By Paul Almond, 22 August 2005

Introduction

This is the first of a series of articles exploring the issue of Occam's razor. An earlier article of mine What is a Low Level Language? relates to this series of articles and is available at http://www.paul-almond.com/WhatIsALowLevelLanguage.htm.

Occam's razor is a philosophical idea proposed by William of Occam (or Ockham), an English philosopher of the thirteenth and fourteenth centuries. There is some controversy about what William of Occam actually meant. This article is about scientific philosophy rather than history and for this reason I will not be focusing very much on what he actually meant. An idea generally known as 'Occam's razor' is of importance in scientific philosophy and even in everyday life where it forms the basis of much that is often called 'common sense': it is this idea that will be the subject of these articles.

Occam's razor is often described in rather vague terms and taken for granted. The articles in this series will explore Occam's razor and attempt to give a formal definition of it which can be justified.

In this series of articles some ideas will be presented, discussed and found to be flawed. This is unavoidable. The subject is an important one and has more complexity than many people think: a rigorous treatment demands that we take the time to examine a range of ideas, including flawed ones.

Extreme Claims and Implausibility

Occam's razor is generally viewed as 'taking the simplest explanation as true.' The idea has relevance in science and everyday life. Occam's razor is all about theories. It is very easy to make up extreme theories that cannot easily be proven wrong. If we have some facts that we wish to explain then there are actually an infinite number of possible explanations - some of them plausible and others extremely implausible. Some of the possible explanations for events that routinely occur in reality would be really extreme by our standards and would clearly be wrong to us, yet it would be hard to prove them wrong. Even if some extreme theory can be proven wrong, a proponent of that theory can simply add more to it to deal with the specific objections that you are making. A well known example of this, for many readers, will be the way that children invent excuses to deal with objections to the Santa Claus myth.

Some theories are implausible no matter what is added to them to protect them from objections. In fact, we would normally regard it as a danger sign when claims are unwieldy and we have to start adding lots of things just do to deal with specific questions.

It does not matter that we may not be able to prove certain claims wrong. We all intuitively know that some claims are implausible. We may all disagree about whether or not particular claims are implausible - for example, I find the idea of alien abductions extremely implausible whereas many people take it seriously - but even an advocate of alien abduction would agree with me on most of the other really extreme claims that could be made about the world.

Some theories are simply implausible and this is what Occam's razor is all about. Occam's razor is about theory or explanation selection. It tells us when a theory is implausible regardless of whether or not we can prove it wrong.

What Did Occam Say?

We should now look at what Occam originally proposed. The idea seems to have been common knowledge during Occam's life, but he is largely credited with using it and explicitly proposing it. This is what Occam said:

which in English is:

or, more casually:

'More things should not be suggested than are needed.'

(Some people say 'entities' instead of 'things'.)

This is generally taken as meaning that when you are trying to make an explanation for something then you should not introduce more things are needed: the best explanation is the one that uses 'the least number of things'.

This does raise issues:

• What is a 'thing'?
• Why is it desirable to use explanations which have a minimum number of 'things'? Is this out of convenience - to stop theories becoming too unwieldy to work with - or are theories with less 'things' better in other ways?

One modern understanding of Occam's razor is that explanations or theories should have as few assumptions as possible. In this sort of context, the 'things' or 'entities' have become 'assumptions' and the idea is to assume as little as possible. According to this idea, when we are faced with a new phenomenon we should attempt to explain it by assuming no more than we need to. In fact, if we can explain it by assuming no more than the assumptions that have already been made to explain other things in the world then we should reuse those assumptions rather than making new ones.

Another modern understanding of Occam's razor tends to be based on one of the following ideas:

• that simplicity is preferred in theories or explanations, so that we should never make an explanation with more complexity than is needed.
• that theories should be as short as possible.

What does 'simplest' mean in this context? Some readers would say that 'simplest' is simply a vague way of saying 'short' so that the two ideas are basically the same. Such readers could have a point: scientific theories are certainly preferred when they are concise. A theory that was ten pages long, for example, would almost certainly be preferred over one that was ten million pages long and only explained the same things.

