Monism, Holism and Nonseparatism

            ________________________________

 

                   Glenn Fitzpatrick

 

              Department of Philosophy

             University of New England

                 Armidale, NSW 2351

                    Australia

 

             gfitzpat@metz.une.edu.au

 

            (received:  July 16, 1996)

 

Abstract

________

 

		There is a tendency in popular Philosophy of Science

	to claim that recent developments in Quantum Mechanics and

	Chaos Theory support Holistic or Monistic views. Often only

	support for a weak form of nonseparatism is warranted. For

	example, the work of Aspect, Dalibard and Roger has indicated

	a non-local statistical connection between remote particles.

	Although a significant finding in its own right, this result

	has often been misinterpreted as supporting Holism or Monism

	where no such interpretation is warranted.

 

		The problem that arises is a form of misclassification.

	A major difficulty with analyzing the alleged Holistic nature

	of physical, psychological and social phenomena is the lack

	of a consistent system of classification.

 

		The purpose of this paper is twofold. I address the

	classification problem by proposing a taxonomy which will

	clarify the distinctions between various forms of Monism,

	Holism and Nonseparatism. Having constructed the taxonomy

	I will proceed to argue two separate *prima facie* cases for

	Holism, one drawn from the superposition of states in Quantum

	theory and the other based on the work of Feigenbaum in Chaos

	theory. A hypothetical publicly verifiable candidate for Monism

	will also be canvassed.

 

 

I. A  PROPOSED TAXONOMY

______________________

 

	In setting the ground work, I propose a taxonomy with three major 

categories -- Monism, Holism and Nonseparatism  -- with a number of 

significant subclassifications. A full taxonomy of possible varieties of 

Monism, Holism and Nonseparatism (assuming such an enterprise is even 

possible) is beyond the scope of this paper.

 

	Nor is a complete taxonomy necessary. The proposed taxonomy is not an 

*a priori* exercise in metaphysics. It is intended as a tool to assess actual 

positions and arguments. As such, there are  metaphysical distinctions that 

are not included here.(4) My purpose is to isolate the significant 

metaphysical distinctions and set them out in a useful fashion.

 

	In addition I will briefly contrast Monism, Holism and Nonseparatism 

with various forms of what I will term Epistemic Atomism. By Epistemic Atomism 

I mean a range of epistemic theories which hold the common tenant that systems 

can be analyzed solely in terms of components (where components may be taken 

to include both parts and the relation between those parts).

 

	The first and strongest position is that of Monism.

 

	MONISM

	______

 

	Monism can be expressed as either: Negative Monism -- denial of 

difference. Positive Monism -- assertion of identity.

 

	By denial of difference I mean the claim that there are no genuine 

(non redundant) differences between things. All difference for the Negative 

Monist is apparent or illusory. The Negative Monist often makes the additional 

claim that there is no meaningful underlying reality.

 

	By assertion of identity I mean the claim that "All things are One". 

The Positive Monist claims all that exists is the one thing which merely 

appears to us, as humans, to be composed of parts. All difference is apparent 

or illusory (as with the Negative Monist) - however the Positive Monist claims 

that there exists a meaningful underlying reality(5).

 

	HOLISM

	______

 

	A weaker position than Monism is Holism. There are two variants of 

Holism which I will term Strong Holism and Weak Holism.

 

	"Strong Holism"  --  A system can neither be described nor understood 

solely in terms of components. Strong Holism is the claim that in some systems 

there is something essential to description and understanding which is not 

analyzable in terms of components.

 

	The Epistemic Atomist can attempt to reinstate a kind of atomism by 

introducing further components - namely the "highly complex structure itself". 

To understand why this manoeuvre fails we need to distinguish structural 

properties from emergent properties.

 

	Whole systems will have properties which are structural but not 

emergent. Structural properties arise from the way the system is "put 

together" - they are directly derived from the other components and relations 

within the system.

 

This is not the case with emergent properties. Emergent properties, at best, 

merely supervene on the components of a system. They cannot be derived from 

rearranging other components or viewing other components "in a different 

light".

 

To simply state that an emergent property is a further component (where the 

sole intellectual purpose of the special extra component is to reinstate 

atomism) will still result in a form of Holism. In such a situation the 

Atomist is merely "playing with names" deeming, with no justification, that 

the the holistic aspect of the system is to be regarded as a component.

