Theories should be as simple as possible, but no simpler.
- attributed to Albert Einstein.

Occam's Razor is a basic - but frequently misused - principle of logic and philosophy that goes by many names. As well as alternative spellings such as Ockham's Razor, it is sometimes known as the Principle of Parsimony, Rejection of Unnecessary Hypotheses or Rejection of Multiplication of Explanations, and is considered fundamental to the scientific method.

Although the principle in various forms dates back to antiquity, for example in the writings of Occam's teacher Duns Scotus or those of the French theologian Durand de Saint-Pourcain, physicists such as Nicole d'Oresme and Gallileo, and even as far back as Aristotle, it is named after the medieval theologian and monk William of Occam.

William of Occam

Nunquam ponenda est pluralitas sine necessitate (Pluralities ought not be posited without necessity)
- William of Occam, from Quaestiones et decisiones in quattuor libros Sententiarum Petri Lombardi

The life of the eponymous proposer of the razor is little-known. William was born circa 1280-1285 (based on the date of his ordination, for which documentation survives), and was ordained as a Franciscan friar in 1306. He has become known as an unwitting champion of atheism and undoubtedly East Horseley's greatest contribution to philosophy. He took his name from the village of his birth, and attended Oxford University from 1309 to 1321. Occam never completed his Master's degree, as he was summoned to the Papal court at Avignon in 1324, accused of heresy. This led to his nickname 'Venerable Inceptor', meaning 'elderly person who has not yet graduated'. He was also occasionally known as the 'More Than Subtle Doctor', by comparison with John Duns Scotus, the 'Subtle Doctor'¹.

Although Occam was never convicted by the Papal court, he was held under house arrest for four years, and became embroiled in an argument between the Franciscan Minister General Michael of Cesena and Pope John XXII, concerning whether the disciples of Jesus had owned property. This was a sensitive point, touching as it did on the legitimacy of the Pope's substantial personal wealth, and led to Occam being excommunicated. He fled, and lived in exile under Louis IV of Bavaria until his death sometime between 1347 and 1349. He is believed to have died during the Black Death, in a convent.

Occam was influenced by Aristotle and probably Peter John Olivi (1248 - 1298)²; he was deeply opposed to the philosophies of another great theologian, Thomas Aquinas³. Occam was considered by many to be the third of the great medieval ecclesiastical scholars, after Aquinas and Duns Scotus. He argued against the validity of either logic or scripture as a method of knowing God, instead claiming that faith was the only valid method of theology. He also argued against the existence of universals (the Platonic idealised examples of objects, of which real-world objects are merely inferior reflections).

What is Occam's Razor?

We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
- Sir Isaac Newton

Occam never clearly stated his principle, and it can be difficult to grasp. Essentially, it is the idea that one should not believe something for which one has no evidence; or, alternatively, that of two ideas which explain the same evidence, the simpler idea is to be preferred. Each of the quotes following the section headers of this article (except the 'Objections' section) is an alternative phrasing of the Razor.

Justifying the Razor

Of two equivalent theories or explanations, all other things being equal, the simpler one is to be preferred.

Parsimony is both logically necessary and the closest that we have to a solution to some very basic philosophical problems.

It is possible to conceive of a vast - possibly infinite - variation of ideas, the majority of which are mutually exclusive and have no possibility of evidence either for or against them. For example, one could imagine a giant chocolate teapot in orbit around Venus. Our most powerful telescopes would not be able to detect this, so we have no direct evidence either for or against it. Another example would be the existence of invisible, intangible fairies. No observation could ever be made that would either prove or disprove their existence. It seems, then, that we should be torn by indecision by the myriad of possible worlds, unable to decide anything for certain.

Occam proposed that it is both illogical and irrational to react with anything but disbelief to such ideas. We do not need disproof of something in order not to believe in it; scepticism and not agnosticism should be our default position. This idea has become integral to the scientific method.

Example 1: When Isaac Newton proposed his Law of Gravity, he did not add clauses such as 'except when applied to objects of a certain shade of purple', despite (presumably) not having tested objects of every colour. Nor did he add in a clause saying, 'until 3rd April 2032, when all gravity will cease.' Clearly, no experiment Newton could have performed would have differentiated his 'plain' version from one with a time-limit. However, the colour-dependence or time limit would be extra layers of complexity for which Newton had no evidence. Since there are an infinite number of possible time limits, to propose any one of them would be senseless. Newton's only logical course of action was not to include any reference to a time limit in his law.

In other words, Newton's Law states:

the force of gravity between two objects is proportional to the product of their masses divided by the square of the separation of their centres of mass.

An alternative would be:

the force of gravity between two objects is proportional to the product of their masses divided by the square of the separation of their centres of mass, until 3rd April 2032 when it becomes zero.

It is clear that the former is simpler, and therefore should be favoured according to Occam.