Choice of Language

If the lengths of theories are going to be important then complications could be caused by language: a theory may be very short in one language and very long in another, so it could be argued that whether or not a theory is short, and hence plausible, is dependent on the choice of language used to describe it. An obvious solution is to use a primitive or low level language to describe theories. This could be met with objections and I do not want choice of language to be a major issue in this series of articles: for this reason I have dealt with it in my previous article [1].

Theories as Predictive Models

When considering how to select theories then we should ask what the true purpose of a theory is. Is it to tell us about the fundamental nature of reality? A problem here is that a theory describes reality in terms of symbols: symbols are the only way in which we can express information in theories. Suppose that we made a theory which described reality in terms of simple particles called 'fundamentalons'. Somebody else could submit a similar theory which described reality in terms of particles called 'simpleons'. We could then ask which theory is 'correct'. If both theories have particles which behaved in the same way then it would not mean anything to say that one theory was preferred above another. 'simpleons' and 'fundamentalons' are simply labels that humans are giving to various things in their theories. The idea that there is no important difference between two theories in which the names of basic things are different is quite obvious, but we can go further. What if the mechanisms in the two theories were different, but gave the same results? Saying that the two theories were different would be meaningless as they would actually be the same theory expressed differently. When we look at it this way it should be apparent that theories can only be meaningfully distinguished from each other in terms of the predictions that they make and this tells us what a theory should do: all we can really expect of a theory is prediction.

Any theory then should work as a predictive model. It should allow us to take data based on observations and when we apply the theory to that data it should tell us what will happen. What does it mean to 'tell us what will happen'? It can only really make sense to say that the theory will tell us what the results of future observations are expected to be, even if only in statistical terms.

As examples, a gravitational theory could tell us how fast an object will accelerate if it falls or an electrical theory could tell us what the readouts should indicate on various instruments in an electrical circuit. We could take it further and imagine a theory encompassing all of reality which tells us what we should expect to happen in reality in general. This last one is of course controversial with such issues such as non-determinism being suggested in quantum mechanics. That need not concern is too much here. The main point is that theories are predictive models.

Let us imagine that we have some observations about reality. Observations can take many forms: they can be instrument readouts, descriptions of things humans have seen with their eyes and so on. All observations have one thing in common: they are data. Any data can be represented as binary numbers, so it makes sense to simplify matters and say that our observations about reality are simply a sequence of binary numbers.

We can imagine reality as being like a machine which constantly feeds a sequence of binary digits to us. It could go 0100011001001001001110101100001101… and so on. We know what binary digits appeared in the past and we want to know what binary digits will appear in the future. This may seem rather similar to problems in IQ tests in which you are shown a sequence of some type and asked to predict what comes next. This is exactly what theories are intended to do. The theory allows us, given a sequence of observations about reality, to predict future observations, not necessarily with total precision: the precision we achieve may vary depending on the quality of the theory, the quality of the observations we have made and other matters.

Now that we have chosen to represent our observations, our experience of reality, as a sequence of bits we can imagine some machine which monitors that sequence of bits, the observed bits being stored in the machine's memory so that it 'knows' what has gone on in the past and the machine then being asked to predict the future bits in the sequence. (See Figure 1) The machine (we can imagine that it is a computer of some kind) would need to have a theory to do this. From this it should be clear that a theory is not simply a static description of reality: It is a method or a process by which the sequence of bits that is known to have occurred in reality and which has previously been observed can be taken, processed and used to generate the sequence of future bits. It is a type of computer algorithm or program that serves as a predictive model.