 

The Atomist must provide independent evidence for this extra component if this 

ploy is to suceed. Without such independent evidence, the attempt to classify 

emergent properties as another component is unacceptably ad hoc and emergent 

properties qualify as a form of Strong Holism.

 

I will argue later in this paper that the superposition of states in Quantum 

theory and the work of Mitchell Feigenbaum in Chaos Theory are both candidates 

for Strong Holism.

 

	"Weak Holism" -- The thesis of Weak Holism is that a system can be 

accurately described in terms of components but cannot be understood in terms 

of those components. Unlike Strong Holism this position allows description in 

terms of components but claims understanding necessitates a Holistic approach.

 

	A good candidate case for Weak Holism is the situation that arises 

with aesthetic appreciation. A work of art may be described in terms of its 

component parts and their relations but its aesthetic value can only be 

assessed holistically.

 

	NONSEPARATISM

	_____________

 

	The final major classification is Nonseparatism6. Nonseparatism is 

weaker than Holism. It allows that reality may be both described and 

understood in terms of parts and relations but insists that some of those 

relations are non-local and non-causal.

 

These Non-local and non-causal relations cannot be Lorenz invariant. Such 

relations cannot be explained in terms of causal influences propogated at 

sub-light speeds. Nonseparatism implies instantaneous non-causal influences 

between spacially separate objects.

 

There are two variants of nonseparatism.

 

	"Strong Nonseparatism". There are non-causal, non-local connections 

between all things.

 

	"Weak Nonseparatism". There are non-causal, non-local connections 

between some things.

 

	Although Nonseparatism may appear to entail a form of Holism this is 

not necessarily the case. More specifically, if a system exhibits 

Nonseparatism it is still feasible to describe and understand everything in 

terms of parts and relations, it is just that some of the relations  are 

nonlocal and noncausal.(7)

 

	OTHER METAPHYSICAL DISTINCTIONS

	_______________________________

 

	That completes the taxonomy. There are, however, a number of other 

significant Metaphysical distinctions which warrant a brief mention. One such 

distinction is between what I will term Epistemological and Metaphysical 

Holism(8).

 

	Epistemological Holism can be interpreted in terms of limitations on 

human knowledge.  While it may, in principle, be possible to understand 

something in terms of components it is not  a practical possibility given the 

limitations of human knowledge.

 

	Metaphysical Holism is the thesis that some thing cannot, even in 

principle, be understood in terms of  components(9).

 

	Metaphysical Holism entails Epistemological Holism but not the 

converse. This is a critical distinction. A system exhibiting Epistemological 

Holism, given a deeper analysis of the components, may eventually be open to 

atomistic description and understanding.

 

	It is also possible that current limitations on atomistic 

understanding may change. With new techniques and more sophisticated analysis, 

atomistic description and understanding may become possible where it was not 

possible before. Epistemological Holism  therefore depends very much on the 

sophistication of our epistemological tools.

 

	Metaphysical Holism is a stronger position than Strong Epistemological 

Holism. With Metaphysical Holism no possible improvement in our 

epistemological tools can ever allow analysis in terms of components - such 

analysis is, in principle, impossible.

 

	A variant of Metaphysical Holism is what I will term 

non-supervenience.

 

	Non-supervenience is the claim that a system is more than its 

components.

 

	Non-supervenience would mean we could have two qualitatively different 

systems with identical parts and identical relations between those parts. 

Non-supervenience initially seems counter intuitive, however variants of the 

non-supervenience thesis underlie a number of philosophical positions 

including the "simple" theory of personal identity and some variants of 

Dualism(10).

 

	METAPHYSICAL ISSUES ARISING

	___________________________

 

	Weak Holism and Nonseparatism are compatible with a form of Epistemic 

Atomism that insists everything is describable in terms of components but 

allows understanding may neeed to be holistic.  What is clear is that neither 

Monism nor Non-supervenience are compatible with any form of Epistemic 

Atomism. Both Monism and Non-supervenience posit features that are not 

describable or analysable in terms of components.

