Close shaves of the Scholastic kind

The star of the Franciscan friar and Scholastic philosopher William of Occam (sometimes 'Ockham', 1287?-1347)^[1] sputtered and went out more than six centuries ago. It did not go entirely black – a cinder still glimmers faintly in the sky: a dictum called 'Occam's Razor'. It's high time that that was extinguished, too.

The title 'Occam's Razor' does not come from Occam, nor is there in his works any clear and consistent statement that would deserve such a title. ^[2] This fact alone should be sufficient to ensure that the phrase 'Occam's Razor' is never used again. We really shouldn't need to write any more on this subject.

Unfortunately, once such constructions have become common currency there is almost no chance of obliterating them. They live on, causing confusion and folly wherever they pop up.

The problem is that, since William of Occam never coined or defined the dictum, writers invent their own formulations and then attribute the result to the innocent William, presumably thereby acquiring a glimmer of Scholastic authority for their conjectures. There is no single, common formulation of this principle. Everyone can have their own pet version of 'Occam's Razor'.

A good example of this tradition of 'definition on the fly' is supplied by Bertrand Russell, who, while accepting the problems of attribution of a 'razor' to William of Occam, invents his own, 'useful' formulation:

Occam is best known for a maxim which is not to be found in his works, but has acquired the name of 'Occam's razor'. This maxim says: 'Entities are not to be multiplied without necessity.' Although he did not say this, he said something that has much the same effect, namely: 'It is vain to do with more what can be done with fewer.' That is to say, if everything in some science can be interpreted without assuming this or that hypothetical entity, there is no ground for assuming it. I have myself found this a most fruitful principle in logical analysis. ^[3]

There is nothing to be said against Russell in this respect. He acknowledges the imposition on William and defines his own understanding of the principle carefully and clearly. That's how to do it. Few, however, are so punctilious.

Without martyring myself on the chore of performing an extensive review of all the principles that are given the title 'Occam's Razor' there seem to be some common ideas that are attributed to William.

Keep it simple

Let us look at formulations of the type: 'keep it simple, don't over-complicate explanations of a phenomenon'. Such statements are absurd. If there is an explanation of a physical phenomenon, then that explanation is as simple or as complicated as it needs to be to explain the phenomenon, otherwise it cannot be an explanation. For every phenomenon there can be only one valid explanation.

The scientific explanation of the blue colour of the sky, for example, is quite complicated. Of course, when answering questions from children or adults without a scientific background we use simplifications that avoid terms such as scattering and absorption. This means that we have not explained the phenomenon, merely obfuscated it in a way that makes the answer credible to the questioner.

For any phenomenon there is one correct explanation (even if we do not know it yet). We may, for our purposes, take away elements from the explanation, but then we are no longer explaining. I find it difficult to conceive of a correct explanation to which one would add meaningless ^[4]– i.e. unrelated – extra information. As long as the core explanation is correct, the addition of meaningless extras is more a matter of style and elegance than validity.

Simplest is best

We frequently read formulations of the type: 'of two explanations, the simpler is to be preferred'. The absurdity of such a statement is clear if we return to our principle: 'for every phenomenon there can be only one valid explanation.' There can of course be multiple hypotheses - a.k.a. speculations - but just picking the simplest of them as the best would be ridiculous. In the end there is one explanation and the simplicity or complexity of that explanation is not in our gift to determine.

Picking the simplest hypothesis as part of validation/refutation strategy is, of course, quite reasonable, but that does not imply that the simplest hypothesis is more likely to be true than the others, just that it is a good place to start. Harold Jeffreys, a champion of Bayesian statistical procedures, stated that 'simpler laws have the greater prior probability',^[5] but that is also in the context of finding the best evaluation strategy. It is a statement that relates only to Bayesian procedures. A simple hypothesis is easier to test and falsify than a complicated one.

The operation of the physical world should be simple

It is a seductive idea that the ultimate laws governing the physical world should be simple and only their ramifications complex. Einstein extended the simplicity of Newton's laws of motion with his own simplicities, but watched in despair as the complexities and uncertainties of what would become quantum physics and the mad variety of nuclear structure developed during his lifetime. The same thing has happened with evolutionary theory, in that the simplicities have exploded into the appalling complexity of modern genetics and biochemistry. We should not be surprised at such increasing complexity: as we weave the ever finer threads of our understanding into ever finer cloth what else can we expect?

We often hear of scientists searching for simplifying theories, but there are no rational grounds for expecting the structure and operation of the physical world to be simple. It is an aesthetic, perhaps a religious desire, but certainly not a logical certitude.

Conclusion

Never use the term 'Occam's Razor'. If you need arguments that favour simplicity then find them elsewhere. William cannot help you.

The ideas behind 'Occam's razor' can often be expressed more clearly and rigorously using the notions of 'sufficient' and 'necessary' conditions from logical analysis. This subject is too extensive to deal with here. As an example, the position taken in our own summary of Global Warming theory is that an estimate of the sensitivity of climate to carbon dioxide is both necessary and sufficient to establish or reject the case for control of carbon dioxide emissions. Where the sensitivity is trivially small, as it appears to be, there is no point proceeding further with complicated temperature reconstructions and measures to control emissions.

This blog has a very low opinion of Scholastic philosophy in general and most Scholastic philosphers in particular. If you need to go to them to claim authority for your reasoning then you are in trouble. Their stars are all spent – leave them that way.

References

1. ^ Apart from a scribble showing an indeterminate image of a monk, no portrait of Occam exists. In the spirit of simplicity we shall therefore refrain from adding a fake image of him.
2. ^ William M. Thorburn, 'The Myth Of Occam's Razor', Mind (1918) XXVII (3): p. 345-353. The article is paywalled but an online text can be found in Wikisource.
3. ^ Bertrand Russell, History Of Western Philosophy, Unwin, London 1946/1961, p 462f.
4. ^ If a sign is not necessary then it is meaningless. That is the meaning of Occam's Razor. (Wittgenstein is here talking about the need for a formal, quasi mathematical language for philosophy in order to avoid the ambiguities of natural languages.)
   Ludwig Wittgenstein (1889-1951), Tractatus Logico-Philosophicus, London/New York, 1922. Proposition 3.328.
5. ^ Harold Jeffreys, Theory of Probability, 1939/1961, 3rd edition, Clarendon Press, Oxford, 1961 p. 47.