Figure 1: Viewing Observations of Reality as a Sequence of Bits

Our machine could apply a theory to make predictions of the future sequence of bits, but let us imagine now that our machine is not given a theory in advance and that it has to devise one itself. How could this be done? One obvious way is for the machine to try every possible theory until it finds one which matches. What would 'match' mean? Presumably, it would mean that the theory agrees with the data that has already been encountered, that is to say if the theory had been applied in the past it would have predicted the sequence of bits which has actually been observed. If the theory would have predicted the past data correctly then will it not go on to predict the future data correctly?
There is a problem with this: the number of possible theories is infinite. The chance of a randomly constructed theory matching the data is remote and a very great amount of time could be taken finding a theory that matches. If any machine is to generate theories automatically then it would need to have an efficient way of searching the space of all possible theories. That, however, need not concern us: at the moment we are more interested in assessing the plausibility of theories than finding ways of constructing possible candidate theories easily.

Another problem, which currently concerns us more directly, is that more than one theory will match. An infinite number of computer programs could be made which will generate a sequence of bits but give entirely different predictions for all the unknown bits that come in the future. As a simple example, if we were dealing with letters of the alphabet instead of bits (purely because they are easier to read), and the sequence we had observed was ABCDEFG, one computer program could be written to generate the sequence ABCDEFG followed by HIJKL and another computer program could be written to generate the sequence ABCDEFG followed by PQZFPKX, and so on. An infinite number of such programs are possible. How do we know which program is the 'correct' one?

We have already discussed how the only standard to use to assess a theory is how accurately it will predict future observations, but we may not know which theory will do the best job of predicting future bits in the sequence. This is really where the idea of plausibility becomes relevant and it gives us an idea of what 'plausible' means. If we have two theories, both of which agree entirely with past data equally well yet give different predictions of future data - that is to say they tell us that we should expect different things to happen in the future - then if we find one theory plausible and the other theory implausible what this means is that one theory is expected to give us an accurate prediction of what happens in the future and the other theory is not expected to give us an accurate prediction.

When we consider Occam's razor plausibility is important. Any theory with characteristics that make it a good theory in Occam's razor terms should also be a theory which is considered plausible in terms of its capability to make accurate predictions. We could ask if Occam's razor relates to any other features of theories, such as how convenient it is to use them, but how Occam's razor relates to plausibility in the predictive sense is the main consideration.

This whole mechanistic idea of observations being regarded as binary digits and theories being treated like programs was described to show how we may start moving towards a formal description of Occam's razor. It will also be apparent to some readers that this could relate closely to real computers and how they may actually generate theories and worldviews, a matter which will be discussed later in this article when we consider artificial intelligence. This whole way of thinking about theories is actually a little simplistic and I intend to introduce a more sophisticated view at a later stage, but it will suffice for now.

Why Does Occam's Razor Matter?

This whole subject may seem to be indulging in philosophical hair-splitting. Why does it really matter what Occam's razor is and how it can be justified? I think it is important because it relates to so many issues in important ways. Some of these issues are:

• Science - The issue of how to determine how plausible particular theories are is of importance in science. It is most of what science does. Occam's razor relates directly to this issue and forms the basis of the scientific method.
• What we are - Occam's razor does not just relate to scientific matters. It relates to us, our everyday ideas about the world and how we think.
• Extreme claims and critical thinking - We often encounter extreme claims. A great deal of work often goes into defending them and arguing that they are plausible. Knowing how to tell the difference between plausible and implausible claims is important.
• Religion - Occam's razor is important if we wish to properly assess the plausibility of religious claims.
• Ontology - This might actually be considered to come under the 'science' heading but there are some ideas about the nature of reality that are outside the realm of 'conventional' science, or near its 'edge' and which could easily, and wrongly, appear either plausible or implausible by inappropriate use of Occam's razor.
• Artificial intelligence - If we want machines to be able to understand reality then it would be helpful to have a good methodology for understanding reality. Occam's razor can provide one.

We will now briefly look at each of these issues:

Science

Scientific theories are made to explain experimental results. For any set of experimental results an infinite number of theories can be generated. We can see why this is the case if we imagine the problem of producing an equation to fit some points on a graph: for any set of points there will actually be an infinite number of equations that fit it. Although there is an infinite number of theories, not all of them are plausible and the very implausible theories tend to be eliminated by a common-sense kind of application of Occam's razor in which 'uneconomical' theories - which we can take to mean theories that are too 'complicated' or too long - are seen to be implausible.