 

	Strong Relativistic Epistemic Atomism, the thesis that a full 

description and understanding of any system is possible solely in terms of 

parts and local (Lorenz invariant) relations, is not compatible with Monism, 

Holism or Nonseparatism. This incompatibility is highly significant in view of 

the work of Aspect, Dalibard and Roger (1982) which supports Nonseparatism. 

Strong Relativistic Epistemic Atomism is an accepted tenant of modern science 

and  is not compatible with Nonseparatism.(11)

 

	Support for the three major classifications (Monism, Holism, 

Nonseparatism) divides neatly into three areas:

 

	1) The main "evidence" for Monism is "mystical" - based on the claimed 

ineffable experience of mystics. Analytic discussion is difficult (ineffable 

experience is not generally open to easy analysis) and publicly verifiable 

evidence unlikely.

 

	These difficulties do not constitute direct evidence against 

Monism.(12) Monists (particularly the Madhyamika Buddhists) claim the 

"experience of oneness" is simply not open to analysis by analytical 

philosophy or empirical science - to attempt such analysis will necessarily 

lead to contradictions and paradoxes.(13)

 

	Monists claim applying the "intellectual" methodology of analytical 

philosophy to "ineffable experience" is to commit the same "category error" 

made by Logical Positivists when they applied empirical methodology to 

non-empirical subjects. (14)

 

	Nevertheless, part of the purpose of this article will be an attempt 

to "demystify" Monism. A coherent account of how Monism might occur would be 

invaluable in analysing otherwise "ineffable" Monistic experiences. I will 

outline a comprehensible example of how Monism may conceivably occur and be 

publicly verified as occurring.

 

	2) Arguments for Holism tend to be philosophical in nature but have 

lacked empirical scientific support. I argue below that there exists *prima 

facie* empirical evidence for Holism, however even these claims will rely on 

philosophical argument (albeit, based in empirical evidence) for their 

support.

 

	3) Nonseparatism is mainly supported by empirical evidence. 

Nonseparatism has philosophical implications but the position cannot be 

supported by *a priori* philosophical argument.

 

	Empirical evidence tends to provide strong support for Nonseparatism, 

weaker support for Holism and very little support for Monism. Clearly a trend 

exists where the stronger the stance taken the weaker the empirical evidence.

 

	In the remainder of this article I will be examining two aspects of 

modern physics, the superposition of states in Quantum theory and Feigenbaum's 

number in Chaos theory. I will argue that both present a *prima facie* case 

for Strong Holism. I will also examine a hypothetical case for Monism based on 

Quantum Theory.

 

II. HOLISM AND QUANTUM MECHANICS

________________________________

 

	It is important to recognise the substantial difference between 

Quantum Mechanics and the more familiar, macroscopic, Classical Mechanics. One 

key difference between Classical Mechanics and Quantum Mechanics is the 

concept of superposition of states.15 Other critical differences between 

Quantum and Classical Mechanics include the fact that particles of the same 

type are indistinguishable and the imposition of a 'symmetry requirement'. The 

symmetry requirement simply says the total values of the parameters being 

monitored, for the system as a whole, must be "balanced out".(16)

 

	Superposition occurs in Classical Physics in electromagnetic field 

theory and acoustics.(17) This superposition does not occur in Classical 

Mechanics. The assertion that a particle may simultaneously have a range of 

valid momentum values or positions would be regarded as outright nonsense in 

Classical Mechanics.(18)

 

	Superposition does occur in Quantum Mechanics. When a measurement is 

made, the process of measurement is described mathematically by a linear 

transform. In effect,  the final state of the system is described by a linear 

sum of the separate state vectors. Such a linear sum of state vectors must, by 

definition, result in a superposition of those state vectors.

 

	The practical consequence of this is that particles, after 

measurement, must be regarded as being in a superposition of states. 

Furthermore each of these states would be the only allowable state in 

Classical Mechanics.  One and only one of the states could occur at any one 

time in Classical Mechanics - a superposition of them would be inconceivable.

 

	In Classical Mechanics a many-particle system is a composite system. 

Composite systems are decomposable - the system can always be analysed in 

terms of the states of the one-particle constituents. We can examine the 

various states of the subcomponents of the system, treat them independently 

and obtain a combined result that is valid for the system as a whole. This 

combined result is a composite of the various sub- states.

