How is Occam's Razor reconciled with consideration of less likely scenarios?

Question

Occam's Razor (AKA "Law of Parsimony") has been established as a foundational principle of modern (or Western) philosophical and scientific thought. It states that:

Among competing hypotheses, the one with the fewest assumptions should be selected.

Under that guideline, if one falls off a ladder, for example, the simplest (or the one making the fewest assumptions) interpretation of the event is that it was a user mistake by not setting it safely enough. On the completely opposite end of the spectrum of interpretations from the Razor would be, for example, that some supernatural forces (God?) punished the victim or some such highly assumptive theory. If those were the only two possible interpretations, it would be easy to pick the safer one. But should we exclude the possibility that someone purposely sabotaged him, causing him to fall, as a theory somewhere in between the above two?

However, phenomena in the world do occur for which the explanation is not quite the easiest one from the spectrum of possibilities. While I fundamentally agree with the Razor, in some ways I see it being interpreted as justifying intellectual laziness and complacency by discouraging investigation of less likely scenarios (now, this is my assumption, so please refute me if wrong).

My question is this: How can one venture into investigating less likely interpretations of a phenomenon than the simplest one yet remain compliant with the Razor? Or another way to ask would be how does the Razor reconcile with considering the less likely scenarios as viable?

Consider finding a body with a gun next to it. Under the Razor (as I understand it, so please again correct me if you find my understanding wrong), the simplest explanation is suicide. But could it be a murder? Would Occam's Razor in this case discourage investigation into this seemingly less likely scenario because just because it is less likely than suicide, under the same circumstances surrounding it?

Answer 1

I find the wording of Occam's razor to lead people astray. Its wording suggests that it is always good to select a hypothesis. I prefer to adulterate his words, and in doing so, believe I get closer to the concept he intended:

If one should select from among competing hypotheses, the one with the fewest assumptions should be selected.

Alternatively, one may also say "the simplest assumptions" rather than "the fewest assumptions," but that's another issue all together.

The point of the wording change is to accentuate that Occam's razor should only be applied in a situation where one should select a hypothesis, or at the very least reject other hypotheses. To take your murder or suicide example, a detective's job is to take their time, gather details, and then draw a conclusion. It would be very poor for him to make a selection early on; in fact, it may defeat his entire purpose. However, if you happened across this fellow, and it was possible the perpetrator might be in the house hunting you down, you may need to select a hypothesis so that you have spare bandwidth for other activities.

This stance is very well defended in artificial intelligence theories. "Multiple Hypothesis Testing" is a powerful tool used in tracking algorithms which intentionally keeps multiple hypotheses going simultaneously and updates each hypothesis as new data arrives. This permits things like the tracking of people who run behind a wall and emerge on the other side. The hypothesis we "want" is "there was one person, and they ran behind the wall." If you selected a hypothesis early, you might instead decide "we saw a person, but they vanished. Now we see a new person on the other side."

Let's set up a scene to show just how valuable it is to choose your selection time wisely. Let's make this a Skynet style wartime scenario, to raise the odds: on screen is a man who the AI needs to kill. That man walks behind a wall. Shortly after that, a man emerges from the other side, also walking. Facial recognition will take time, so the AI is not 100% sure the identity of this man. It may have been his target, sprinting while he was behind the wall, and then resuming his walk. It may be another person, potentially one the AI has to protect.

One misapplication of Occam's Razor could suggest the simplest answer is "there are very few people on the field, so if one disappears and reappears, it's probably the same guy." By this misapplication, the AI would open fire immediately. Another misapplication could be "People generally don't change speeds all the often, so a solution with fewer rapid speed changes is better." By this misapplication, the AI would hold its fire because the man is clearly a secondary person.

The AI may look at its hypotheses and say, "well, no matter which hypothesis is true, he can't get out of my field of view in less than 5 seconds." The AI now knows it can wait as long as 5 seconds before having to select a hypothesis. It then continue both hypothesis ("one man sprinting" vs "two men walking"), analyzing the results. This additional observation time may be sufficient to determine that this man is walking differently than the AI's target, removing that hypothesis.

Alternatively, the AI may see no clear indication in 5 seconds. At this point, the AI should make a selection. It has to either open fire or not. At this time, it applies Occam's razor, and gets a result, because its logic dictated that it should select one of them.

