems introduced above. The trajectories of a CNDS converge on a highly complicated shape that is typically a fractal i. This shape is a topologically closed set of non-periodic trajectories, and it is characteristically a set of closely packed highly similar trajectories something like a filo pastry.
An example of a CNDS is a driven hinged pendulum. The behavior of this kind of system is highly sensitive to the initial speed and angle at which it is swung, and such a system will behave in a seemingly random fashion. This is sometimes called the 'butterfly effect'. This means that very small perturbations of the state of a CNDS will have relatively large effects on its behavior typically the effects are an exponential function of the perturbation, while non-chaotic systems may respond to perturbations in a linear or non-exponential way.
The attractors that describe the behavior of CNDSs are known as 'strange attractors'. Using the property of sensitive dependence on initial conditions, it is possible to show that CNDSs have emergent properties. In some CNDSs, perturbations so small as to be immeasurable can have effects on the behavior of the system that are so large as to invalidate any possible prediction of the course of a CNDS' behavior Kellert Because we can only measure the state of a system with finite precision, and because any error in our measurement is magnified in an extreme way by a CNDS' sensitive dependence on initial conditions, there is a sense in which it is impossible to define the states of some CNDSs.
For the same reason, it is impossible to define or measure the strange attractor of such a CNDS. However, if we understand the dynamics of a CNDS, we can determine an equivalence class of strange attractors within which its behavior will fall. This property supervenes on the physical state of the CNDS, so clause 1 of the definition above is met. Because the states and attractors of the system cannot be defined, it is impossible to reduce the basin of attraction to physical terms, and clause 2 of the definition is met. Finally, because the behavior of the system can be explained in virtue of the equivalence class of strange attractors, clause 3 of the definition is met.
Thus, there are physical systems that have emergent properties, and one of the remaining worries regarding emergence is eliminated. The arguments below regarding the emergence of mental properties depend on the fact that the brain is a CNDS. There are two basic reasons to think that this is the case: the first is empirical, the second is theoretical.
- Nfpa 79 Electrical Standard For Industrial Machinery.
- Hyperinnovation: Multidimensional Enterprise in the Connected Economy.
- The Culture of the New Capitalism;
- Chaos, Emergence, and the Mind-Body Problem.
- Philosophy of mind;
- Supervenience and Mind | Internet Encyclopedia of Philosophy.
Empirically speaking, there are two sets of results that suggest the brain is a CNDS. First, there are a number of studies that find strange attractors in human EEG recordings Basar Second, Skarda and Freeman have found that rabbit olfactory systems exhibit different strange attractors when presented with different odors Skarda and Freeman Theoretically speaking, the brain is just the kind of nonlinear dynamical system that typically has chaotic dynamics.
The constituent neurons and synapses of the brain exhibit nonlinear behavior, and they are connected together in such a way that sensitive dependence on initial conditions will result at a higher level Foss Thus, although further empirical work remains to be done, it seems very likely that human brains are CNDSs. It is now possible to consider the possibility that mental properties are emergent. If being in a mental state is analysed in terms of being in the basin of attraction of a strange attractor of the brain, then mental states are emergent because the basins of attraction of the strange attractors of any CNDS are emergent, as discussed above.
The mental states I am concerned with here are the occurrent mental states.
Joseph Margolis: Persons and Minds: The Prospects of Nonreductive materialism - Semantic Scholar
These are the states that are most closely associated with consciousness, subjectivity, and the mind-body problem as characterized by Nagel et. They are the states that are most difficult to explain, and they are the states that the emergence account is intended to handle. They include sensations, emotions, and having a thought, and they are typically defined in terms of their content. I argue here that we should understand these states in terms of strange attractors because our folk psychological understanding of these states requires that they be analyzed in terms of the basins of attraction of strange attractors rather than the basins of attraction of point attractors, limit cycle attractors, or torus attractors.
There are a number of features of occurrent mental states that are easily noted, and which can be used to show that mental states should be associated with strange attractors. The first thing to notice about occurrent mental states is that they are part of a dynamical system, and that they are extended in time Morton Mental states are part of an 'ecology' of the mind in which states come and go, and in which states and their relations to each other change as time passes. For example, if one is angry, one can also be hungry, and the hunger can come and go while the anger remains.
Further, the state of anger itself may evolve over time, becoming e. Thus, mental states have duration and are not completely uniform through that duration. In addition, mental states are not noticeably rhythmic: they do not have reoccurring features that occur at regular time intervals.
Supervenience and Mind
Finally, mental states are neither predictable nor strictly random; no one can precisely predict the sequence, duration, or quality of our mental states, yet our mental states are not normally so random that they are surprising or shocking. Because the mind is plausibly constituted of a number of dynamical systems e.
By doing this, we will be able to show that mental states are plausibly considered to be emergent properties. The folk psychological properties of mental states examined above make it plausible that mental states should not be modeled by point attractors, limit cycles or torii. Since mental states show no evidence of periodicity, we can also eliminate limit cycles from the possible features of the phase space of the mind. For the same reason, we can eliminate torii since the mind would exhibit periodicity with respect to a particular set of features though not with respect to its total state if there were torii in its phase space.
Thus, by elimination, mental states should be modeled by strange attractors. There are also positive reasons to think that mental states are like strange attractors. For example, the seeming randomness of behavior characterized by a strange attractor may be likened to the unpredictability of human nature, and the sensitivity of human mental states to very small stimuli may be indicative of sensitive dependence on initial conditions.