 

	Most states of Quantum Mechanical many-particle systems are not 

analysable as composites of one-particle states. Instead, the states must be 

considered as superpositions of one-particle states. An attempt to analyse the 

system directly as a a composite of one-particle states will give the wrong 

results.(19)

 

	To compound matters, a decomposable state of a system of two or more 

particles of the same kind is physically impossible because only symmetrical 

(or anti-symmetrical) superpositions of such states occur. There are, 

therefore, no physically possible states corresponding to essential 

intervening steps in the analysis of the state of two or more particles of the 

same kind. But if we are to regard such states as analysable into simpler ones 

we must hold some form of realism about these intervening states(20).

 

	What is the significance of all this? Simply that in Quantum Mechanics 

there exist many-particle systems that cannot be analysed as superpositions of 

decomposable states without holding a form of Realism about physically 

impossible states. Realism about the final result of such analysis requires 

realism about the intervening steps and some essential intervening steps 

involve physically impossible states. If we reject Realism about physically 

impossible states the system cannot be analysed into one-particle states. 

Hence a many-particle system can neither be described nor understood in terms 

of components.

 

	This constitutes Strong Holism.

 

	We are thus faced with a dilemma. It seems we must hold either Realism 

about physically impossible states or Strong Holism.

 

	To avoid the dilemma requires that the Quantum formalism be incorrect. 

Unfortunately for those wishing to avoid Holism at all costs, the formalism of 

Quantum Mechanics has been rigorously tested experimentally. In particular the 

work of Aspect, Dalibard and Roger provides convincing support for the 

correctness of the formalism of Quantum Mechanics.

 

	One way out of the dilemma for the diehard atomist is to "bite the 

bullet" and state that actual systems can have real but non-actual 

constituents. However in the case of two or more identical particles these 

non-actual constituents are physically impossible. Our diehard atomist 

therefore needs to invoke a "possible world" theory (such as that proposed by 

David Lewis) and place the non-actual constituents in another possible world. 

Realism about possible worlds seems a high price to pay for rejecting Holism. 

Furthermore, if the non-actual constituents are in another possible world 

surely we are not analysing the system into its constituents - the non-actual 

constituents are not even in the same possible  world.

 

	Given that  Realism about  physically impossible states appears 

untenable the superposition of states of two particles of the same type is a 

*prima facie* case of Strong  Holism.

 

	Furthermore, the superposition of states is evidence for Strong 

Metaphysical Holism for there is, in principle, no way of describing or 

understanding the superposition of states of two identical particles in terms 

of parts. (Even a being with God-like powers could not describe the 

superposition of two identical particles in terms of parts which exist in this 

world).

 

	It may seem we can avoid this Holism by abandoning the  Copenhagen 

Interpretation of Quantum Mechanics, however Non-local Hidden Variable 

theories are implicitely Holistic and to avoid Holism a Many Worlds 

interpretation would need to adopt the same type of Realism about other worlds 

that faces the "Lewis style atomist"  described above.

 

	MONISM AND QUANTUM MECHANICS

	____________________________

 

	As stated above, arguments for Monism tend to revolve around claims of 

ineffable mystical experience and as such are often obscure and lack any 

public verifiability. This incomprehensibility which surrounds Monism is 

unnecessary.

 

	One empirical theory with Monistic implications arises from work by 

Richard Feynman. Fenman found that antimatter particles could be seen as 

normal particles travelling backwards in time. A positron, for example, may be 

regarded as an electron travelling backwards in time. Feynmans technique 

greatly simplified the analysis of subatomic interactions and is now a 

standard procedure in Quantum mechanics. Feynman proposed that the universe 

may consist of a single particle travelling backwards and forwards in time - 

manifesting as a normal particle on the forward path and an antimatter 

particle on the reverse path. Such a universe would be inherently Monistic.

 

	Our diehard atomist may wish to claim that this system is still 

decomposable as we can treat each manifestation of the particle as a separate 

part. This ploy would not work, as the superposition of states (in this case 

between the various manifestations of our single particle) would still cause 

the system to be Holistic and the entire physical universe is part of the 

Holistic system. This is Monism.

