Three versions of Occam's razor

In today's post I will be discussing differing interpretations of Occam's razor.

Wikipedia defines it as recommending that "the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory"

I shall give three common interpretations of how the razor should be applied.  I have come across each of these versions in use but they are not equivalent to each other.

1) One should always assume the existence of the fewest objects necessary to achieve an explanation.

This version has major problems.  It depends on what you consider your basic level of reality to be and how you measure quantity.  So for example  if we consider matter to be the basic level of reality and quantity to be mass then we should assume only those galaxies exist we have direct measurements from.  However, our best cosmological theories imply the existence of a multitude of galaxies for which we have no other evidence.

But had we applied such a principle with stars or planets in the past then we would have been proved wrong.  Indeed its hard to think of an instance where it could have been correctly implied.  Occam's razor is often justified by a claim that "its worked in the past!".  Although this is circular (similar to the sentence "I think I make accurate claims") its still the case that if it hadn't worked in the past this would be evidence against it (similar to the sentence "I think I make innacurate claims").

I have a further criticism of this version using the coding equivalence principle.  The problem is that universes with differing ontologies (accounts of what exists) are equivalent under this principle.  So this is going to cause inconsistencies.  There are ways to get around this but they're messy and not easy to justify.

2) Of two theories the simplest is more likely to be true.

Note that this version makes a strong truth claim for the simplest theory (it doesn't just say that the simplest theory is closest to the truth).

In particular according to this version one should always assume any theory that matches reality is true if there are no simpler theories that do.  But this is problematic because almost every theory of physics so far  proposed has been proven false including ones which at some point had no evidence against them.  Again as it hasn't worked in the past we shouldn't trust it in the future.

Note also that this version is supportive of the idea of a general unified theory in that it will always assign a non-zero probability to such a theory existing.

3) The simplest theory is the best choice of theory.  If two theories produce identical predictions choose the simpler presentation.

This version I am happier with.  But why is it good?  Is it because it is easier to have a theory that is simple for making calculations?  I would argue no as complex theories are often easier to compute with in practice.

I think that this version of Occam produces theories that are better because they produce better predictions.

One example would be continental drift as opposed to the various ad hoc explanations previously accepted (land bridges and the like).

A second example would be how Newtonian dynamics was better than previous theories of planatery motion.

Note that Einstein's theory of relativity does not harm this version of Occam's razor as it makes no truth claims concerning simpler theories.  Simple theories are often replaced by better theories that are more complicated.  Never the less one cannot necessarily tell which more complicated theory will end up replacing the current theory so this does not invalidate this version of Occam as a heuristic.

This is the only version of the razor of the three which has worked well in the past and I argue that it is the version that we should use in the future.

There are some interesting applications of the first two versions that do not follow from the third:

A) The 2nd version is used to argue that the 2nd law of thermodynamics is probably absolutely true (not just approximately true).

The prediction of the heat death of universe needs the 2nd law of thermodynamics to be absolute.

B) The first version supports the assumption that the universe is finite and the second the assumption that a general unified theory exists.

Neither of these assumptions are supported by the third version.  Indeed it it difficult to see how one could ever have positive evidence of either of these claims. 

The third version of the razor also gives us the advantage of being able to ignore silly questions such as are photons particles or waves.  For the third version What matters is the mathematical form of the theories and whether these forms make accurate predictions or not.

Comments

[Anon]

Three versions of Occam's razor? Don't you know that the simplest version is probably the right version?

[Barnaby Dawson]

I think the anonymous comment may have been intended as a joke. But I think it can actually be phrased as valid application of Occam's razor. The issue then would be that the first two 'versions' of Occam's razor have substantial evidence against them whereas the third does not. Hence we should accept the only version which is not contradicted by the evidence.