Answer 2

This is a great question, but I think it's based on a slight misunderstanding of the Razor. The principle does not suggest that you should not consider or investigate less likely interpretations — on the contrary, by all means investigate all possible explanations where you can. However, when all your investigations are done and the evidence does not conclusively lead you to a particular explanation, all other things being equal you should tend to accept the explanation that makes the fewest assumptions.

That said, it's used as more of a general heuristic, not a "logical law of the universe" which enables one to acquire irrefutable knowledge. As you point out, sometimes the simplest explanations are not actually the correct explanations. Just because you rest with a particular explanation at the end of the day does not mean the strength of your conviction (in the truth of said explanation) is 100%. Beliefs are not on-off switches, as if you either believe something with complete conviction or not at all. Occam's Razor just says, "Hey look, all other things being equal, if you have competing explanations but one invokes a completely unproven giant spaghetti monster from outer space, it is likely that the simpler one is true and you should live your life assuming that the alien spaghetti monster is not true until proven otherwise."

See also: Solomonoff's theory of inductive inference

To me, even more interesting are the related questions:

1. By what criteria do you determine which of competing explanations is the most "simple"? People come from different backgrounds of knowledge... A particular explanation may be simple to the physicist but not simple to the layperson, for example. How do we (or can we ever) know when a particular explanation is truly the simplest? Is that even possible?
2. Occam's Razor has us compare possible explanations. However, some people may come up with more explanations than others. For example, with your gun death example, some people may only see two possible explanations: suicide or murder. But maybe someone else may see the gun was not loaded and the deceased person lived alone and had no friends or enemies, and thus conclude that an accident happened? In other words, not everyone will come up with the same number of explanations for a given scenario. It would seem then our duty to try our best to find all possible explanations within reason. At what point do we stop this search? Given that technically any scenario can have an infinite number of explanations, when do we give up looking for more?

(reminds me of The Ethics of Belief by W. K. Clifford, a great read)

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I didn't verify Wikipedia's sources (you may want to do this depending on how much you care about the answer), but as for your bonus question it suggests:

Ockham believed that an explanation has no sufficient basis in reality when it does not harmonize with reason, experience, or the Bible. However, unlike many theologians of his time, Ockham did not believe God could be logically proven with arguments. To Ockham, science was a matter of discovery, but theology was a matter of revelation and faith. He states: "only faith gives us access to theological truths. The ways of God are not open to reason, for God has freely chosen to create a world and establish a way of salvation within it apart from any necessary laws that human logic or rationality can uncover."

Answer 3

Comment for "Bonus question"

The original "context" of Ockham's Razor was quite different from modern "naive" interpretations :

Ockham's “nominalism,” [...] is often viewed as derived from a common source: an underlying concern for ontological parsimony. This is summed up in the famous slogan known as “Ockham's Razor,” often expressed as

“Don't multiply entities beyond necessity.”

Although the sentiment is certainly Ockham's, that particular formulation is nowhere to be found in his texts. [...]

Ockham's Razor, in the senses in which it can be found in Ockham himself, never allows us to deny putative entities; at best it allows us to refrain from positing them in the absence of known compelling reasons for doing so. In part, this is because human beings can never be sure they know what is and what is not “beyond necessity”; the necessities are not always clear to us. But even if we did know them, Ockham would still not allow that his Razor allows us to deny entities that are unnecessary. For Ockham, the only truly necessary entity is God; everything else, the whole of creation, is radically contingent through and through. In short, Ockham does not accept the Principle of Sufficient Reason.

Answer 4

Your question has two different aspects, a historical aspect and a methodological one.

1) Historical: What did Ockham say?

As Mauro explains, the statement „Among competing hypotheses, the one with the fewest assumptions should be selected.“ cannot be found literally in Ockham ‘s work. Instead, according to SEP Ockham advocated the following position:

• To deny metaphysical universals.

• To reduce one's ontology to a bare minimum (Ockham’s razor).

Hence Ockham did not speak about hypotheses as a means for explanation in general. Therefore the objections from your question do not meet Ockham’s razor. Instead Ockham focused on the field of ontology, dealing with entities in the ontological sense.

2) Methodological: How to apply Ockham‘s principle as a useful heuristics?