 

	We do not, however, need a theory as extreme as Feynman's to find a 

comprehensible way Monism could be seen to be true. If Quantum Theorists were 

to find a single primitive type of sub-particle from which all other particles 

are derived (such a primitive type of sub- particle is speculative but not 

impossible) then decomposition of the superposition of states of these 

identical sub-particles would require physically impossible states.

 

	We thus would have a system exhibiting Strong Metaphysical Holism. As 

every particle in the physical universe would be derived from these identical 

sub-particles the entire physical universe would be part of the one Holistic 

system. This would constitute Monism. Furthermore this would be a form of 

Monism that is comprehensible,  coherent, analysable and publicly verifiable.

 

	CHAOS AND HOLISM

	________________

 

	In this section I present an argument that an "atomistic" approach to 

nonlinear time variant processes fails to provide a complete description or 

understanding of the system involved and hence these systems exhibit Strong 

Holism.

 

	Simple linear systems (systems that can be described in a straight- 

forward way by linear equations) can usually be analysed in terms of parts and 

relations. The superposition of states in Quantum theory is an example of such 

a system. Analysis in terms of constituents is possible, even though that 

analysis in terms of constituents requires a problematic reference to 

physically impossible states.

 

	There are vast numbers of systems that cannot be described in terms of 

linear equations. These complex nonlinear systems were traditionally regarded 

as impossible to analyse in practical situations. Solutions were derived by 

rules of thumb and trial and error.

 

	What Chaos theory provided was a means of understanding these complex 

systems in a universal fashion - without resorting to the individual linear 

equations (equations which were notoriously susceptible to radical variations 

in final results for very small changes in initial conditions). Chaos 

solutions are universal simply because the same patterns of behaviour can be 

predicted to occur regardless of the particular physical implementation of a 

system or particular non-linear equation involved.

 

	An example of this universality comes from the work of Mitchell 

Feigenbaum(21). Feigenbaum began by looking at periodic doubling in nonlinear 

difference equations of the form: 	

 

			x    =  3 D a  x  (1 - x )

			 n+1            n       n

 

Rearranging this equation shows it is actually a simple quadratic equation: 

	

			                           2

			x    =  3 D  ( a  x  -  a x   )

			 n+1               n       n

 

This equation has one linear (axn) and one nonlinear (axn2) term.

 

	Equations of this form are often used to model changes in a biological 

population over time. When the original population is small the nonlinear term 

can be ignored. In such a case if a < 1 the population undergoes exponential 

decay and invariably becomes extinct, while if a > 1 the population undergoes 

exponential growth.

 

	However exponential growth means the population xn will eventually 

grow to the point where the nonlinear term axn2  becomes significant. Since 

this term is negative it represents a nonlinear decay rate.

 

	Thus for high populations values of  a > 1 will not result in a simple 

exponential growth. In our particular example, for values of a between one and 

three the population almost always converges on a single fixed population - 

the linear and non-linear terms eventually balance.

 

	With values of a greater than three, in our example, something occurs 

which was of great interest to Feigenbaum. The population no longer converges 

on a single population. Instead it enters a stable periodic cycle, alternating 

between a large and a small population every second time period. In effect the 

population oscillates with a period of two, high one period low the next, 

returning to the same value every second period. For an actual biological 

population this would represent a situation where the population fluctuates on 

alternate years - dropping low one year and returning to a high level on the 

second year. If the value of a is again increased this cycle becomes unstable 

and a new stable cycle takes over, still alternating high and low but 

returning to the original value every four time periods and cycling through 

four repeating values instead of two. If a is increased again we see a 

succession of longer and longer stable cycles of periods eight, sixteen, 

thirty two, sixty four and so forth. This phenomena is known as periodic 

doubling.

 

	A cycle of infinite period occurs, in our example, when a  reaches 

3.57. For values of a beyond 3.57 the population is aperiodic, the system 

breaks down into chaos.

 

	Feigenbaum was interested in the periodic doubling that occurred 

before the system broke down into chaos. He found that the doubling points 

converged as the chaotic point was approached - and this convergence was at a 

constant rate. The variation in the value of a required to move from one 

stable cycle to the next was equal to the variation required to reach the 

previous stable cycle divided by a constant (4.6692016090).

 

	Later work with other forms of nonlinear equations(22) showed the same 

convergence - and at the same rate. The rate of convergence was a constant  

regardless of the nonlinear equation under study.

