MA Thesis of Timothy Hilgenberg

What is Reduction

1. Principle of Reduction

While there are several different types of reduction the main principle is stated simply as an attempt to describe something by means of a minimal set. That is using only those elements, be they parts or laws, that are essential to give a full description of what appears to be a complex object. The further we advance with our analysis of ourselves and the world, the more our enquiries seem to focus on ever more complex stuff. Increasingly we are having to rely on approximation and conceptualisation of what it is that we are trying to understand.

The more complex anything is the more we find ourselves falling back on the tried and tested approach breaking things up into its constituent parts - reduction, in a word, trying to deconstruct the observed into "bite-size" chunks, which we feel more readily able to deal with. Take any manual - say the piece of paper that comes with a flat-packed sofa for example. There are pictures of the various parts that were found in the package, a list of tools you may need to provide yourself, and a "plan" detailing how to assemble these parts so that when it is finished and has been done correctly, the sofa will look just like the model in the shop did. The sofa was reduced to its constituent parts packed and sold and all one needed to do was to put those parts back together again.

So the complex entity, here a sofa, is made up of a number of less complex elements. When faced with a new complex system many will attempt to disassemble the object of enquiry and seek out those parts that are already understood in an attempt to isolate those parts that are new or little understood so far. These new parts will then be analysed in the same fashion, until all mechanisms are discovered. The analogy to a Russian doll is often used, where on opening it, you find a smaller doll, which in turn houses yet a smaller one and so on.

There is an assumption that whatever is complex is made up from less complex, more fundamental parts and that there are some elements that play an active role and others perhaps only an aesthetic one. In the sofa example it matters little whether the screws are one colour or another where they are not visible. So it is the aim of any reduction to find those elements that are fundamental and active and discard those that do not matter in this case. It is an extension to Occam’s Razor (1) to use entities only as far as they are needed.

Reduction is often separated into three types: Methodological , Ontological and Theory Reduction. It is beneficial to have a distinct look at each of these as they each highlight slightly different issues. (top)

2. Methodological Reduction

Methodological Reduction takes the baton of Occam’s Razor and carries it forcefully. The minimum set of fundamentals to explicate is the only true way for this kind of reduction, parsimony is the key virtue for any description. The quest is for those elements that really play an explanatory part in understanding the complex entity. This is as much about laying down acceptable paths as about identifying active elements. This is a contentious branch of reductionism, essentially because it inherently assumes a mechanistic worldview.

An example may be an attempt to describe a society’s behaviour by looking at the behaviour of the its members. A sociologist and a psychologist would most likely want to draw the line way before the question of how these individual members work on a molecular basis. A biologist, however might be an ardent believer in the omnipotence of the double helix, i.e. that we are prisoners to our genes (2) and so she might well think that actually the behaviour of society is governed by the way things are on a molecular basis.

The question methodological reduction deals with, is that of how it is that something works, how is it that a certain chemical reaction runs this way in these conditions and another way in others. It is the attempt do describe things in schemata. Knitting patterns, cooking recipes, even Rubik’s cube (3), all these rely on discovering the underlying mechanics, the pattern for getting from the simple, fundamental to the complex.

One of the problems with this approach is the assumption that there always is a mechanistic explanation how to get from fundamentals to the complex, within social philosophy, there are views, such as Marxism, that fundamentally object to this kind of approach, that of a mechanistic predetermination, instead taking it that the whole can be more than the sum of its parts. (top)

3. Ontological Reduction

Ontological Reduction is the attempt to limit the number of building blocks or entities to those alone which are necessary from which to construct all other more complex ones. A very good example of this kind of reduction is found in particle physics. By "deconstructing" matter the physicists’ aim is to discover the fundamental elements, those from which all others can be built.

The idea of ontological reduction is perhaps as old as humankind, with first philosophical attempts by the ancient Greeks to formalise what those building blocks might be. Moving from the "four element" theory of air, earth, fire and water being the basis of everything, Democritus and Leukippus, around the 5th and 4th Century BC came up with atomism, replacing the four elements with just atoms and the void. There were particles that were no longer devisable (Greek: atomos) and nothing (4). Although their view of atoms was somewhat different to that of modern day physicists it was a fundamentally reductive account of the world, one that stayed with us through the ages.

