# Reduction and emergence

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### Introduction

The changing world is due the development of science and science is relentlessly amended itself. [4] Theories of the past are changed today and may change in near future. The changes for the developed theories are due to create latest ideas. Theories are prepared by reduction and emergence. These two approaches are needed to understand the world and one approach has its own traits of good and bad and not appropriate in all aspects.

In this essay I first discuss about general concept of reduction specially Nagel's view, its type, arguments about reduction. Next section covers counterpart part of reduction that is emergence and statements goes for emergence. Finally conclusion is stated.

### Reductionism

Today's world view of reductionism grows from the success of modern physics but rooted from Greek philosophy, that the all things are made up of mud, air, fire, water, or from atoms.[9]

According to Ernest Nagel the term "reduction" has no typical definition. Nagel also said "reduction is not a phenomenon which can be deduced from other phenomena, rather statements about phenomena from other statements". This reduction approach is usually used to give explanation. For scientific explanation there is a series of statements that comprise the reduction. Among the statements one is conclusion statement that is the statement which is reduced and rest of the statements are called premises or reducing statements. Homogeneous reduction and Inhomogeneous reduction are two key types of reductions found in paper "Issues in the logic of reductive explanation" of Nagel. [1]

### Homogeneous Reduction

According to Nagel any term in the reduced statement is found in the premises or reducing statement in homogeneous type reduction. Newtonian mechanics and gravitational theory is a perfect and most recurrently uttered example of homogeneous reduction. This theory encompasses different laws of motion of bodies which embraces Galileo's law for "freely falling bodies near the earth surface" and Kepler's laws of "planetary motion".[1]

According to the law Galileo motion of falling bodies if air is absent to act on the falling objects, only gravitational force exists then all bodies fall with equal constant acceleration, regardless of their size, mass, density, or horizontal velocity. That is mathematically denoted as acceleration a=dv/dt=constant.[14]

Kepler provides three laws for motion of planetary objects and those are: [14]

Law 1: "The orbit of each planet is an ellipse with the sun at one focus of the ellipse and with the other focus at an unoccupied point in space."

Law 2: "Each planet revolves around the sun so that a line connecting the planet to the sun (the radius vector) sweeps over equal areas in equal times."

Law 3: "The square of the sidereal period of any planet is proportional to the cube of its mean distance from the sun."

But Newton reduces the above into one. Newton's explanation is homogeneous because the terms occurring in the reducing laws for example distance, time, and acceleration are available in Newtonian theory (reduced statement) and Newtonian theory is a reduction one because Newton avoids the traditional categorization of spatial regions whereas the reducing statements (i.e. Galileo's law and Kepler's law) consider some constrained region. According to Nagel's model in homogeneous reduction, reduced statement is deduced logically from reducing statements and this thinking is contradicted by other philosophers. Because according to Newton's theory acceleration for a freely falling object is not steady and varies with the distance of the falling object from the earth's centre of mass. As Newton's law is unified and sound one, it replaces Galelio's law. This replaced law is derived from the Newtonians assumptions. That's why Nagel's thesis of homogeneous reduction is that - deduction does not occur in homogeneous reduction rather replacement occurs from correct assumptions and new one is more accurate and precise. Nagel's comments on homogeneous reduction are: [1]

• "Reduced laws are either derivable from the descriptive premises, or are good approximations derivable from the latter."
• In factual scientific practice simplification and approximation of various things are needed to derive a law from theories. In this regard Nagel mentions the example of deriving the law for the period of a pendulum. The pendulum is simple and some approximate assumptions for some parameters of the pendulum are considered which are: weight of pendulum, the gravitational force acting on pendulum, the angle through which the pendulum may oscillate. Considering the above parameters in accepted ranges, then only, the law "period of a pendulum is directly proportional to the square root of its length divided by the constant of acceleration" is derivable from Newtonian theory. [1]
• There are some cases of homogeneous reduction where the law actually derived from the reducing theory and exercise the notion, but not applied to the reducing theory. [1] Kepler did not know the value for K but could remove it. He assumed that K was the same for all planets and can be written as a ratio P2/Pe2=a3/ae2 , (e for earth) [14] and this ratio is constant but Newtonian's conclusion is that this ratio varies with planet's masses. The notion of mass is not found in Kepler's third law (reducing theory) but in Newton's law (reduced). Mass of the sun is huge in compare to planets. That is why according to Nagel Kepler's third law is a close approximation to Newton's law but not equivalent neither are the two dissimilar in content or sense.