 

	Feigenbaum's results were found to be applicable to any system which 

underwent stable periodic doubling - regardless of the physical instantiation 

of the system or the type of nonlinear equation involved. With further 

refinements(23) Feigenbaum was able to predict the actual values of the 

recurring points in the various cycles of a system. Feigenbaum had a technique 

which allowed him to predict when a new stable cycle would occur, the period 

of the cycle and the actual values the system would cycle through without  

knowing the physical details of the system and regardless of the type of 

nonlinear equation being used to represent it.

 

	A significant breakthrough occurred when the Feigenbaum results were 

proven applicable to actual empirical experiment. One such experiment, 

conducted by Albert Libchaber(24) in the late 1970's, investigated turbulence 

in supercooled helium and produced spectral diagrams which reproduced 

precisely the results predicted by Feigenbaum. Commenting on the invaluable 

nature of Feigenbaum's  Libchaber states: The great accomplishment of 

dynamical systems theory and experiment has been  to establish that the same 

basic description of behaviour can apply to a wide range of systems. This 

universal behaviour is independent of the detailed structure which gives rise 

to it. The same language can describe both Josephson junctions and slime 

moulds  ... The recognition of universality in behaviour is a tremendous 

advance in the way we think about complex systems. It tells us what sorts of 

behaviour we can expect from unknown systems, and what questions to ask to 

establish the class to which a system belongs.

 

	There are practical limitations to the application of Feigenbaum's 

work. Nevertheless Feigenbaum has shown that there is a class of nonlinear 

systems, namely those systems exhibiting stable periodic doubling, which have 

a shared feature. This feature is the convergence of periodic doubling - a 

feature governed by a constant (which can be calculated to a very high decree 

of accuracy) that is the same for all systems.

 

	This shared feature is not analysable in terms of the components of 

the individual systems. Whilst an atomistic analysis may reveal that the 

convergence of periodic doubling occurs in the system being analysed it gives 

no indication as to why the system exhibits periodic doubling. Nor can an 

atomistic analysis explain why the convergence of periodic doubling should be 

governed by a constant that is shared by all systems which exhibit periodic 

doubling.

 

	Any useful explanation for the convergence of periodic doubling must 

take into account the fact that other systems share the phenomena. Yet there 

is no feature these systems have in common apart from the convergence of 

periodic doubling. The best explanation for periodic doubling is therefore in 

terms of a property which may supervene on, but is not explainable in terms 

of, the constituents of the systems in question.

 

	Such a systems clearly exhibit Strong Epistemological Holism. The 

best, and perhaps only, way for us as human beings to understand these systems 

is Holistically. Closer examination will show that Feigenbaum's work also 

provides a *prima facie* case for Strong Metaphysical Holism.

 

	The universal nature of Feigenbaum's constant is not derivable from 

the physical parts of any particular system nor the mathematical relationship 

between those parts. This independence of any particular physical 

instantiation means the convergence of periodic doubling is not a "secondary 

quality" in the sense that the colour "red" can be regarded as a secondary 

quality. The colour red supervenes on a more primitive physical property, the 

range of the visible spectrum the object reflects (or emits for luminescent 

objects).

 

	No such primitive physical property lies behind the convergence of 

periodic doubling. As no other primitive property can be called upon to 

explain the phenomena of periodic doubling, either the convergence of periodic 

doubling is not a property at all or the convergence of periodic doubling must 

 itself be a primitive property.

 

	Feigenbaum's work demonstrate that periodic doubling does indeed 

qualify as a property of the systems in question. There is a class of systems 

which share a common property, namely the rate of convergence of periodic 

doubling, which can be calculated to a high degree of accuracy.

 

	Given that the convergence of periodic doubling is a property of the 

systems in question it must therefore be a  primitive property of those 

systems.

 

	The nature of that primitive property remains to be determined. As 

there is often no other feature shared by the various systems exhibiting this 

phenomena, I propose the best explanation for the phenomena of periodic 

doubling is in terms of an emergent property of systems as a whole. The rate 

of convergence of periodic doubling is therefore an emergent primitive 

property.

