## Comments about "Occam's razor" in Wikipedia

This document contains comments about the article Occam's razor in Wikipedia
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
It is sometimes paraphrased by a statement like "the simplest solution is most likely the right one".
In principle each solution should be correct i.e. give the same solution.
Occam's razor says that when presented with competing hypotheses that make the same predictions, one should select the solution with the fewest assumptions,
When the predictions are the same the solution is also the same.
The difficulty in this sentence is the concept: 'competing hypotheses' (meaning?) versus assumptions.
The second half of this sentence reads:
and it is not meant to be a way of choosing between hypotheses that make different predictions.
This also means different solutions.
The tricky part is if predictions are considered the same as solution.
In the scientific method, Occam's razor is not considered an irrefutable principle of logic or a scientific result; the preference for simplicity in the scientific method is based on the falsifiability criterion.

### 1.3 Later formulations

To quote Isaac Newton, "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore, to the same natural effects we must, as far as possible, assign the same causes."
This remark is difficult to use in relation to Newton's Law.
Or different: The relation of this quote with Newton's Law is difficult.
Another technical approach to Occam's razor is ontological parsimony. Parsimony means spareness and is also referred to as the Rule of Simplicity.
My understanding is that Parsimony means something like redundancy.
Ernst Mach formulated the stronger version of Occam's razor into physics, which he called the Principle of Economy stating: "Scientists must use the simplest means of arriving at their results and exclude everything not perceived by the senses."
The last part of this sentence does not seem very helpfull.
The idea of parsimony or simplicity in deciding between theories, though not the intent of the original expression of Occam's razor, has been assimilated into our culture as the widespread layman's formulation that "the simplest explanation is usually the correct one."
That seems to be a rule of thumb, but in a real case not very helpfull to rely on.

### 2.5.1 Karl Popper

Our preference for simplicity may be justified by its falsifiability criterion: we prefer simpler theories to more complex ones "because their empirical content is greater; and because they are better testable".
To understand this sentence you must have a clear definition of what is a theory.
Testable means to 'prove', in a certain way, that the theory is correct.

### 2.5.2 Elliott Sober

He now believes that simplicity considerations (and considerations of parsimony in particular) do not count unless they reflect something more fundamental.
When fundamental considerations imply that they are in some sense the building blocks of the simple considerations, than that is a better approach.

### 2.5.4 Ludwig Wittgenstein

The procedure of induction consists in accepting as true the simplest law that can be reconciled with our experiences.
This sentence, I expect, has to be studied in a broader context.

### 3.1 Science and the scientific method

In physics, parsimony was an important heuristic in Albert Einstein's formulation of special relativity, in the development and application of the principle of least action by Pierre Louis Maupertuis and Leonhard Euler, and in the development of quantum mechanics by Max Planck, Werner Heisenberg and Louis de Broglie.
As a logical principle, Occam's razor would demand that scientists accept the simplest possible theoretical explanation for existing data.
Why use the word 'theoretical'?
However, science has shown repeatedly that future data often support more complex theories than do existing data.
It has been suggested that Occam's razor is a widely accepted example of extraevidential consideration, even though it is entirely a metaphysical assumption.
Okay. Next sentence:
There is little empirical evidence that the world is actually simple or that simple accounts are more likely to be true than complex ones.
This seems logical, however this statement is very difficult to test by means of experiments.
Three axioms presupposed by the scientific method are realism (the existence of objective reality), the existence of natural laws, and the constancy of natural law.
IMO this a wrong description of the postulates by Albert Einstein.
• It is impossible to prove that there exists an objective reality. What does it mean?
• Natural laws are not something that exist.
• The claim that natural laws are constant is nonsense. Natural laws i.e mathematical descriptions of the behaviour of physical processes can be improved by new experiments.
Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified.
The three axioms are not clear and as such can not be falsified.
Occam's razor and parsimony support, but do not prove, these axioms of science.
Occam's razor and parsimony (keep it simple) does not prove anything.
The general principle of science is that theories (or models) of natural law must be consistent with repeatable experimental observations.
That is correct.
It is better science that experiments come first.
Science often does not demand arbitration or selection criteria between models that make the same testable predictions.
IMO in general.

### 3.5 Probability theory and statistics

Marcus Hutter's universal artificial intelligence builds upon Solomonoff's mathematical formalization of the razor to calculate the expected value of an action.
I think this sentence requires more information to understand.

### 5 Anti-razors

Karl Menger found mathematicians to be too parsimonious with regard to variables, so he formulated his Law Against Miserliness, which took one of two forms: "Entities must not be reduced to the point of inadequacy" and "It is vain to do with fewer what requires more."
Very nicely statement, but this has no practical value in physical science.
There is also Crabtree's Bludgeon, which cynically states that "[n]o set of mutually inconsistent observations can exist for which some human intellect cannot conceive a coherent explanation, however complicated."
How do 'you' know that 'I' have inconsistent observations?

### 6. See also

Following is a list with "Comments in Wikipedia" about related subjects
• Scientific method
• Special relativity
• Turing machine

• ### Reflection 1 - General

IMO the 'simple' definition of Occam'razor as: To keep it simple or simplicity wins is not in general a good tool to decide if a theory is correct. The problems is what are the true aspects (parameters) of a theory that can be kept simple?
1. Are this a set of hypothesis used in the theory?
2. Are this the postulates used?
3. Are this the axioms used?
4. Are this the mathematical equations used?
IMO none of these can be compared with each other. The most important in any scientific project are the mathematical equations used. The problem simple can not be used in that context. To claim that GR is simple is an understatement. The mathematics involved is very complex.
At the same time Newton's Law can be considered simple. The problem is, it does not match observations.

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Created: 28 March 2020

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