Other justifications include the aesthetic (simpler explanations are easier to understand; nature prefers simpler mechanisms) or the inductive (simpler theories have been shown to be correct more often in the past). Karl Popper⁴ points out that they are easier to test. Jerrold Katz⁵ proposed that if two hypotheses are supported by the same evidence, but one has more entities, the evidence has to support more for the more complicated hypothesis; it is 'stretched thinner', as it were. Finally, Richard Swinburne⁶ argues that in the absence of evidentiary means of choosing between theories, we must either use simplicity or make a choice based on no reason at all.

Ultimately, for many the best justification of Occam's razor is its success; it has become a fundamental tenet of the scientific method, the most successful method of natural philosophy mankind has yet devised. Whether this success alone is enough to justify a philosophical principle is still a matter of some contention among philosophers (see the note on inductive reasoning in the next section).

Consequences

Entia non sunt multiplicanda praeter necessitatem (Entities should not be multiplied beyond necessity.)
- attributed to William of Occam.

The principle of parsimony has become central to both the scientific method and the philosophical argument for atheism. It also provides interesting arguments in other, widely separated philosophical conundrums.

For instance, one of the oldest problems in philosophy asks whether we have any reason to think that the Sun will rise tomorrow. Although the answer is an instinctive 'yes', it can be difficult to justify this philosophically. We believe that the Sun will rise in the future because it always has in the past. This is known as inductive reasoning. Yet how can we justify the belief that the future will resemble the past? We can, of course, point out that in the past the future has always resembled the past (or the not-quite-so-distant past has always resembled the more distant past), but this is a circular argument - how can we know that future and past will continue to resemble each-other in the future? This is known as the problem of induction, since extrapolating general laws from past examples is known as inductive learning, and is the basis of almost all human knowledge.

Parsimony allows us an exit from this circle. We know, of course, that the concept of the Sun 'rising' is our interpretation of the rotation of the Earth, which is in turn due to certain laws of physics such as the conservation of rotational momentum. In order for the sun not to rise, we would require those laws to cease working, or to alter dramatically. Occam tells us that this is an unreasonable assumption - the simplest option is for us to think that the laws do not have a time limit. Although this does not constitute absolute proof, it does mean that we have a rational reason to think that it is very likely that the Sun will rise. The key point is that Occam's Razor is not based upon observation combined with induction - it is a purely logical deduction.

Objections and Counter-Arguments

Absence of evidence is not evidence of absence.

The main objection to Occam's reasoning is that although each alternative is infinitely unlikely, there is an infinite number of these alternatives. There is thus still a finite probability that, taken as a whole, they will be correct. This is a long-winded way of saying that it must be stressed that although Occam's Razor can provide evidence for one interpretation, it never constitutes proof that the simpler explanation is the correct one.

Example 2: Consider a black box. The box is sealed, and we cannot see inside or make any other internal measurements of it. On the side of the box is a rocker switch, and on the top is a light-bulb. When the switch is moved to the 'on' position, the bulb lights up; when the switch is moved back, the bulb turns off. Clearly, there are a large number of ways that the box could be configured internally to give this effect. The simplest is an internal power-source and some wires. More complex ideas might include an internal light-bulb attached to the switch and a light-detector on a separate circuit attached to the external bulb, so that when the switch is flicked, the internal bulb lights, causing the light detector to switch on the external bulb. Yet a third possibility would be tiny fairies who switch on the bulb whenever they see that the switch has been pressed.

Since we have no evidence for fairies or light detectors, it seems that Occam's Razor tells us that we should believe that there is a simple wire and power source inside the box. However, it would lead us to that conclusion whatever the truth may be, even if there were an internal light detector in the box.

We must therefore be cautious in our application of Occam's Razor. It does not and cannot prove that the simplest answer is correct. All it can tell us is that it is senseless to propose a more complex answer than necessary, since the chances of being correct are infinity to one against (i.e. zero).

Example 3: If we return to our example of Newton's Law of Gravity, we can see that another exception Newton could have made would be for speed: 'Gravity works this way except if you are moving very rapidly, in which case it works differently.' Newton did not propose this for the same reasons that he did not propose the exceptions for colour or time. However, 150 years later, Einstein showed that in fact gravity does work differently at speeds approaching that of light, in his Theories of Relativity. It may be debated whether Newton was 'wrong' to exclude a speed-limit on his theory, even though he had no reason to suspect one, but it is certain that it would not have been accepted by other natural philosophers, and equally certain that Newton was following the best possible course of investigation by not including it.

Another valid objection to Occam's Razor is that it can be viewed as being instrumentalist (concerned with predictions) rather than realist (accurately reflecting the way the world is). Supporters of the Razor would claim that instrumentalism is the best way of testing the realism of a theory. Opponents would point out that a 'best way of testing' something is not a guarantee of accuracy.