 

	Both the description and understanding of the convergence of periodic 

doubling requires reference to this primitive emergent property. A property 

that may supervene on, but is not derivable from, the physical parts or the 

mathematical relationship between the parts of the individual system. Thus 

description and understanding is not , in principle, possible in terms of 

parts and relations. This is Strong Metaphysical Holism.

 

III. Conclusion

_______________

 

	Both Feigenbaum's work and the superposition of states in Quantum 

Mechanics provide *prima facie* evidence for Strong Metaphysical Holism in 

Nature. The difference between the two cases is that the superposition of 

states, being governed by linear equations, would normally be open to analysis 

in terms of components. This "atomistic" understanding is rejected in the case 

of the superposition of states because of the realism about physically 

impossible states that such a position entails.

 

	Feigenbaum's work, on the other hand, involves nonlinear equations 

where analysis in terms of components generally would not be expected to 

provide an adequate understanding of the system. Chaos theory, in general, 

therefore exhibits Weak Holism. Feigenbaum's work, however, provides a *prima 

facie* case for Strong Metaphysical Holism. It seems likely, given the nature 

of nonlinear processes, that many other examples of Strong Metaphysical Holism 

could be expected to arise in a wide variety of  nonlinear systems. Chaos 

Theory promises to provide exceptionally fruitful pickings for metaphysicians.

 

	A particularly promising application for theories involving holistic 

emergent orders, of the type revealed by Feigenbaum, is in the cognitive 

sciences.

 

	One problem for cognitive scientists is the apparent unitary nature of 

consciousness. While the model of preference is a linear Von-Neumann executive 

controlling a non-linear parallel-processing substructure there is no evidence 

for a central linear processing area in the brain.

 

	Recently, Daniel Dennett(25)  develop a controversial theory of 

consciousness in an attempt to overcome this problem. Many commentators claim 

Dennett actually eliminated consciousness, removing any purpose or function 

for it. I would suggest that any attempt to explain consciousness solely in 

terms of component brain systems must effectively eliminate unitary 

consciousness in this way, "explaining consciousness away" rather than 

providing an understanding of it.

 

	A model of consciousness as a unitary-holistic-emergent property 

arising from underlying non-linear brain functions may provide a solution to 

this dilemma. A genuine understanding of consciousness as a unitary phenomena, 

supervening on, but not directly explainable in terms of, the material 

components of the brain is feasible with such a model.

 

	Another problem for cognitive science and Philosophy of Mind is the 

nature of "intuitive" judgements. If the brain is capable of responding 

holistic emergent order, and extrapolating from it, a more satisfactory 

explanation of  "intuition" may be possible. Such an explanation would have 

greater explanatory power and than any atomistic model. A better understanding 

of intuitive judgements could also provide significant insights in the area of 

decision theory.

 

	A related area of interest is aesthetics. A possible theory of 

aesthetic appreciation could encompass the recognition of holistic emergent 

orders arising from nonlinear patterns in nature. This may even lead to a 

viable evolutionary theory of aesthetic appreciation. Aesthetic sensibilities 

may reinforce the development of 'holistic emergent order recognition  

circuits' - circuits which clearly would have a survival value in nature.

 

	Finally, the superposition of states in Quantum mechanics gives us a 

comprehensible, if speculative, model of how Monism may be both seen to occur 

and be publicly verified  as occurring. Such a model may be useful in 

analysing more "mystical" claims to Monism.

 

References

__________

 

(1) Examples include Gary Zukav, The Dancing Wu Li Masters, ( Rider, 1979) and 

Fritjov Capra, The Tao of Physics, (Fontana, 1983).

 

(2) Aspect, A., Dalibard, J. & Roger, G., 1982, "Experimental Realization of 

Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's 

Inequality", Physics Review Letters, Volume 49, 2, (12 July, 1982)

 

(3) David Bohm and David Hiley in The Undivided Universe (Routledge, 1992) 

give a comprehensive Holistic interpretation of Quantum theory which 

encompasses non-locality. I am addressing here the more simplistic assumptions 

about non-locality such as those made by Capra and Zukav (see note 1. above).

 

(4) For a discussion of some of the issues not treated here and an alternative 

formulation of Holism and Non-separability see Richard Healey "Holism and 

Nonseparability" (The Journal of Philosophy, Volume LXXXVIII, 8, August 

1991)..