This intuitive way of applying Occam's razor is inadequate for dealing with all situations in science. While it may be fine for really extreme theories it does not help us to decide easily between competing theories that are all reasonably plausible.

It is also possible to have situations in which differences of opinion in what Occam's razor means cause controversy. An example of this is the many worlds interpretation of quantum mechanics [2, 3], proposed by Everett to deal with strange experimental results in quantum mechanics. Some experiments, such as the double-slit experiment, suggested that particles of matter have a wave nature in addition to their particle nature - an idea known as wave-particle duality. For a particle to exhibit wave nature is strange. As an example, the double-slit experiment can involve a single photon going through the apparatus and apparently following one of two courses, yet the statistics for many such photons, one after another and one at a time, seem to show that interference between light following different paths takes place. When we see interference between the different courses that a single particle could follow it is almost as if each particle is undergoing interference from events that did not happen but almost happened. In the double-slit experiment a photon can go along course A or course B and it seems that if it goes along course B then it is affected by the fact that it could have gone along course A. Likewise, if a photon goes along course B then it seems to be affected by the fact that it could have gone along course A. It is almost as if the photon is interfered with by 'ghosts' of itself - each 'ghost' being a version of a photon that shares almost the same past, with the exception that it very recently took a different course. Many attempts have been made to explain this, one of them, the Copenhagen Interpretation, suggesting that we should just accept the weirdness at face value and others trying to find various physical models that would explain this.

Everett's many worlds interpretation involved taking one aspect the situation at face value. Quantum mechanics makes use of the wave function, an equation describing the probability that a particle will be found at various places, and the wave function takes account of this apparent interference that a particle has with the ghosts of itself. Everett's approach was to suggest that the wave function describes the true reality of what we experience as particles. In Everett's universe parts of the system cease to interact with other parts and become separate 'worlds'. This process goes on all the time with reality splitting into more 'worlds'. These worlds are not separate 'places'. They all co-exist in the same place, but the particles in one world do not interact with the particles in another world, creating the appearance of separate worlds. In fact, it is only this that creates the appearance of particles at all: to a being who could look at the entire system there would not be any separate worlds or separate particles: there would simply be waves. The inhabitants of a single 'world' in this system observe particles rather than the overall picture. When they see a quantum event happen all the other possible events that could have happened instead look like alternative events, because they only experience a thin slice of the possibilities: in fact they all happen in one system.

We might ask what the point is of suggesting the existence of other 'worlds' that we cannot see and that do not interact with ours. According to many worlds interpretation, interference can be observed between the different routes that a photon can take and in various other ways and it is this interference that causes the strange quantum mechanical results.

Is the many worlds interpretation true? The idea is highly controversial and this is where Occam's razor becomes important: both sides use Occam's razor to suggest that the many worlds interpretation is valid or invalid.

Scientists arguing against the many worlds interpretation sometimes say that the idea violates Occam's razor. They say that suggesting the existence of all these other worlds amounts to a monstrous assumption of unnecessary things. The objection is, basically, that in assuming that a lot more of reality is there to explain the reality that we have, the theory is uneconomical. There is no point in even trying to work out if the many worlds interpretation's expansion of reality - which is always increasing anyway - is large enough to make it too uneconomical. If the idea of the objection has any merit at all then the huge extension of reality which it suggests is surely large enough to make the many worlds interpretation worse than almost any other theory that we could imagine.

Advocates of the idea, however, say that Occam's razor favours the many-worlds interpretation. They say that Occam's razor is not about 'how much of reality' is assumed to exist but about the complexity of the theory that has to be assumed. While the reality suggested by the many worlds interpretation is huge in extent, including not only our world, but lots of others that we do not see, they argue that the theoretical ideas that explain why separate worlds exist, why worlds continuously split and how interference can account for the quantum mechanics results are actually very simple and they say that this is all that matters.

Regardless of whether or not the many worlds interpretation is true, this illustrates the relevance of Occam's razor to science and the importance of having a good formal description of it so that we can correctly apply it to situations like this.