An alternative might be 'coherence', the idea that we judge ideas according to how well they match our pre-existing ideas about reality. One objection to this would be that it is very relative; ideas are judged by comparison to each-other and not by any external criteria.

The Loveless Monk? Occam and Emotions

K.I.S.S. (Keep It Simple, Stupid!)

One of the biggest perceived failings of Occam's Razor is when it comes to emotions.

Example 4: If an individual - say a spouse - acts as though they love another person, is it rational to assume that they do love that person? Opponents of Occam would say that we require faith to say so. Certainly, on the face of it this is a failing for Occam's ideas - it appears that the idea of 'love' (or any emotion) does not explain the observed facts any better than emotionlessness does. It may be that the razor is best viewed as a tool that must be used selectively - which, of course, raises the question of how we decide when to use it (Occam himself held the existence of God to be immune to attack by the razor).

A number of counter-arguments have been put forward for this. Many hold that parsimony can only give us meaningful information when applied to the physical world. Foundationalists hold that all knowledge must be based upon 'properly basic' beliefs - by which they usually mean direct sensory experience, self-evident logical propositions or our own emotions. Everything else is deduced from these, or is not true knowledge. For many, this seemingly arbitrary ruling smacks of an ad hoc justification. Alvin Plantinga⁷ has proposed that the existence of God should also be classed as a properly basic belief, a view known as Reformed Epistemology.

Others have pointed out that the idea that we are being deceived is itself a layer of complexity that the razor might strip away. This is perhaps the most powerful argument. By this line of reasoning, we should not believe that someone is deceiving us when they say 'I love you' unless we have some prior reason to suspect dishonesty (for example, if the addressee is very rich and infirm, and the supposed admirer very greedy). To counter-counter-argue, some might suggest that deception is not a 'thing' to which the Razor might apply; to be deceptive is no more 'complex' than not to be. However, denying that the razor can apply to mental states leads us directly to the Foundationalist belief described above. It appears therefore that Occam's Razor survives this test.

Parsimony and Modern Science

The simplest answer is usually the correct answer

There is no universally agreed 'scientific method'. Instead, there are a group of techniques of thought that are usually clustered together under this heading. Among these techniques are the ideas of testable predictions (as proposed by philosopher of science Karl Popper), repeatability of measurements and, of course, parsimony.

One area where parsimony is a subject of debate at the time of writing is quantum physics. Several theories exist to explain the behaviour of sub-atomic particles. These include the Copenhagen interpretation, string theory, quantum loop gravity and the many worlds hypothesis. The mathematics underlying each of these is identical, so there are no current tests that can distinguish between them. For a long time, the most promising of these explanations has been string theory. However, without direct evidence to distinguish string theory from other theories, many scientists feel that it is unscientific. They prefer simpler theories that explain less, but do not require the existence of extra dimensions.

String theory's big advantage is that it explains how universal physical constants (such as the mass of an electron or the speed of light) could arise. However, string theory can be rewritten so that almost any conceivable set of physical laws could be deduced. It appears capable of explaining anything, and therefore, according to Occamists, explains nothing. Defenders of string theory point out that they are working towards developing tests that could distinguish string theory from, for example, quantum loop gravity.

In an unrelated area of science, parsimony is used as the basis for cladistics - the classification of living organisms by their descent. When determining how closely related a group of creatures are from their genetics, biologists assume that the history with the smallest possible number of mutations (the most parsimonious history) is the genuine phylogeny (family tree). Thus, if two brothers are both haemophiliac, it is more likely that they have a haemophiliac mother⁸ than that they both developed spontaneous mutations that gave them haemophilia. If the form of haemophilia is the same in both brothers, this chance is increased. On the other hand, if only one of several brothers has haemophilia, it becomes more likely to have arisen from a mutation. Although convergent evolution is always possible, a similar principle is used to determine the phylogenies of species, with species with many features in common being classified as more closely related than those with few common features. Care must, of course, be taken not to count linked features separately - for instance, a honeycomb bone structure and a beak, rather than a jaw and teeth, both reduce the weight of a bird, and so are adaptive advantages to flight.

Other Related Uses

Frustra fit per plura quod potest fieri per pauciora (It is pointless to do with more what can be done with less)
- William of Occam

Most modern legal codes assume that a crime has not been committed unless the prosecution can prove that one has been. This is separate from but similar to the principle of 'innocent until proved guilty', which is less Occamistic (since there is no difference in complexity between the accused committing the crime and someone else committing it once it has been established that a crime has indeed been committed).

From these examples, it can be seen that Occam's Razor is an important principle, but not one that can prove or disprove anything. Instead, it can tell us when we are drawing conclusions that are almost certain to be wrong. As a philosophical principle, its day-to-day applications are limited, but it can be helpful for those who spend time thinking through the 'higher' things in life, the universe and everything.