### Inhomogeneous Reduction

Nagel says in this type of reduction the reduced statement has at least one descriptive term which neither occurs in the reducing statements nor in reduced statement.[1]

Inhomogeneous reduction is what where the concepts of the reducing theory do not contain all terms of the reduced theory. [16]

Nagel says that three extensive types of schemes for the construction of inhomogeneous reduction are found in recent text of philosophy of science. These are "instrumentalist", "the correspondence" and "replacement". [1]

Usually "instrumentalist" is supported by theorists who do not agree with cognitive status to scientific theories and consider them as rules it doesn't matter either it is true or false and infer them as "observation statement". Instrumentalists speak about set of rules to predict things rather than fact. Correspondence analysis or bridge law is made under assumption and within these assumptions Nagel says that "If a law T is to be reduced to a theory T' not containing terms occurring in T, T' must be supplemented by what is called rules of correspondence or bridge laws," [1] that set up connections between the distinguishing terms of T and some terms in T'. Nagel exemplifies this by second law of thermodynamics. This law deals with heat transfer but it is not possible to deduce this second law from reducing theory (classical mechanics) because it does not possess the word heat. It can be deduced only when the term heat is associated with mechanics. [1]

Paul Feyerabend cited about reduction is that "the meaning of every term we use depends upon the theoretical context in which it occurs". This postulation is applicable to scientific theory as well as to describe a matter of common observation. He further says that theories have meaning without the consideration of what is observed from the theory but observational view is not meaningful until they are connected with the theory. [1]

Though it is known that " The last 400 years science has advanced by reductionism...the idea that you could understand the world, all of nature, by examining smaller and smaller pieces of it" [4] this approach is argued for and against by critics.

By breaking down a fact to its ingredient it is quite easy to understand the whole. It is appropriate for certain level of explanation for example if it is need to be understand about living cells then we need to explore cellular biology not psychology. [3]

The reduction is deemed to be useful because reduced theory is a more general theory-that is, it explains more events than reducing theories. [12]

Strong reductionist Richard Dawkins inaugurates the term "hierarchical reduction" in his book "The Blind watchmaker" to discuss the sight of a complex system in a hierarchical level and to support the concept a computer system is taken as an example. [12]

Human mind can be explained in terms of the human brain, brain in terms of neuron, neuron in biochemistry, the latter in term of atomic physics and atomic physics in terms of quantum mechanics. So it can be claimed in light of reduction - that the mind is a primitive component. [7]

Though reductionism has gained impressive success in science, it is artificial and in that logic it is false. Because by opening from total and stirring down into component, one has to walk in the opposite direction from the path the matter come up. [2]

Reduction is too simple. On the other side Human behavior, traits and experiences are too complex to understand. Human behavior has a different number of causes for different activities and it is not possible to explain all in one level of reduced explanation. [3]

By using reduction any complex scheme can be comprehended from cramming the properties of its constituent parts. But the main challenge is to locate the starting points from where to concentrate on the particular of the scheme. [5]

It is common axiom is that" know more and more about less and less". But to divide a system to its smallest unit is a hindrance for flow of information. [10]

### Emergence

Psychologist G. H. Lewes coined the term "emergent" and noted down as: every ensuing is found from a sum or a discrepancy of the co-operant forces; when their directions are the alike the sum is gained and latter is achieved, when their directions are contrary. (....) He also mentioned that emergent is not similar to its components and cannot be reduced to their sum or their discrepancy. [13]

Professor Jeffrey Goldstein presents emergence as: "the arising of novel and coherent structures, patterns and properties during the process of self-organization in complex systems". [13] A view regarding this in ecology is that emergent characteristics of races are the resultant of interactions among the species that comprise the communities. And similar voice is found from Ernst Mayr, who says that "Systems almost always have the peculiarity that the characteristics of the whole cannot (even in theory) be deduced from the most complete knowledge of the components, taken separately or in other partial combinations. This appearance of new characteristics in wholes has been designated as emergence". [15]

In emergence it is important to understand how joint properties take place from the properties of constituent parts more precisely how macroscopic pattern arise from microscopic pattern. A used maxim is that "Do not miss the trees for the forest." Now the question who wants to see what? There are two types of viewers one type want to see the trees and the other type want to see forest. The former viewer considers the details and unable to see the pattern and the latter one do not perceive the detail. If one shifts his views back and forth it is easy to understand in what aspect parts are related to whole. [11]

Complex biological wholes, some abstract view such as 'life', 'mind' and 'consciousness', and also some epiphenomenal traits of matter like color, sound, smell and taste are understood clearly by the principle of emergence.[15] Philosopher Rom Harre mentions in his paper "Resolving the emergence-reduction debate" about determinable property. If a determinable property is possessed by both the whole and it parts then that property is not called an emergent property. Color and melody are perceived as emergence way not possible to view or hear in terms of their part.

Democritus voiced that "while things are customarily said to be sweet or bitter, warm or cold, of one color rather than another, in truth there are only the atoms and the void".[1] For some aspect it cannot be agreed. It is true that any object is made of only "atoms and void" but to distinguishable from one object from another this type reduction is not appropriate. Extreme reduction may direct the theory that is neither functional nor testable. [8]

Many physicists show doubt about the adequacy of reductionism as a sole scientific standard to explain the features of the entire world and the new trend is emergence which deals with whole rather than part.[9]

Emergent trait comes up as a corollary of relationships between objects. Consider the relationship between atoms. According to chemistry one atom in chemical reaction interacts with other and creates a chemical bond and a new atom or compound atom is found, so breed emergent result in terms of their energy and form. For water molecule it has two hydrogen atoms and one oxygen atom. When hydrogen atoms and oxygen atom are kept in convenient environment water molecule with energy is created and individual properties of hydrogen and oxygen are disappeared. Water has its own property reduction is not applicable here as a general theory. [2] Emergence theory is best to describe the characteristics of water not reduction theory.