What We Are

Occam's razor is not restricted to formal ideas like scientific theories: we appear to use it in everyday life. Our brains contain a description of the world - a 'worldview'. It is a mental representation of what is around is and how the various things in reality behave and relate to each other. Each of our brains has had to create this worldview and must continually modify it, but all it has to base this on is the data received via the senses. Putting this data together to make a description of the world has similarities with using experimental data to make theories in science and shares the same problem: for any set of experimental data there is an infinite number of possible worldviews which could fit it.

Humans usually have no trouble constructing an appropriate model of the world. Some of this is done unconsciously: we usually know what is around us without having to think about it very much. Some of it is done consciously: sometimes we have to think hard to come to some decision about what the world is like and humans who are doing science are engaged in probably the most extreme form of this.

Human views of the world generally seem to be constructed to meet the requirements of Occam's razor. Some readers may ask how I know just how human models of the world are made, but I would say that this is where we mainly get our idea of Occam's razor from: plausible models of the world have some 'property' that implausible ones lack and we find it easy, in most everyday situations, to distinguish between models that have this property and models that lack it. Occam made use of a more formal version of this, and we could argue about exactly how plausibility can be assessed, but it is probably no accident that science is based around Occam's razor. If the methodology behind assessing the plausibility of scientific theories were vastly different from the way we choose models of reality then it is doubtful that humans could do science.

Human brains, therefore, are excellent 'Occam's razor machines' and Occam's razor plays a major role in how they work. Any knowledge about Occam's razor itself, therefore, gives an insight into our own neurology, psychology, nature and evolution.

Extreme Claims and Critical Thinking

Many extreme claims are made in human society, many of them in sensationalist books that promise to reveal deep secrets of the universe which are often claimed to be unknown to mainstream science or deliberately covered up. One example of an extreme claim, in my opinion, is that people are regularly being left with strange memories after being abducted by aliens from another planet, time or 'dimension'. If you disagree with my example because you find alien abduction plausible then just imagine some claim that you do find extreme - there will almost certainly be at least one. The makers of these claims have arguments to deal with objections and use many methods to make the claims appear plausible: their income depends on it and they may even believe their own claims. Occam's razor is relevant to this and a formal version of it which we can justify, properly applied, could be used to show the implausibility of such claims.

Some extreme claims are believed by significant numbers of people. If we do not wish people to be fooled by extreme claims then we should desire that knowledge of how to assess claim plausibility is as widespread as possible. It could be suggested that formally describing Occam's razor, or attempting to justify it, is not relevant and that people who fall for extreme ideas really need some basic, sensible thinking. Even academic ideas, however, tend to get into the population in some way and someone needs to know all about Occam's razor for society to gain the skills that it needs later. If nothing else, good knowledge of Occam's razor can guide those who actively argue against extreme claims - even if they simplify their own presentations.

We might even say that Occam's razor is not just important to critical thinking - that it is really its entire basis. With people being exposed to so many extreme or unjustifiable claims, sometimes deliberately, the idea of teaching critical thinking as a separate subject in which people would learn to assess the plausibility of claims could be useful. Such a subject would have relevance to many areas in which claims are made, including science, politics, religion and advertising. Without more formal knowledge about how to assess claims such teaching could easily become biased or be unjustly accused of bias and a formal understanding of Occam's razor can be useful here.

Religion

I am an atheist. I think that religious claims are implausible and that Occam's razor works against the idea that a god exists. In fact, it is only the widespread occurrence of religious belief and its importance in human societies that causes me to discuss it under a separate heading at all rather than just regarding religious claims as 'extreme claims' discussed in the previous section.

My view that Occam's razor works against some religious claims may not be universal amongst atheists - some atheists probably reject religious claims on entirely different grounds - but it is probably a common one [4]. Some theists think that Occam's razor supports the existence of god, an example being Richard Swinburne, who states:

This is a clear invocation of Occam's razor.

