# Explain the answer from Reddit and give an explanation about Occam's Razor

It says that Occam's razor can only be applied to competing theories:

"Occam's Razor is a heuristic, not a hard-and-fast rule. It tells us that if you have competing theories explaining the same thing, the simpler one is likely the better one; this is easily seeable if you compare"

And here it is said that Occam's razor cannot be applied because the theories are competing:

"The Razor can't help you cause both are competing theories; there are no additional entities or premises you can cut out of one to arrive at the other."

I did not understand. That is, Occam's razor can be applied only to competing theories, but at the same time it cannot be applied because the theories are competing?

Maybe I don't understand something. Please explain.

2. Am I not quite understanding how important Occam's Razor is? If Occam's razor says that the explanation that contains the fewest entities is better, does that mean that the explanation that contains the fewest entities will be the most likely?

That is, even if it is a heuristic, it will still be more plausible to adhere to the minimum number of entities because for some reason this rule was formed precisely in favor of a smaller number of entities?

I've asked somewhat similar questions before, but I can't figure out whether the lower number of entities or Occam's Razor is a priori statement and how much it increases the probability?

thank you

• Occam's razor is only heuristic, i.e. an advice how to manage explanations; it is not a rule that can be applied mechanically to produce a clear and undisputable result. Commented May 3 at 12:13
• Commented May 3 at 12:14
• Regarding the above contradiction... who knows. Are the two statements from the same page? Maybe a misprint. Commented May 3 at 12:15
• Abou the meaning of the rule: "the explanation that contains the fewest entities is better," we have to add: "provided that the explanation is the correct one." Commented May 3 at 12:16
• You could self-study an introductory statistics course and know what Occam meant better than Occam did. Occam lived 400 years too early to learn statistics, but you get to stand on the shoulders of giants.
– g s
Commented May 4 at 23:38

You might find it helpful to think in terms of probabilities. Suppose you have a theory that makes several independent assumptions. The probability of all your assumptions being correct is then the product of the individual probabilities. If you can find a way to eliminate one or more of the assumptions, then the probability of your remaining assumptions all being correct will be higher, so the slimmed-down theory is always more likely than the original. However, you cannot generally say that an argument with fewer assumptions is always better than an argument with more, since it depends on the probabilities of the individual assumptions.

For example, an argument that makes ten assumptions, each of which has a 90% chance of being correct will have an overall probability of 0.9 to the power of 10, which is about 35%. If you can eliminate one of those assumptions while leaving the rest unchanged, then the overall probability becomes 0.9 to the power of 9, which is about 39%. However, clearly both of those arguments are better than an entirely different argument that makes only one assumption with a 10% chance of being correct.

So eliminating assumptions from an argument while leaving the rest unchanged should always strengthen the argument. However, you cannot compare two entirely different arguments simply on the number of assumptions they make.

• but what about the number of entities? The number of assumptions and the number of entities are different concepts. Commented May 4 at 18:46
• Entities, per se, are irrelevant. Commented May 4 at 19:36
• this is plausible, but it would definitely help to cite someone that interprets the razor this way Commented May 4 at 20:55
• Could you show in which situation solipsism would be considered a better explanation due to fewer entities? In what situation would the minimum number of entities matter. thank you Commented May 4 at 21:00

Occam's Razor isn't about quantitative parsimony, it's about qualitative parsimony. And solipsism is qualitatively unparsimonious because it requires you to explain why only you have consciousness and all other humans (although seeming to be just like you in every other respect) do not have consciousness.

Occam's Razor is subtler than most people realize. A better formulation of it would be:

For comparable theories, the theory which explains the most observations with the fewest a priori assertions is preferred

But this has (at least) three dimensions to consider:

• comparability: whether theories are actually discussing the same subject, in part or whole, or whether they are incommensurate
• explanatory range: whether a theory covers what other theories cover, plus more (e.g., how Einstein's theory of relativity explains everything that Newtonian mechanics explains, and some stuff Newton doesn't)
• Parsimonious assumptions: how little or much the theory has to 'take on faith', such as assumptions, axioms, unverified logical necessities, etc

It makes for a complex assessment. We can visualize the first two as Venn diagrams, where the size of a circle shows the explanatory range of a given theory and the way circles overlap shows the respective theories' comparability. But then we have to factor in parsimony. So what do we do when we're faced with two theories that partially overlap (each explains something the other doesn't) and that have different assumptions?

The confusion in the reddit post about 'competing theories' is that the word 'competing' implies a comparability that might not exist, and that confuses people. Sure, Creationism might be seen as competing with Evolution, but it's not at all clear that the theories are comparable since the first merely dismisses all of the empirical evidence of the second; they don't seem to cover the same ground at all. Occam's Razor might or might not apply to 'competing' theories, so people thinking about different arenas come to different conclusions.

All that being said, though, Occam's Razor is still useful because it puts a check on magical and wishful thinking. As we know from the current uptick in internet conspiracy theory, it's both natural and easy for people to assert "I know that X is true", and then string out an ever-growing and ever-complexifying narrative whose only purpose is to keep that assertion alive. It's a kind of psychological hysteresis, where the mind actively resists efforts to change its view. All Occam is saying is that at some point we have to see everything we're importing to keep a favored theory going, and give up that effort as excessive.