I consider the elimination of the aether concept from electrodynamics by Einstein a useful application of Ockham’s razor. Physics of the 19. century postulated a substrate for the expansion of light which was called aether. It was necessary to ascribe rather unusual properties to this hypothetical substance. In addition all attempts to observe a physical effect of aether failed. Both difficulties encouraged Einstein to abandon a concept which did not explain anything.

This insight can be generalized: It is useful to apply Ockham’s razor to a concept which does not explain anything but creates additional questions.

Aside: As science progressed a new aether concept entered physics in the form of an ubiquitous Higg’s field. Since the experimental evidence for the simplest Higg’s boson one can continue with employing the Higg’s field to explain mass generation, see „The Return of the Aether“ in Greene, Brian: The Fabric of the Cosmos. p. 268f.

Concerning your bonus question I follow Mauro's quote from SEP:

For Ockham, the only truly necessary entity is God; everything else, the whole of creation, is radically contingent through and through.

Answer 5

The way I understand it, "having the fewest assumptions" and "simplest" are not always the same thing.

Both the ideas of suicide and murder make assumptions if there is no proof (e.g. the person was killed by a bullet). Investigation can produce proof so that one can reach a conclusion without assumptions (e.g. finding a bullet hole in the head). Or investigation can reveal a more complex explanation (the person was strangled while he was trying to defend himself with the gun) but that's what one should choose as long as less assumptions are involved.

So Occam's razor promotes investigation as it can provide evidence and thus reduce the number of necessary assumptions.

Answer 6

While Ockham's Razor is a simple statement of a principle that is important in philosophy and science, in that simplified form it is not actually deployed all that widely in the many of the sciences.

First, Ockham's Razor doesn't tell you to ignore other hypotheses, just to take one with the fewest assumptions (all else being approximately equal). But you absolutely have to investigate other hypotheses to make sure that they're approximately equal. This leads to questions like: does this improvement in our ability to explain our observations warrant that many additional assumptions? It turns out that this question is also faced when your "assumptions" are how many variables to include in some model that is fit to quantitative data. Here, at least, there are reasonably sensible statistical or comparative tests that will tell you which model is better supported.

Secondly, in many cases, especially in biology, one can have prior information that, for instance gene regulatory networks tend to be complex. So if you are interested in, say, how a fly decides to build a wing, and you find a gene that is needed for wings, your model might be X -> genes-that-build-wing-parts. It's the simplest model. But your priors indicate that it probably looks a lot more like

^{From Shulman, Perrimon & Axelrod, "Frizzled signaling and the developmental control of cell polarity", Trends in Genetics v14 pp452-458 (1998)}

So if you don't know anything else, even if X -> wing building genes is the simplest hypothesis, it is very unlikely to be true as compared to the family of stuff -> X -> more stuff -> wing building genes hypotheses. (And, actually, there are very likely side-paths also; the figure above is simplified and more is known now than in 1998.) Therefore, you should probably tentatively reject the simplest hypothesis.

The deeper point is that Ockham's Razor isn't, any more, taken as some sort of gospel. In science, we have much more sophisticated models of the tradeoff between explanatory power and model complexity, and awareness of prior knowledge shaping what are reasonable expectations; and in philosophy even if the quantitative tools from science cannot be applied, we can still take the intuitions to heart.

Perhaps the best pithy modern wording was modified from a less pithy version written by Einstein: "Everything should be made as simple as possible, but no simpler.". (Search for "simple as possible" to see the discussion.) Much more than Ockham's razor, Einstein's razor succinctly describes how modern science selects hypotheses (explicitly warning against oversimplification).

Answer 7

Determining which scenario requires the fewest assumptions is mandatory before making a cut using the Razor. However it is not trivial at all. You quickly shift, while writing, from "using the fewest assumptions" to "most likely". This is to be done with care because the latter already contains an implicit jugement. Yet, some cases require more than only listing the assumptions, because each assumption has a weight (whether it is preconceived or under consensus is another issue). These weights give assumptions a likelihood value, and to scenarios as well by aggregation.

In your suicide or murder example, the murder scenario contains more assumptions than the suicide one. However, their aggregated likelihood may keep both in balance. Indeed, the assumption that a hypothetical murderer will try to hide the crime is very likely, and this is a meta-assumption as it suggests that the decision between the scenarios itself has been made more difficult on purpose. This explains why there is no safest choice in the case of having an adversary intelligence working to confuse us, until a conclusive evidence is found.