With both sides in a debate turning to Occam's razor at least one side must be misusing it and more formalization of Occam's razor, together with greater understanding of such formalization could help to show some arguments in this debate to be flawed.

Regardless of whether a god exists or not, the issue is an important one: as just one example, religion is used to support the passing of specific laws in some countries, or even the entire legal framework. Formal knowledge of Occam's razor is essential in this debate as it could be used to show that flawed arguments, based on a misunderstanding of Occam's razor, are invalid.

If you are a theist this point still stands: you should want a formal description of Occam's razor to deal with people like me.

Ontology

There are some issues that relate to the nature of existence. It may be asked why these should be dealt with separately from the discussion of science. It is because they involve such wide-sweeping questions about existence, and consider possible situations so remote from anything to which we are accustomed, that we have no or little experience of how to deal with them. They may or may not be part of mainstream science but they deal with issues so far away from our everyday thinking that our intuitive ideas about how to apply Occam's razor may not serve us very well.

One good way of thinking about this is that Occam's razor is usually used to consider the plausibility of things within that part of reality which is easily accessible to; however the situation could become harder when we are considering the very nature of that part of reality itself and asking what, if anything may be beyond it. I am not talking here about the question of 'What is outside reality?' - a question that I find incoherent - but rather questions about what, if anything, may be outside or beyond the usual part of reality: what, if anything is beyond, or responsible for, everything that humans have ever encountered?

An example may help here:

Let us imagine someone who has lived in a single room all his/her life and has no experience of anything else outside it, the door of the room being locked and no tools capable of breaking out of the room being obviously available. There is a number of cupboards in this room and he/she has looked in some of them. From observations of what tends to be in the cupboards he/she has a good statistical understanding of what is likely to be found on opening a previously unopened cupboard.

Occam's razor could help the person to determine the chances of finding some unknown sort of object inside such a cupboard: even if he/she has not previously seen such an object he/she can use Occam's razor to make a reasonable guess. That is how Occam's razor is routinely applied by us, whether formally or informally. Let us consider, however, a more extreme situation. Let us imagine that he/she is asked what is outside the room. The door of the room is locked so he/she cannot venture outside, and never has done, so he/she cannot know what is beyond the door with certainty. This is a situation which some readers will recognize as being similar to Plato's cave allegory.

Although the person cannot venture outside the room it does not mean that questions about what is beyond the door are nonsensical. The room is a limited part of reality and the person's experience of reality is being restricted by his/her own limited position. We, on the other hand, considering the situation from outside the room can easily see how the room and the universe beyond it form a single, unbroken and entirely consistent reality.

Just as there are restrictions for the inhabitant of our hypothetical room, there could be restrictions on what we can perceive of reality, due to our own nature and our position within reality, that mean that we have difficulty answering certain questions about the wider scope of reality beyond our usual experience.

As an example of one such issue there is the question of what, if anything, came before the big bang. Does it even mean anything to ask if there was any 'before the big bang'? Some scientists say, 'no,' but it is difficult actually to prove things in science: science is not really in the 'proving business'. How do we know the big bang did not occur within some larger system? How do we know that many big bangs do not occur in some larger system all the time? This is an extreme ontological question dealing with a wider scope of reality far removed from what we usually experience. If it is a larger system in which big bangs routinely occur then to assess the probability of that idea we will have to somehow measure it against other similarly wide-scope ontological ideas, all of them looking at reality somehow beyond the big bang or outside the scope of the big bang. This would not be an easy matter and we would really need a formal idea of Occam's razor to avoid falling into various traps.

As a more extreme example, there is the question asked by some philosophers, and recently in particular by Martin Rees, the Astronomer Royal in Britain, of whether what we see of reality is artificially created, to the extent that even the laws of physics are not the 'true' laws of physics, but are actually being 'simulated' by physical processes in some wider system that we do not see. Some readers might regard this as a purely a religious question, but, irrespective of how plausible this idea is - and it is not being raised here to advocate it, but simply to have something ontologically extreme to think about - it is not really about religion. Religion generally makes assertions about things being 'outside reality'and suggests that such an idea as 'outside of reality' has meaning. Gods in religions are not typically suggested to have created part of reality: it is suggested that they created all of it. Likewise there is not supposed to be any explanation possible for the existence of God, who is supposed to be a final, self-contained explanation in himself, but suppose we asked the question merely about the part of reality we routinely experience? Suppose we asked if anything could exist outside that part of reality, but still within reality as a whole, so that the part of reality we lived in, including its apparent laws of physics, was effectively artificial?