The Prospects of Nonreductive Materialism
Finally, Skarda and Freeman's result concerning rabbit olfactory systems is very suggestive Skarda and Freeman Since rabbits' brains exhibit different strange attractors when presented with different odors, and since experiencing a smell is a typical mental state of the kind that we seek to explain, it seems reasonable to conclude that rabbit mental states are associated with strange attractors. From this conclusion, it is a small leap to suppose that other mammals, including humans, have mental states similar to rabbits' mental states. Thus, when the mind is treated as a dynamical system, mental states should be modeled using the basins of attraction of strange attractors, and they are thus emergent by the argument above that being in the basin of attraction of a strange attractor is an emergent property of any chaotic system.
On this account, mental states are defined in terms of classes of similar strange attractors of brain subsystems. More precisely, being in a mental state is being in the basin of attraction of a strange attractor of some subsystem of the brain.
- E-Commerce and Web Technologies: 12th International Conference, EC-Web 2011, Toulouse, France, August 30 - September 1, 2011. Proceedings!
- The Physics of Viruses.
- Does My Child Have a Speech Problem?.
- Physicalism, Reductive and Nonreductive.
- Trapped Fools: Thirty Years of Israeli Policy in the Territories (Israeli History, Politics and Society)!
Mental states are thus constituted by the basins of attraction of all members of a class of similar strange attractors in the phase space of the brain. This is not a reductive account since our inability to measure the brain with precision sufficient to overcome its sensitive dependence on initial conditions prevents us from defining any instance of a mental state in physical terms.
In other words, we cannot identify mental state occurrences with the basin of attraction of particular strange attractors. Because we regard mental states as the basins of attraction of classes of strange attractors, this view is a kind of functionalism broadly construed. Using a class of similar strange attractors to define a mental state is a functional definition of a mental state, since any physical state that instantiates the causal dynamics of the strange attractors in the class is a mental state of the corresponding kind.
Unlike computational functionalism, the emergence account has a story to tell about the special character of mental states.
Like computational functionalism, the emergence account suggests that mental states are multiply realizable. Further, because mental states are described by a class of strange attractors that all have similar features, we can explain the general features of those mental states even though we cannot identify them precisely. The level of precision available here seems to be about the level of precision afforded by folk psychology.
If an account of mental states in terms of classes of strange attractors can explain the predictive successes and failures of folk psychology, then this is another reason to think that it is plausible. The key question, however, is whether or not the theory advanced here can solve Chalmers' hard problem. Can this theory bridge the explanatory gap?
For two reasons, I believe that it can. First, the emergence theory postulates the existence of special physical properties fundamentally different from other physical properties. Since the emergent properties with which I analyze mental properties are supervenient on the physical, they are firmly grounded in accepted metaphysical entities. Since they are not reducible to the physical, emergent mental properties are fundamentally different from traditional physical properties like those considered in reductive or functional approaches to the mind-body problem.
These two features suggests the foundations or footings of the desired bridge between the physical and the mental. The bridge itself is the holistic explanation of groups of emergent properties in terms of their supervenience base. The difficulty of constructing the bridge lies in the fact that individual emergent properties cannot be explained.
This failure of individual explanation comes about because mental properties are fundamentally non-reductive and hence anomalous: mental properties are not finitely definable and they consequently cannot participate in any finitely expressible laws or explanations. Thus, if emergent properties are plausibly identifiable with mental properties the emergence theory relates the mental and the physical in a way that explains why the mind-body problem is so difficult.
The emergence theory thus provides at least a plausible solution to the mind body problem. However, some will still be unsatisfied for the reason that the explanation given so far does not address the question of qualia. The second reason I think that the emergence theory can bridge the explanatory gap is that I believe the emergence theory can explain some of the interesting features of qualia. Emergent properties are plausibly identifiable with mental properties if we consider the properties shared by all qualia rather than those of particular qualia. This procedure is required because the theory presented here suggests that no individual mental state can be explained.
This comes about because the individual mental states cannot be adequately identified since they are states of chaotic systems, which have the property of sensitive dependence on initial conditions. Mental states that are not finitely definable would be inherently private since it would be impossible to make measurements precisely enough to distinguish one mental state from another similar mental state.
Similarly, any definition proposed for something that is not finitely definable would be incomplete, allowing a further-how question to be asked. Thus, the emergence theory agrees with the other investigators who have suggested that the subjective quality of mental states is inexplicable. However, the emergence theory offers an explanation for why this is the case, and still provides a materialistic foundation for those mental states and their unusual properties. The emergence theory also allows for some explanation of other qualities of experience as described by William James using the metaphor of the stream of consciousness James James' metaphor suggests that occurrent mental states have a dynamic kind of flow in which the boundaries between particular mental states are unclear, and in which the distinctions between different mental states are very subtle.
If being in a mental state is being in the basin of attraction of a strange attractor of a brain subsystem, the subtlety of the boundaries between mental states and the subtlety of their differences is explained by the fact that the basins of attraction of strange attractors can have fractal dimension, meaning that their boundaries are so complicated that they cannot be easily characterized. Furthermore, several such basins of attraction can be tangled together in a complex way, making the differences between them very small.