The risk with ontological reductionism is that it has a monist tendency, with its aim to reduce all and everything to as fundamental as possible a structure. One famous equation, Einstein’s E=mc2 which equates matter and energy, could be regarded as one of the most fundamental ontological reductions. (top)

4. Theory Reduction

The third broad type is Theory Reduction. This has received considerable attention in the last few decades. As with the other kinds of reduction again the minimum set is sought, here to reduce to a minimum the number of theories in use, either through incorporating one theory within another, judged a more comprehensive one or to show that the theory under inspection has become obsolete.

One view is that of a better, more advanced theory "swallowing up" an older theory, an organic development where the old becomes a subset of a newer, more general theory. An example often cited is the way Newton’s theory of mechanics has been subsumed within Einstein’s Special Theory of Relativity. In the 1930s a movement, The Unity of Science was a manifestation of this approach taken to an extreme, believing that eventually all science could be reduced to one single TOE - a Theory Of Everything.

Natural laws are an example. As generalisations of observed behaviour, they are reduced to a formulaic description. However some terms that are part of a fuller description do not feature initially because they are not easily detected. Only later, when better experimental methods are available, do scientists discover that shortcoming. Newton’s Third Law is a useful example to illustrate.

The Law of the Conservation of Momentum, described by Newton as the product of mass and velocity, its results hold well for everyday situations, where speeds are very much slower than the speed of light. However, once velocities go beyond a certain threshold, Newton’s theory produces errors. This is because relativistic effects on mass have not been accounted for. His description needs to be corrected, taking account of Einstein’s Special Theory of Relativity (5).

To avoid errors we should use the complete description, in the case of Newton’s Third Law, we should use it taking into account factors provided by the Special Theory of Relativity. However when looking at any specific case we may make certain allowances, permitting us to "simplify" the formulae by leaving out the terms that will have no bearing on calculations, within the margin of error allowed.

As a result these cases, though, have become special instances and must not be used for generalisation. It is clear that we must note the reasons why this pseudo reduction was possible, in science this is often called "under idealised conditions". It is important to note that any result is then only an approximation, perhaps one that lies well within any margin of error, perhaps beyond what could be discovered by empirical methods at hand, but an approximation nontheless.

However while the above fits nicely within that schema of reduction, the subsumption of the old within the new is not always the case. The move from the Ptolemaic world view, with the earth at its centre to Copernicus’ helio-centric model, with the earth circling the sun, is a case in point. Here the old theory was not subsumed, but apparently wholly replaced. But even where theory reduction, such as is arguably found with the transition from Newton to Einstein, there have been criticisms voiced.

To bring out those issues, the next section will take a look at, what I take to be the four main papers on the subject of reduction in the Philosophy of Science. These articles, by Nagel, Feyerabend, Nickles and Kitcher are central to today’s discussion of Reductionism (6).

Footnotes (top)

(1) William of Occam 1285-1347, practised parsimony of metaphysics. (back)

(2) Apart from a few right wing politicians, there do not seem to be any serious biologists actually advancing this view. Within the scientific community this is still very much an open question. (back)

(3) A cube, each side of which was made up of 9 squares, painted in one of six colours. The aim was to make each cube side sport nine same coloured squares through rotating individual squares along 3-dimensional pathways. (back)

(4) If there had been anything else between the atoms, it would either have had to be devisable or not. If it was neither devisable nor an atom it could only be nothing - the void. (back)

(5) In the equation p=mv the mass component m needs to be adjusted for relativistic effects. An example: Even at its cruising speed of 1336 mph Concorde’s relativistic mass increase is imperceptible. The square root factor is 0.999999999998, so small in fact that a normal calculator will just treat it as 1! Compared to fuel consumption of 22.6 tonnes per hour any relativistic effects would truly be masked. (back) or (back to views)

(6) These four articles have been reprinted in Martin Curd & J. A. Cover, Philosophy of Science, The Central Issues (1998), Norton. For this dissertation all page numbers refer to this tome. (back)