An obvious example of this sort of situation is the scenario in the movie The Matrix, in which the protagonist discovers that the world around him is really a computer simulation made by artificially intelligent machines (AIs). This may be an extreme idea, but it is certainly not religious in nature. The AIs in the movie do not exist outside of reality - it is just that humans are seeing a very limited part of reality - and the AIs are not uncaused in the way that gods are generally presumed to be: to someone who is able to see things outside the computer simulation the history of their origins may be readily apparent.

What would be the probability of such an idea being correct? We may not think it is very high, but what if we wanted to consider it anyway? We may find it very difficult to actually apply Occam's razor to such a matter because it has serious ontological implications. The other ideas which compete with such a possibility are quite hard to assess because they are all ontologically quite removed from our everyday considerations - even everyday scientific ones. Such matters as these would be easier to consider with a more formal version of Occam's razor.

Artificial Intelligence

What constitutes artificial intelligence largely depends on who is doing it and how ambitious they are. To some people artificial intelligence means capturing all the sophistication of human brains in machinery and algorithms so that a machine can behave as humans do, having the same sorts of skills, awareness of its environment and ability to deal with the world as humans. To others artificial intelligence simply means attempting to capture specific skills, usually ones which have economic usefulness, in computer software. Examples of the latter would be pattern recognition and being able to answer simple questions about specific subjects with apparent intelligence.

Occam's razor is relevant to artificial intelligence and it is largely in this context that it interests me. To see why it is so important in artificial intelligence let us imagine a machine which is able to satisfy certain goals that are built into it. Those goals may involve its own continued existence, similar to the preference for survival in humans, or they may be goals given to it by a designer who had some other objectives in mind.

To satisfy its goals the machine needs planning ability: given knowledge of its current situation it must be able to decide how to increase its chances of achieving its goals in the future, or how to maximise its expected success in the future according to how its goals define 'success'. For planning to be possible the machine must have knowledge of its current situation. Furthermore it must understand how its actions are likely to affect that situation so that it understands how various possible sequences of actions performed as part of a plan could affect its ability to achieve its goals. The machine also needs to know how various events beyond its own control can change its situation and its chances of attaining its goals or the actions needed to fulfil them. All of this means that, as well as planning capability, the machine needs modelling capability. This means the ability to receive data via its input devices from its environment and construct a model of its environment - a worldview which describes what is happening around the machine and which it can use to simulate the expected results of hypothetical actions.

Assessing the plausibility of a worldview, or features in a worldview, requires Occam's razor to be applied, making it important in artificial intelligence.

Isn't Occam's razor sometimes wrong?

Some people give examples of situations in which Occam's Razor is claimed to have failed. An example could be some area of science where a theory that does not appear to meet the criteria which would cause application of Occam's Razor to suggest adopting it is now known by us to have been the correct choice. People who make statements like this then often go on to suggest one of these ideas:

• that Occam's razor is wrong and simply does not work.
• that Occam's razor may work in many situations, but is not appropriate for all situations. If this is true Occam's razor cannot be used to make a convincing argument for the implausibility of a claim. An advocate of the claim could simply say that it was one of those claims which is true in spite of Occam's razor apparently ruling it out. In this view anyone who attempted to use Occam's razor to make arguments for the implausibility of various claims would simply be small-minded or close-minded and Occam's razor will only be a small part of some wider system of correct reasoning about the about the true nature of things.