 

(5) An example of Negative Monism is the concept of Sunyata or "emptiness" as 

expressed by Nagarjuna in Madhyamika Buddhism. An example of Positive Monism 

would be the views of the "Non Dualist" Advaita Vedantan school of Hinduism 

founded by Shankara. (Forrest, 1992, 75-91)Forrest, P., 1989, "Some Varieties 

of Monism" in Roy Perrett (Ed.) Indian Philosophy of Religion, Kluwer Academic 

Publishers, 1989, pp. 75-91

 

(6) Or Non-locality the terms are interchangeable.

 

(7) The distinction between Nonseparatism and Holism has become important in 

the philosophy of science where many quantum phenomena are clearly 

Non-separatist but may or may not be truly holistic.

 

(8) This distinction applies equally to both Weak and Strong Holism.

 

(9) Even with Godlike powers we could not understand in terms of components.

 

(10) Namely, those which deny Physicalism while refusing to aver the existence 

of anything non-physical.

 

(11) The Aspect experiments also provides yet another practical difficulty for 

the verificationist. Possible non-local connections allow many more statements 

to be meaningful than the traditional verificationist strategy intends to 

allow.

 

(12) The status of ineffable experiences is open to debate and it is not the 

place here to open that particular can of worms. Nevertheless, if we assume 

that ineffable experiences are at least possible than the Monists are correct 

- we cannot dismiss Monistic claims out of hand simply because they are beyond 

the scope of contemporary analytic philosophy.

 

(13) A parallel claim was made by Kant who claimed that human understanding 

lost itself in contradictions when it attempted to deal with 

things-in-themselves.

 

(14) The analogy between analytical philosophy and verificationism is a 

pertinent one. Analytical philosophy evolved out of verificationism - many of 

it's champions (such as Rudolph Carnap, Herbert Feigl and A.J. Ayer) where 

former Logical Positivists.

 

(15) Mathematically superposition is a property of linear differential 

equations, namely given two solutions to a differential equation any linear 

combination of these is also a solution.

 

(16) For example,  a pair of quantum systems, each with a spin of 1/2, may be 

in what is termed a spin-singlet state. They form a single system whose total 

spin in any direction must be zero. If the spin  of each of the component 

systems is measured along the same axis, the probability of them being the 

same value is zero whereas the probability of them having opposite values is 

one.

 

(17) If we combine two or more waveforms the result is a single waveform that 

is a superposition of the originals, mathematically this is represented by a 

Fourier Transform.

 

(18) Systems in Classical Mechanics are composites of the individual 

components. In Classical Statistical Mechanics systems are mixtures of 

individual components. In neither case are systems ever a superposition of the 

individual components. A superposition should not be confused with a mixture 

or a composite.

 

(19) As a somewhat whimsical example of superposition, I will consider a 

Classical Mechanics equivalent of the Quantum Mechanical Spin Singlet state. 

Imagine two physicists, Jack and Jill, perched on respective ends of a 

children's see-saw. This  see-saw has two allowable states - Jack up and Jill 

down or visa versa. Jack and Jill being both up or both down is impossible. We 

always know which is Jack and which is Jill and they can never miraculously 

swap places. In Quantum Mechanics we must view the system as in a 

superposition of states. Jack and Jill are indistinguishable and the symmetry 

requirement is enforced. In effect a superposition of four states exists 

simultaneously: Jack on the left up with Jill on the right down; Jack on the 

left down with Jill on the right up; Jill on the left up with Jack on the 

right down and finally Jill on the left down with Jack on the right up.

 

(20) Even where we have two different particles decomposition requires 

reference to non-actual but possible (or "fictitious") states. I will 

concentrate on the clear cut case of two identical particles where 

decomposition requires reference to physically impossible states.

 

(21) For a good non-technical overview of Feigenbaum's work see James Gleick, 

Chaos: Making a New Science (Heinnemann, 1988)

 

(22) Such as the trigonometric function:  xt+1 = 3D r sin p xt

 

(23) Feigenbaum refinements involved treating the process as a form of scaling 

and importing renormalisation group theory from Quantum Mechanics.

 

(24) See Hao Bai-Lin (Ed.) Chaos II, (World Scientific Publishing, 1990)

 

(25) Daniel Dennett, Consciouness Explained , (Little, Brown and Co, 1991)