The Rev Dodgson said:
I always thought that the words that Occam actually used to define his razor were:
“entities must not be multiplied beyond necessity” or actually “entia non sunt multiplicanda praeter necessitate”,
but I now discover that he did not actually write these words; they were written by someone else.
So my question is:
What formulation of Occam’s Razor best states the intent of the principle?
Which is best? Many variations on the statement of Occam’s Razor can be found in the wikipedia article:
1. Avoid superfluous ontological apparatus
2. (Solomonoff’s theory of inductive inference is a mathematically formalized Occam’s razor:) shorter computable theories have more weight when calculating the probability of the next observation
3. Simpler theories are preferable to more complex ones because they are more testable
4. Entities must not be multiplied beyond necessity
5. Make the simplest suppositions that are necessary to describe
6. We may assume the superiority of the demonstration which derives from fewer postulates or hypotheses.
7. It is vain to do with more what can be done with fewer
8. That is better and more valuable which requires fewer, other circumstances being equal
9. It is superfluous to suppose that what can be accounted for by a few principles has been produced by many
10. To make two suppositions when one is enough is to err by way of excessive supposition
11. Plurality must never be posited without necessity
12. Allow no more causes of natural things than such as are both true and sufficient to explain their appearances
13. Whenever possible, substitute constructions out of known entities for inferences from unknown entities
14. The simplest explanation is usually the correct one
15. All assumptions introduce possibilities for error; if an assumption does not improve the accuracy of a theory, its only effect is to increase the probability that the overall theory is wrong
16. A hypothesis with fewer adjustable parameters will automatically have an enhanced posterior probability, due to the fact that the predictions it makes are sharp
17. We prefer simpler theories to more complex ones because their empirical content is greater; and because they are better testable
18. The simplest theory is the more informative
19. Simplicity is evidence for truth
20. The principle of simplicity is a fundamental synthetic a priori truth
21. Unnecessary elements in a symbolism mean nothing
22. The procedure of induction consists in accepting as true the simplest law that can be reconciled with our experiences
23. Parsimony is an important heuristic
24. Parsimony is an epistemological, metaphysical or heuristic preference
“Most of the time, Occam’s razor is a conservative tool, cutting out crazy, complicated constructions and assuring that hypotheses are grounded in the science of the day, thus yielding normal science: models of explanation and prediction. There are, however, notable exceptions where Occam’s razor turns a conservative scientist into a reluctant revolutionary. For example, Max Planck interpolated between the Wien and Jeans radiation laws and used Occam’s razor logic to formulate the quantum hypothesis, even resisting that hypothesis as it became more obvious that it was correct.”
So, which is best? I actually like number 17 because it includes two valid reasons why Occam’s razor should be used.