So, how do we answer such people? One of the following answers would generally apply in this sort of situation:

• Occam's razor should probably be regarded more as a statistical idea. We should really regard the theory which is apparently favoured by Occam's razor as being more probable than theories which are disfavoured by Occam's rather than as being certainly correct. In this view there is no single theory which is favoured by Occam's razor but a continuum of theories. At one end of the continuum are those theories that are simple or short: such theories are highly favoured by Occam's razor and are very likely to be correct. At the other end are theories that are extremely uneconomical, complex or long. These are not favoured by Occam's razor and are implausible. Although such reasoning allows the possibility of implausible claims, in no sense does it actually give them any plausibility: implausible claims still remain very unlikely to be true. The possibility of a claim being true is merely a mathematical detail and counts for very little.
• When a theory which is regarded as plausible, or which has been accepted as true, is said to be apparently inconsistent with Occam's razor in spite of this, exactly who has decided that such inconsistency with Occam's razor exists, and on what basis? Just because the theory seems to be complex or uneconomical, this does not mean that this is necessarily the case. If we have a formal view of Occam's razor for dealing with these theories it may be that they are seen to be favoured by Occam's razor. In the absence of such a formal method then errors may occur in which a theory which would have appeared economical if formally described and dealt with by a formal version of Occam's razor appears uneconomical in its absence, when processed by the human brain and when a value judgment is made about it based on flawed premises about complexity of theories, plausibility and economy.

Occam's razor is basically what stops us from believing in really, really implausible things such as invisible pixies that run the planet or control people's minds. If you wish to reject Occam's razor then you need another reason for rejecting such ideas. If you maintain that Occam's razor has no validity, or is only valid in certain situations, then it would seem to me that you have no good reason for rejecting implausible theories. Even if you say that extreme theories are simply 'ridiculous' or 'stupid' you are simply performing an intuitive application of Occam's razor. In reality a person who was open-minded enough to accept all claims that could be imagined as viable and plausible would probably be unable to function in society.

Conclusion

This article has examined the idea of Occam's razor. Occam's razor relates to theories and to explore it we need to have a good understanding of what a theory is. This article has taken the view, not uncommon, that a theory is a predictive model. Theories can deal with relatively limited matters or they can form entire worldviews describing reality and enabling us to predict what we expect to happen in general. Worldviews, theories and prediction are relevant to science, human brains and artificial intelligence. In particular, a sound knowledge about these subjects would be useful for making progress in artificial intelligence.

'Occam's razor' is the name commonly given to the method that we use to assess the plausibility of theories. For any given set of observations an infinite number of theories will be consistent with those observations, but most of these theories will be implausible. Occam's razor is all about determining the plausibility of a theory based on some characteristic or characteristics. This characteristic is often viewed as being the simplicity of the theory and many people interpret this as meaning the length of the theory's description. We have described theories in computational terms and in this context the length of a theory would clearly correspond to the length of the computer program which can be used to make predictions. Occam's razor is an important subject and relates to a number of matters including human psychology, the philosophy of science and artificial intelligence research.

This article is only an introduction to the sort of ideas which will be considered in later articles. What is needed now is a way of formally describing Occam's razor and also justifying it so that we can see why a theory which with certain characteristics would be more plausible than a theory lacking them. This will be the subject of later articles.

References

[1] Almond, P. (2005). What is a Low Level Language? Retrieved 17 July 2005 from http://www.paul-almond.com/WhatIsALowLevelLanguage.htm.

[2] Everett, H. (1957), Relative State Formulation of Quantum Mechanics, Reviews of Modern Physics 29, pp454-462.

[3] Vaidman, L. (2002). Many-Worlds Interpretation of Quantum Mechanics, Stanford Encylopedia of Philosophy. Retrieved 19 August 2005 from http://plato.stanford.edu/entries/qm-manyworlds/#1.
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[4] Mathew. (1995-2004). Common Arguments: What is Occam's Razor? The Atheism Web. Retrieved 6 August 2005 from http://www.infidels.org/news/atheism/arguments.html#occam.

[5] Swinburne, R.G. (2002?) The Justification of Theism, LeadershipU. Retrieved 19 August 2005 from http://www.leaderu.com/truth/3truth09.html.