Another interesting example in chemistry where reduction is not appropriate to understand the features of entity is NaCl (Sodium Chloride). It is a common salt and has ionic crystal structure contains the same numbers of sodium and chlorine atoms and is a necessary component in the human food. Key features of common salt or food salt are cubic crystalline structure, clear when pure, , is soluble in water, is odorless, has taste and many more.[17] But its constituent part that is Na and Cl has different properties which are disparate from Nacl. And they have some dangerous feature if they are kept separate. It is possible to make bomb- one is chlorine bomb and another one is sodium bomb which can make our live to death on the contrary emergent nature of NaCl is for life. In this case it is said that "the whole is greater than the sum of its parts". [2]

Nobel Laureate Philip Anderson argues about reductionism that it is not adequate but it is superb. A computer which is made of transistors can run on multiple platforms but reducing the computer into any particular physical basis is insufficient to explain the computer. [9]

Willy argues for both reduction and emergence by a new term "intra-disciplinarity". He says "It stems from the differences in focus that there are no automatic or necessary contradictions between the two 'isms'. The one focuses on the properties of parts, the other on the relationship between them. Put together, they stand out as supplementary rather than conflicting, as inclusive rather than exclusive." [5]

### Conclusion

Science today is contributed by the culture of creation and modification of theories. Philosophers discuss these theories by different approaches from their analysis. Two approaches are briefed here one is reduction and the other is emergent. Some argues against and for these approaches. Scientists are trying to develop a general unified theory which can explain the all. Triumph of reduction approach is not new one but not enough in all aspect. Some time whole is appropriate and in some cases reduction. Some argues for both as a supplementary to each other.

### Reference

1. Curd, Martin and Cover, J.A., "Philosophy of Science, The Central Issues", Chapter 8, "Intertheoretic Reduction", Page 903-917 W. W. Norton & Company, 1998
2. Goodenough and Deacon 2003, [Online] http://thegreatstory.org/goodenough-deacon.pdf, The Oxford Handbook of Religion and Science , chapter 50, p 853-856
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6. Rom Harre , "Resolving the emergence-reduction debate"
7. Synthese , Springer Netherlands , ISSN 0039-7857 (Print) 1573-0964 (Online) Volume 151, Number 3 / August, 2006 , Original Paper , DOI 10.1007/s11229-006-9020-5, Pages 499-509 , Humanities, Social Sciences and Law Date Tuesday, August 08, 2006, [Online] http://www.springerlink.com/content/31p5272618t81544/
8. Jargodzki, Christopher, "From Reductionism to Emergence: Science Takes A Cooperative Turn", Department of Physics, Central Missouri State University, Warrensburg, MO [Online] http://www.metanexus.net/conferences/pdf/conference2006/Jargodski.pdf
9. Notebooks, 10 Apr 2009 17:40 ," Reductionism, Centre for the study of complex system", [Online] http://www.cscs.umich.edu/~crshalizi/notabene/reductionism.html
10. A. Kauffman "BEYOND REDUCTIONISM: Reinventing The Sacred By Stuart", THE THIRD CULTURE , Edge 197-November 20, 2006, [Online] http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html
11. "Beyond Reductionism", Richard Gallagher and Tim Appenzeller, Science 2 April 1999: Vol. 284. no. 5411, p. 79 , DOI: 10.1126/science.284.5411.79 , ISSN 0036-8075 (print), 1095-9203 [Online] http://www.sciencemag.org/cgi/content/short/284/5411/79
12. 2000, Yaneer Bar-Yam , "Concepts in Complex Systems" , [Online] http://necsi.org/guide/concepts/reductionism.html
13. Wikipedia[Online] http://en.wikipedia.org/wiki/Reductionism [Accessed on: 10/03/2010]
14. Wikipedia [Online] http://en.wikipedia.org/wiki/Emergence[Accessed on: 10/03/2010]
15. Think Quest, [Online] http://library.thinkquest.org/29033/noframes.htm, [Accessed on 17.03.10]
16. 2003-2007 RUG : The University of Groningen, Powered By WildFire,[Online] http://dissertations.ub.rug.nl/faculties/fil/1998/r.c.looijen/, chapter 5 , page 72
17. Paul Needham , "Nagel's analysis of reduction: Comments in defense as well as critique " doi:10.1016/j.shpsb.2009.06.006, Department of Philosophy, University of Stockholm, SE-106 91 Stockholm, Sweden , Received 14 January 2009; revised 28 May 2009.Available online 19 August 2009, [Online] http://www.sciencedirect.com/science