Reflection and Occam’s Razor

‘Ned thought for a while. […] ‘Some – I don’t know – some conspiracy brought me here and I need to understand what it was.’
‘We are merely the stars‘ tennis balls, Ned, struck and banded which way please them.’
‘You don’t believe that. You believe in will. You told me so.’
‘Like anyone with a sliver of honesty in them I believe what I find I believe when I wake up each morning. Sometimes I can only think we are determined by the writing in our genes, sometimes it seems to me that we are made or unmade by our upbringings. On better days, it is true that I hope with some conviction that we and we alone make ourselves everything that we are.’
‘Nature, Nurture or Nietzsche in fact.’
‘Ha!’ Babe clapped Ned in the back. ‘It’s coming on, the creature is coming on,’ he boomed to the wide uncomprehending lawn. ‘Listen,’ he said, tucking has arm in Ned’s, ‘if you want to understand your own situation, can you not apply some of the logic it has cost me so much brain blood to teach you? Take out Occam’s Razor and cut away the irrelevant and the obfuscatory. Set down only what you know.’

– Fry. S. 2010. The Stars’ Tennis Balls London, Great Britain: Arrow Books (2014) p. 210-211

Problems with Occam’s Razor

‘Three axioms presupposed by the scientific method are realism (the existence of objective reality), the existence of observable natural laws, and the constancy of observable natural law. Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified.

Occam’s razor and related appeals to simplicity are epistemological preferences, not general principles of science. The general principle of science is that theories (or models) of natural law must be consistent with repeatable experimental observations. This principle rests upon the unproven axioms mentioned above. Occam’s razor supports, but does not prove, these axioms.’

– Courtney. A., Courtney. M. On the Nature of Science, Physics in Canada, Vol. 64, No. 3 (2008), p. 7-8

Wittgenstein on Occam’s Razor

As for Occam’s Razor, consider Ludwig Wittgenstein’s Tractatus Logico-Philosophicus:

3.328 If a sign is not necessary then it is meaningless. That is the meaning of Occam’s Razor. (If everything in the symbolism works as though a sign had meaning, then it has meaning.)

4.04 In the proposition there must be exactly as many things distinguishable as there are in the state of affairs which it represents. They must both possess the same logical (mathematical) multiplicity (cf. Hertz’s Mechanics, on Dynamic Models).

5.47321 Occam’s Razor is, of course, not an arbitrary rule nor one justified by its practical success. It simply says that unnecessary elements in a symbolism mean nothing. Signs which serve one purpose are logically equivalent, signs which serve no purpose are logically meaningless.

6.363 The procedure of induction consists in accepting as true the simplest law that can be reconciled with our experiences.

Occam’s Razor

Occam’s razor is a logical and philosophical principle stated by the medieval scholar William of Ockham (1285–1347/49). It gives precedence to simplicity; that is to say, of two or more competing theories, the simpler explanation of an entity is to be preferred. The principle is also expressed as “Entities are not to be multiplied beyond necessity.”

In other words, Ockham used the principle to dispense with relations, which he held to be nothing distinct from their foundation in things. According to Ockham:

pluralitas non est ponenda sine necessitate
“Plurality should not be posited without necessity.”

Explanations can become needlessly complex. It could become coherent to add the involvement of say, leprechauns to any explanation, but Occam’s Razor would prevent such additions, unless they were causally necessary.

“The simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth.” – Richard Swinburne

Consider the following example: Two trees have fallen down during a windy night. There could be two possible explanations to account for the fallen trees:

1. The wind has blown them down.
2. Two meteorites have each taken one tree down, and after that hit each other and removed any trace of themselves – that, or those pesky leprechauns again.